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History-Gradient Aided Batch Size Adaptation for Variance Reduced Algorithms | null | Variance-reduced algorithms, although achieve great theoretical performance, can run slowly in practice due to the periodic gradient estimation with a large batch of data. Batch-size adaptation thus arises as a promising approach to accelerate such algorithms. However, existing schemes either apply prescribed batch-size adaption rule or exploit the information along optimization path via additional backtracking and condition verification steps. In this paper, we propose a novel scheme, which eliminates backtracking line search but still exploits the information along optimization path by adapting the batch size via history stochastic gradients. We further theoretically show that such a scheme substantially reduces the overall complexity for popular variance-reduced algorithms SVRG and SARAH/SPIDER for both conventional nonconvex optimization and reinforcement learning problems. To this end, we develop a new convergence analysis framework to handle the dependence of the batch size on history stochastic gradients. Extensive experiments validate the effectiveness of the proposed batch-size adaptation scheme. | Kaiyi Ji, Zhe Wang, Bowen Weng, Yi Zhou, Wei Zhang, Yingbin Liang | null | null | 2,020 | icml |
T-GD: Transferable GAN-generated Images Detection Framework | null | Recent advancements in Generative Adversarial Networks (GANs) enable the generation of highly realistic images, raising concerns about their misuse for malicious purposes. Detecting these GAN-generated images (GAN-images) becomes increasingly challenging due to the significant reduction of underlying artifacts and specific patterns. The absence of such traces can hinder detection algorithms from identifying GAN-images and transferring knowledge to identify other types of GAN-images as well. In this work, we present the Transferable GAN-images Detection framework T-GD, a robust transferable framework for an effective detection of GAN-images. T-GD is composed of a teacher and a student model that can iteratively teach and evaluate each other to improve the detection performance. First, we train the teacher model on the source dataset and use it as a starting point for learning the target dataset. To train the student model, we inject noise by mixing up the source and target datasets, while constraining the weight variation to preserve the starting point. Our approach is a self-training method, but distinguishes itself from prior approaches by focusing on improving the transferability of GAN-image detection. T-GD achieves high performance on the source dataset by overcoming catastrophic forgetting and effectively detecting state-of-the-art GAN-images with only a small volume of data without any metadata information. | Hyeonseong Jeon, Young Oh Bang, Junyaup Kim, Simon Woo | null | null | 2,020 | icml |
BINOCULARS for efficient, nonmyopic sequential experimental design | null | Finite-horizon sequential experimental design (SED) arises naturally in many contexts, including hyperparameter tuning in machine learning among more traditional settings. Computing the optimal policy for such problems requires solving Bellman equations, which are generally intractable. Most existing work resorts to severely myopic approximations by limiting the decision horizon to only a single time-step, which can underweight exploration in favor of exploitation. We present BINOCULARS: Batch-Informed NOnmyopic Choices, Using Long-horizons for Adaptive, Rapid SED, a general framework for deriving efficient, nonmyopic approximations to the optimal experimental policy. Our key idea is simple and surprisingly effective: we first compute a one-step optimal batch of experiments, then select a single point from this batch to evaluate. We realize BINOCULARS for Bayesian optimization and Bayesian quadrature – two notable example problems with radically different objectives – and demonstrate that BINOCULARS significantly outperforms significantly outperforms myopic alternatives in real-world scenarios. | Shali Jiang, Henry Chai, Javier Gonzalez, Roman Garnett | null | null | 2,020 | icml |
Implicit Class-Conditioned Domain Alignment for Unsupervised Domain Adaptation | null | We present an approach for unsupervised domain adaptation{—}with a strong focus on practical considerations of within-domain class imbalance and between-domain class distribution shift{—}from a class-conditioned domain alignment perspective. Current methods for class-conditioned domain alignment aim to explicitly minimize a loss function based on pseudo-label estimations of the target domain. However, these methods suffer from pseudo-label bias in the form of error accumulation. We propose a method that removes the need for explicit optimization of model parameters from pseudo-labels. Instead, we present a sampling-based implicit alignment approach, where the sample selection is implicitly guided by the pseudo-labels. Theoretical analysis reveals the existence of a domain-discriminator shortcut in misaligned classes, which is addressed by the proposed approach to facilitate domain-adversarial learning. Empirical results and ablation studies confirm the effectiveness of the proposed approach, especially in the presence of within-domain class imbalance and between-domain class distribution shift. | Xiang Jiang, Qicheng Lao, Stan Matwin, Mohammad Havaei | null | null | 2,020 | icml |
Guided Learning of Nonconvex Models through Successive Functional Gradient Optimization | null | This paper presents a framework of successive functional gradient optimization for training nonconvex models such as neural networks, where training is driven by mirror descent in a function space. We provide a theoretical analysis and empirical study of the training method derived from this framework. It is shown that the method leads to better performance than that of standard training techniques. | Rie Johnson, Tong Zhang | null | null | 2,020 | icml |
Learning Adversarial Markov Decision Processes with Bandit Feedback and Unknown Transition | null | We consider the task of learning in episodic finite-horizon Markov decision processes with an unknown transition function, bandit feedback, and adversarial losses. We propose an efficient algorithm that achieves $\mathcal{\tilde{O}}(L|X|\sqrt{|A|T})$ regret with high probability, where $L$ is the horizon, $|X|$ the number of states, $|A|$ the number of actions, and T the number of episodes. To our knowledge, our algorithm is the first to ensure $\mathcal{\tilde{O}}(\sqrt{T})$ regret in this challenging setting; in fact, it achieves the same regret as (Rosenberg & Mansour, 2019a) who consider the easier setting with full-information. Our key contributions are two-fold: a tighter confidence set for the transition function; and an optimistic loss estimator that is inversely weighted by an "upper occupancy bound". | Chi Jin, Tiancheng Jin, Haipeng Luo, Suvrit Sra, Tiancheng Yu | null | null | 2,020 | icml |
Fair k-Centers via Maximum Matching | null | The field of algorithms has seen a push for fairness, or the removal of inherent bias, in recent history. In data summarization, where a much smaller subset of a data set is chosen to represent the whole of the data, fairness can be introduced by guaranteeing each "demographic group" a specific portion of the representative subset. Specifically, this paper examines this fair variant of the k-centers problem, where a subset of the data with cardinality k is chosen to minimize distance to the rest of the data. Previous papers working on this problem presented both a 3-approximation algorithm with a super-linear runtime and a linear-time algorithm whose approximation factor is exponential in the number of demographic groups. This paper combines the best of each algorithm by presenting a linear-time algorithm with a guaranteed 3-approximation factor and provides empirical evidence of both the algorithm’s runtime and effectiveness. | Matthew Jones, Huy Nguyen, Thy Nguyen | null | null | 2,020 | icml |
A simpler approach to accelerated optimization: iterative averaging meets optimism | null | Recently there have been several attempts to extend Nesterov’s accelerated algorithm to smooth stochastic and variance-reduced optimization. In this paper, we show that there is a simpler approach to acceleration: applying optimistic online learning algorithms and querying the gradient oracle at the online average of the intermediate optimization iterates. In particular, we tighten a recent result of Cutkosky (2019) to demonstrate theoretically that online iterate averaging results in a reduced optimization gap, independently of the algorithm involved. We show that carefully combining this technique with existing generic optimistic online learning algorithms yields the optimal accelerated rates for optimizing strongly-convex and non-strongly-convex, possibly composite objectives, with deterministic as well as stochastic first-order oracles. We further extend this idea to variance-reduced optimization. Finally, we also provide “universal” algorithms that achieve the optimal rate for smooth and non-smooth composite objectives simultaneously without further tuning, generalizing the results of Kavis et al. (2019) and solving a number of their open problems. | Pooria Joulani, Anant Raj, Andras Gyorgy, Csaba Szepesvari | null | null | 2,020 | icml |
On Relativistic f-Divergences | null | We take a more rigorous look at Relativistic Generative Adversarial Networks (RGANs) and prove that the objective function of the discriminator is a statistical divergence for any concave function f with minimal properties. We devise additional variants of relativistic f-divergences. We show that the Wasserstein distance is weaker than f-divergences which are weaker than relativistic f-divergences. Given the good performance of RGANs, this suggests that Wasserstein GAN does not performs well primarily because of the weak metric, but rather because of regularization and the use of a relativistic discriminator. We introduce the minimum-variance unbiased estimator (MVUE) for Relativistic paired GANs (RpGANs; originally called RGANs which could bring confusion) and show that it does not perform better. We show that the estimator of Relativistic average GANs (RaGANs) is asymptotically unbiased and that the finite-sample bias is small; removing this bias does not improve performance. | Alexia Jolicoeur-Martineau | null | null | 2,020 | icml |
Computational and Statistical Tradeoffs in Inferring Combinatorial Structures of Ising Model | null | We study the computational and statistical tradeoffs in inferring combinatorial structures of high dimensional simple zero-field ferromagnetic Ising model. Under the framework of oracle computational model where an algorithm interacts with an oracle that discourses a randomized version of truth, we characterize the computational lower bounds of learning combinatorial structures in polynomial time, under which no algorithms within polynomial-time can distinguish between graphs with and without certain structures. This hardness of learning with limited computational budget is shown to be characterized by a novel quantity called vertex overlap ratio. Such quantity is universally valid for many specific graph structures including cliques and nearest neighbors. On the other side, we attain the optimal rates for testing these structures against empty graph by proposing the quadratic testing statistics to match the lower bounds. We also investigate the relationship between computational bounds and information-theoretic bounds for such problems, and found gaps between the two boundaries in inferring some particular structures, especially for those with dense edges. | Ying Jin, Zhaoran Wang, Junwei Lu | null | null | 2,020 | icml |
Distribution Augmentation for Generative Modeling | null | We present distribution augmentation (DistAug), a simple and powerful method of regularizing generative models. Our approach applies augmentation functions to data and, importantly, conditions the generative model on the specific function used. Unlike typical data augmentation, DistAug allows usage of functions which modify the target density, enabling aggressive augmentations more commonly seen in supervised and self-supervised learning. We demonstrate this is a more effective regularizer than standard methods, and use it to train a 152M parameter autoregressive model on CIFAR-10 to 2.56 bits per dim (relative to the state-of-the-art 2.80). Samples from this model attain FID 12.75 and IS 8.40, outperforming the majority of GANs. We further demonstrate the technique is broadly applicable across model architectures and problem domains. | Heewoo Jun, Rewon Child, Mark Chen, John Schulman, Aditya Ramesh, Alec Radford, Ilya Sutskever | null | null | 2,020 | icml |
Sub-Goal Trees a Framework for Goal-Based Reinforcement Learning | null | Many AI problems, in robotics and other domains, are goal-directed, essentially seeking a trajectory leading to some goal state. Reinforcement learning (RL), building on Bellman’s optimality equation, naturally optimizes for a single goal, yet can be made goal-directed by augmenting the state with the goal. Instead, we propose a new RL framework, derived from a dynamic programming equation for the all pairs shortest path (APSP) problem, which naturally solves goal-directed queries. We show that this approach has computational benefits for both standard and approximate dynamic programming. Interestingly, our formulation prescribes a novel protocol for computing a trajectory: instead of predicting the next state given its predecessor, as in standard RL, a goal-conditioned trajectory is constructed by first predicting an intermediate state between start and goal, partitioning the trajectory into two. Then, recursively, predicting intermediate points on each sub-segment, until a complete trajectory is obtained. We call this trajectory structure a sub-goal tree. Building on it, we additionally extend the policy gradient methodology to recursively predict sub-goals, resulting in novel goal-based algorithms. Finally, we apply our method to neural motion planning, where we demonstrate significant improvements compared to standard RL on navigating a 7-DoF robot arm between obstacles. | Tom Jurgenson, Or Avner, Edward Groshev, Aviv Tamar | null | null | 2,020 | icml |
Double Reinforcement Learning for Efficient and Robust Off-Policy Evaluation | null | Off-policy evaluation (OPE) in reinforcement learning allows one to evaluate novel decision policies without needing to conduct exploration, which is often costly or otherwise infeasible. We consider for the first time the semiparametric efficiency limits of OPE in Markov decision processes (MDPs), where actions, rewards, and states are memoryless. We show existing OPE estimators may fail to be efficient in this setting. We develop a new estimator based on cross-fold estimation of $q$-functions and marginalized density ratios, which we term double reinforcement learning (DRL). We show that DRL is efficient when both components are estimated at fourth-root rates and is also doubly robust when only one component is consistent. We investigate these properties empirically and demonstrate the performance benefits due to harnessing memorylessness. | Nathan Kallus, Masatoshi Uehara | null | null | 2,020 | icml |
DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Training | null | We study optimal covariate balance for causal inferences from observational data when rich covariates and complex relationships necessitate flexible modeling with neural networks. Standard approaches such as propensity weighting and matching/balancing fail in such settings due to miscalibrated propensity nets and inappropriate covariate representations, respectively. We propose a new method based on adversarial training of a weighting and a discriminator network that effectively addresses this methodological gap. This is demonstrated through new theoretical characterizations and empirical results on both synthetic and clinical data showing how causal analyses can be salvaged in such challenging settings. | Nathan Kallus | null | null | 2,020 | icml |
Strategyproof Mean Estimation from Multiple-Choice Questions | null | Given n values possessed by n agents, we study the problem of estimating the mean by truthfully eliciting agents’ answers to multiple-choice questions about their values. We consider two natural candidates for estimation error: mean squared error (MSE) and mean absolute error (MAE). We design a randomized estimator which is asymptotically optimal for both measures in the worst case. In the case where prior distributions over the agents’ values are known, we give an optimal, polynomial-time algorithm for MSE, and show that the task of computing an optimal estimate for MAE is #P-hard. Finally, we demonstrate empirically that knowledge of prior distributions gives a significant edge. | Anson Kahng, Gregory Kehne, Ariel Procaccia | null | null | 2,020 | icml |
On the Power of Compressed Sensing with Generative Models | null | The goal of compressed sensing is to learn a structured signal $x$ from a limited number of noisy linear measurements $y \approx Ax$. In traditional compressed sensing, “structure” is represented by sparsity in some known basis. Inspired by the success of deep learning in modeling images, recent work starting with Bora-Jalal-Price-Dimakis’17 has instead considered structure to come from a generative model $G: \mathbb{R}^k \to \mathbb{R}^n$. We present two results establishing the difficulty and strength of this latter task, showing that existing bounds are tight: First, we provide a lower bound matching the Bora et.al upper bound for compressed sensing with $L$-Lipschitz generative models $G$ which holds even for the more relaxed goal of \emph{non-uniform} recovery. Second, we show that generative models generalize sparsity as a representation of structure by constructing a ReLU-based neural network with $2$ hidden layers and $O(n)$ activations per layer whose range is precisely the set of all $k$-sparse vectors. | Akshay Kamath, Eric Price, Sushrut Karmalkar | null | null | 2,020 | icml |
Rate-distortion optimization guided autoencoder for isometric embedding in Euclidean latent space | null | To analyze high-dimensional and complex data in the real world, deep generative models, such as variational autoencoder (VAE) embed data in a low-dimensional space (latent space) and learn a probabilistic model in the latent space. However, they struggle to accurately reproduce the probability distribution function (PDF) in the input space from that in the latent space. If the embedding were isometric, this issue can be solved, because the relation of PDFs can become tractable. To achieve isometric property, we propose Rate-Distortion Optimization guided autoencoder inspired by orthonormal transform coding. We show our method has the following properties: (i) the Jacobian matrix between the input space and a Euclidean latent space forms a constantly-scaled orthonormal system and enables isometric data embedding; (ii) the relation of PDFs in both spaces can become tractable one such as proportional relation. Furthermore, our method outperforms state-of-the-art methods in unsupervised anomaly detection with four public datasets. | Keizo Kato, Jing Zhou, Tomotake Sasaki, Akira Nakagawa | null | null | 2,020 | icml |
Non-autoregressive Machine Translation with Disentangled Context Transformer | null | State-of-the-art neural machine translation models generate a translation from left to right and every step is conditioned on the previously generated tokens. The sequential nature of this generation process causes fundamental latency in inference since we cannot generate multiple tokens in each sentence in parallel. We propose an attention-masking based model, called Disentangled Context (DisCo) transformer, that simultaneously generates all tokens given different contexts. The DisCo transformer is trained to predict every output token given an arbitrary subset of the other reference tokens. We also develop the parallel easy-first inference algorithm, which iteratively refines every token in parallel and reduces the number of required iterations. Our extensive experiments on 7 translation directions with varying data sizes demonstrate that our model achieves competitive, if not better, performance compared to the state of the art in non-autoregressive machine translation while significantly reducing decoding time on average. | Jungo Kasai, James Cross, Marjan Ghazvininejad, Jiatao Gu | null | null | 2,020 | icml |
Efficient Non-conjugate Gaussian Process Factor Models for Spike Count Data using Polynomial Approximations | null | Gaussian Process Factor Analysis (GPFA) has been broadly applied to the problem of identifying smooth, low-dimensional temporal structure underlying large-scale neural recordings. However, spike trains are non-Gaussian, which motivates combining GPFA with discrete observation models for binned spike count data. The drawback to this approach is that GPFA priors are not conjugate to count model likelihoods, which makes inference challenging. Here we address this obstacle by introducing a fast, approximate inference method for non-conjugate GPFA models. Our approach uses orthogonal second-order polynomials to approximate the nonlinear terms in the non-conjugate log-likelihood, resulting in a method we refer to as polynomial approximate log-likelihood (PAL) estimators. This approximation allows for accurate closed-form evaluation of marginal likelihoods and fast numerical optimization for parameters and hyperparameters. We derive PAL estimators for GPFA models with binomial, Poisson, and negative binomial observations and find the PAL estimation is highly accurate, and achieves faster convergence times compared to existing state-of-the-art inference methods. We also find that PAL hyperparameters can provide sensible initialization for black box variational inference (BBVI), which improves BBVI accuracy. We demonstrate that PAL estimators achieve fast and accurate extraction of latent structure from multi-neuron spike train data. | Stephen Keeley, David Zoltowski, Yiyi Yu, Spencer Smith, Jonathan Pillow | null | null | 2,020 | icml |
Differentiable Likelihoods for Fast Inversion of ’Likelihood-Free’ Dynamical Systems | null | Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically approximated by an ODE solver. This, however, is not a fundamental constraint but just a lack of functionality in classic ODE solvers, which do not return a likelihood but a point estimate. To address this shortcoming, we employ Gaussian ODE filtering (a probabilistic numerical method for ODEs) to construct a local Gaussian approximation to the likelihood. This approximation yields tractable estimators for the gradient and Hessian of the (log-)likelihood. Insertion of these estimators into existing gradient-based optimization and sampling methods engenders new solvers for ODE inverse problems. We demonstrate that these methods outperform standard likelihood-free approaches on three benchmark-systems. | Hans Kersting, Nicholas Krämer, Martin Schiegg, Christian Daniel, Michael Tiemann, Philipp Hennig | null | null | 2,020 | icml |
Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention | null | Transformers achieve remarkable performance in several tasks but due to their quadratic complexity, with respect to the input’s length, they are prohibitively slow for very long sequences. To address this limitation, we express the self-attention as a linear dot-product of kernel feature maps and make use of the associativity property of matrix products to reduce the complexity from $\bigO{N^2}$ to $\bigO{N}$, where $N$ is the sequence length. We show that this formulation permits an iterative implementation that dramatically accelerates autoregressive transformers and reveals their relationship to recurrent neural networks. Our \emph{Linear Transformers} achieve similar performance to vanilla Transformers and they are up to 4000x faster on autoregressive prediction of very long sequences. | Angelos Katharopoulos, Apoorv Vyas, Nikolaos Pappas, François Fleuret | null | null | 2,020 | icml |
Uniform Convergence of Rank-weighted Learning | null | The decision-theoretic foundations of classical machine learning models have largely focused on estimating model parameters that minimize the expectation of a given loss function. However, as machine learning models are deployed in varied contexts, such as in high-stakes decision-making and societal settings, it is clear that these models are not just evaluated by their average performances. In this work, we study a novel notion of L-Risk based on the classical idea of rank-weighted learning. These L-Risks, induced by rank-dependent weighting functions with bounded variation, is a unification of popular risk measures such as conditional value-at-risk and those defined by cumulative prospect theory. We give uniform convergence bounds of this broad class of risk measures and study their consequences on a logistic regression example. | Justin Khim, Liu Leqi, Adarsh Prasad, Pradeep Ravikumar | null | null | 2,020 | icml |
Quantum Expectation-Maximization for Gaussian mixture models | null | We define a quantum version of Expectation-Maximization (QEM), a fundamental tool in unsupervised machine learning, often used to solve Maximum Likelihood (ML) and Maximum A Posteriori (MAP) estimation problems. We use QEM to fit a Gaussian Mixture Model, and show how to generalize it to fit mixture models with base distributions in the exponential family. Given quantum access to a dataset, our algorithm has convergence and precision guarantees similar to the classical algorithm, while the runtime is polylogarithmic in the number of elements in the training set and polynomial in other parameters, such as the dimension of the feature space and the number of components in the mixture. We discuss the performance of the algorithm on a dataset that is expected to be classified successfully by classical EM and provide guarantees for its runtime. | Iordanis Kerenidis, Alessandro Luongo, Anupam Prakash | null | null | 2,020 | icml |
A Unified Theory of Decentralized SGD with Changing Topology and Local Updates | null | Decentralized stochastic optimization methods have gained a lot of attention recently, mainly because of their cheap per iteration cost, data locality, and their communication-efficiency. In this paper we introduce a unified convergence analysis that covers a large variety of decentralized SGD methods which so far have required different intuitions, have different applications, and which have been developed separately in various communities. Our algorithmic framework covers local SGD updates and synchronous and pairwise gossip updates on adaptive network topology. We derive universal convergence rates for smooth (convex and non-convex) problems and the rates interpolate between the heterogeneous (non-identically distributed data) and iid-data settings, recovering linear convergence rates in many special cases, for instance for over-parametrized models. Our proofs rely on weak assumptions (typically improving over prior work in several aspects) and recover (and improve) the best known complexity results for a host of important scenarios, such as for instance coorperative SGD and federated averaging (local SGD). | Anastasia Koloskova, Nicolas Loizou, Sadra Boreiri, Martin Jaggi, Sebastian Stich | null | null | 2,020 | icml |
Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities | null | Normalizing flows are exact-likelihood generative neural networks which approximately transform samples from a simple prior distribution to samples of the probability distribution of interest. Recent work showed that such generative models can be utilized in statistical mechanics to sample equilibrium states of many-body systems in physics and chemistry. To scale and generalize these results, it is essential that the natural symmetries in the probability density – in physics defined by the invariances of the target potential – are built into the flow. We provide a theoretical sufficient criterion showing that the distribution generated by equivariant normalizing flows is invariant with respect to these symmetries by design. Furthermore, we propose building blocks for flows which preserve symmetries which are usually found in physical/chemical many-body particle systems. Using benchmark systems motivated from molecular physics, we demonstrate that those symmetry preserving flows can provide better generalization capabilities and sampling efficiency. | Jonas Köhler, Leon Klein, Frank Noe | null | null | 2,020 | icml |
Variational Inference for Sequential Data with Future Likelihood Estimates | null | The recent development of flexible and scalable variational inference algorithms has popularized the use of deep probabilistic models in a wide range of applications. However, learning and reasoning about high-dimensional models with nondifferentiable densities are still a challenge. For such a model, inference algorithms struggle to estimate the gradients of variational objectives accurately, due to high variance in their estimates. To tackle this challenge, we present a novel variational inference algorithm for sequential data, which performs well even when the density from the model is not differentiable, for instance, due to the use of discrete random variables. The key feature of our algorithm is that it estimates future likelihoods at all time steps. The estimated future likelihoods form the core of our new low-variance gradient estimator. We formally analyze our gradient estimator from the perspective of variational objective, and show the effectiveness of our algorithm with synthetic and real datasets. | Geon-Hyeong Kim, Youngsoo Jang, Hongseok Yang, Kee-Eung Kim | null | null | 2,020 | icml |
Efficient Identification in Linear Structural Causal Models with Auxiliary Cutsets | null | We develop a polynomial-time algorithm for identification of structural coefficients in linear causal models that subsumes previous efficient state-of-the-art methods, unifying several disparate approaches to identification in this setting. Building on these results, we develop a procedure for identifying total causal effects in linear systems. | Daniel Kumor, Carlos Cinelli, Elias Bareinboim | null | null | 2,020 | icml |
Problems with Shapley-value-based explanations as feature importance measures | null | Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements using some form of the game’s unique Shapley values. Justification for these methods rests on two pillars: their desirable mathematical properties, and their applicability to specific motivations for explanations. We show that mathematical problems arise when Shapley values are used for feature importance and that the solutions to mitigate these necessarily induce further complexity, such as the need for causal reasoning. We also draw on additional literature to argue that Shapley values do not provide explanations which suit human-centric goals of explainability. | I. Elizabeth Kumar, Suresh Venkatasubramanian, Carlos Scheidegger, Sorelle Friedler | null | null | 2,020 | icml |
A Sequential Self Teaching Approach for Improving Generalization in Sound Event Recognition | null | An important problem in machine auditory perception is to recognize and detect sound events. In this paper, we propose a sequential self-teaching approach to learning sounds. Our main proposition is that it is harder to learn sounds in adverse situations such as from weakly labeled and/or noisy labeled data, and in these situations a single stage of learning is not sufficient. Our proposal is a sequential stage-wise learning process that improves generalization capabilities of a given modeling system. We justify this method via technical results and on Audioset, the largest sound events dataset, our sequential learning approach can lead to up to 9% improvement in performance. A comprehensive evaluation also shows that the method leads to improved transferability of knowledge from previously trained models, thereby leading to improved generalization capabilities on transfer learning tasks. | Anurag Kumar, Vamsi Ithapu | null | null | 2,020 | icml |
Curse of Dimensionality on Randomized Smoothing for Certifiable Robustness | null | Randomized smoothing, using just a simple isotropic Gaussian distribution, has been shown to produce good robustness guarantees against $\ell_2$-norm bounded adversaries. In this work, we show that extending the smoothing technique to defend against other attack models can be challenging, especially in the high-dimensional regime. In particular, for a vast class of i.i.d. smoothing distributions, we prove that the largest $\ell_p$-radius that can be certified decreases as $O(1/d^{\frac{1}{2} - \frac{1}{p}})$ with dimension $d$ for $p > 2$. Notably, for $p \geq 2$, this dependence on $d$ is no better than that of the $\ell_p$-radius that can be certified using isotropic Gaussian smoothing, essentially putting a matching lower bound on the robustness radius. When restricted to \emph{generalized} Gaussian smoothing, these two bounds can be shown to be within a constant factor of each other in an asymptotic sense, establishing that Gaussian smoothing provides the best possible results, up to a constant factor, when $p \geq 2$. We present experimental results on CIFAR to validate our theory. For other smoothing distributions, such as, a uniform distribution within an $\ell_1$ or an $\ell_\infty$-norm ball, we show upper bounds of the form $O(1 / d)$ and $O(1 / d^{1 - \frac{1}{p}})$ respectively, which have an even worse dependence on $d$. | Aounon Kumar, Alexander Levine, Tom Goldstein, Soheil Feizi | null | null | 2,020 | icml |
Bayesian Experimental Design for Implicit Models by Mutual Information Neural Estimation | null | Implicit stochastic models, where the data-generation distribution is intractable but sampling is possible, are ubiquitous in the natural sciences. The models typically have free parameters that need to be inferred from data collected in scientific experiments. A fundamental question is how to design the experiments so that the collected data are most useful. The field of Bayesian experimental design advocates that, ideally, we should choose designs that maximise the mutual information (MI) between the data and the parameters. For implicit models, however, this approach is severely hampered by the high computational cost of computing posteriors and maximising MI, in particular when we have more than a handful of design variables to optimise. In this paper, we propose a new approach to Bayesian experimental design for implicit models that leverages recent advances in neural MI estimation to deal with these issues. We show that training a neural network to maximise a lower bound on MI allows us to jointly determine the optimal design and the posterior. Simulation studies illustrate that this gracefully extends Bayesian experimental design for implicit models to higher design dimensions. | Steven Kleinegesse, Michael U. Gutmann | null | null | 2,020 | icml |
Meta-learning for Mixed Linear Regression | null | In modern supervised learning, there are a large number of tasks, but many of them are associated with only a small amount of labelled data. These include data from medical image processing and robotic interaction. Even though each individual task cannot be meaningfully trained in isolation, one seeks to meta-learn across the tasks from past experiences by exploiting some similarities. We study a fundamental question of interest: When can abundant tasks with small data compensate for lack of tasks with big data? We focus on a canonical scenario where each task is drawn from a mixture of $k$ linear regressions, and identify sufficient conditions for such a graceful exchange to hold; there is little loss in sample complexity even when we only have access to small data tasks. To this end, we introduce a novel spectral approach and show that we can efficiently utilize small data tasks with the help of $\tilde\Omega(k^{3/2})$ medium data tasks each with $\tilde\Omega(k^{1/2})$ examples. | Weihao Kong, Raghav Somani, Zhao Song, Sham Kakade, Sewoong Oh | null | null | 2,020 | icml |
Principled learning method for Wasserstein distributionally robust optimization with local perturbations | null | Wasserstein distributionally robust optimization (WDRO) attempts to learn a model that minimizes the local worst-case risk in the vicinity of the empirical data distribution defined by Wasserstein ball. While WDRO has received attention as a promising tool for inference since its introduction, its theoretical understanding has not been fully matured. Gao et al. (2017) proposed a minimizer based on a tractable approximation of the local worst-case risk, but without showing risk consistency. In this paper, we propose a minimizer based on a novel approximation theorem and provide the corresponding risk consistency results. Furthermore, we develop WDRO inference for locally perturbed data that include the Mixup (Zhang et al., 2017) as a special case. We show that our approximation and risk consistency results naturally extend to the cases when data are locally perturbed. Numerical experiments demonstrate robustness of the proposed method using image classification datasets. Our results show that the proposed method achieves significantly higher accuracy than baseline models on noisy datasets. | Yongchan Kwon, Wonyoung Kim, Joong-Ho Won, Myunghee Cho Paik | null | null | 2,020 | icml |
On Implicit Regularization in $β$-VAEs | null | While the impact of variational inference (VI) on posterior inference in a fixed generative model is well-characterized, its role in regularizing a learned generative model when used in variational autoencoders (VAEs) is poorly understood. We study the regularizing effects of variational distributions on learning in generative models from two perspectives. First, we analyze the role that the choice of variational family plays in imparting uniqueness to the learned model by restricting the set of optimal generative models. Second, we study the regularization effect of the variational family on the local geometry of the decoding model. This analysis uncovers the regularizer implicit in the $\beta$-VAE objective, and leads to an approximation consisting of a deterministic autoencoding objective plus analytic regularizers that depend on the Hessian or Jacobian of the decoding model, unifying VAEs with recent heuristics proposed for training regularized autoencoders. We empirically verify these findings, observing that the proposed deterministic objective exhibits similar behavior to the $\beta$-VAE in terms of objective value and sample quality. | Abhishek Kumar, Ben Poole | null | null | 2,020 | icml |
Controlling Overestimation Bias with Truncated Mixture of Continuous Distributional Quantile Critics | null | The overestimation bias is one of the major impediments to accurate off-policy learning. This paper investigates a novel way to alleviate the overestimation bias in a continuous control setting. Our method—Truncated Quantile Critics, TQC,—blends three ideas: distributional representation of a critic, truncation of critics prediction, and ensembling of multiple critics. Distributional representation and truncation allow for arbitrary granular overestimation control, while ensembling provides additional score improvements. TQC outperforms the current state of the art on all environments from the continuous control benchmark suite, demonstrating 25% improvement on the most challenging Humanoid environment. | Arsenii Kuznetsov, Pavel Shvechikov, Alexander Grishin, Dmitry Vetrov | null | null | 2,020 | icml |
Concentration bounds for CVaR estimation: The cases of light-tailed and heavy-tailed distributions | null | Conditional Value-at-Risk (CVaR) is a widely used risk metric in applications such as finance. We derive concentration bounds for CVaR estimates, considering separately the cases of sub-Gaussian, light-tailed and heavy-tailed distributions. For the sub-Gaussian and light-tailed cases, we use a classical CVaR estimator based on the empirical distribution constructed from the samples. For heavy-tailed random variables, we assume a mild ‘bounded moment’ condition, and derive a concentration bound for a truncation-based estimator. Our concentration bounds exhibit exponential decay in the sample size, and are tighter than those available in the literature for the above distribution classes. To demonstrate the applicability of our concentration results, we consider the CVaR optimization problem in a multi-armed bandit setting. Specifically, we address the best CVaR-arm identification problem under a fixed budget. Using our CVaR concentration results, we derive an upper-bound on the probability of incorrect arm identification. | Prashanth L.A., Krishna Jagannathan, Ravi Kolla | null | null | 2,020 | icml |
Inducing and Exploiting Activation Sparsity for Fast Inference on Deep Neural Networks | null | Optimizing convolutional neural networks for fast inference has recently become an extremely active area of research. One of the go-to solutions in this context is weight pruning, which aims to reduce computational and memory footprint by removing large subsets of the connections in a neural network. Surprisingly, much less attention has been given to exploiting sparsity in the activation maps, which tend to be naturally sparse in many settings thanks to the structure of rectified linear (ReLU) activation functions. In this paper, we present an in-depth analysis of methods for maximizing the sparsity of the activations in a trained neural network, and show that, when coupled with an efficient sparse-input convolution algorithm, we can leverage this sparsity for significant performance gains. To induce highly sparse activation maps without accuracy loss, we introduce a new regularization technique, coupled with a new threshold-based sparsification method based on a parameterized activation function called Forced-Activation-Threshold Rectified Linear Unit (FATReLU). We examine the impact of our methods on popular image classification models, showing that most architectures can adapt to significantly sparser activation maps without any accuracy loss. Our second contribution is showing that these these compression gains can be translated into inference speedups: we provide a new algorithm to enable fast convolution operations over networks with sparse activations, and show that it can enable significant speedups for end-to-end inference on a range of popular models on the large-scale ImageNet image classification task on modern Intel CPUs, with little or no retraining cost. | Mark Kurtz, Justin Kopinsky, Rati Gelashvili, Alexander Matveev, John Carr, Michael Goin, William Leiserson, Sage Moore, Nir Shavit, Dan Alistarh | null | null | 2,020 | icml |
CURL: Contrastive Unsupervised Representations for Reinforcement Learning | null | We present CURL: Contrastive Unsupervised Representations for Reinforcement Learning. CURL extracts high-level features from raw pixels using contrastive learning and performs off-policy control on top of the extracted features. CURL outperforms prior pixel-based methods, both model-based and model-free, on complex tasks in the DeepMind Control Suite and Atari Games showing 1.9x and 1.2x performance gains at the 100K environment and interaction steps benchmarks respectively. On the DeepMind Control Suite, CURL is the first image-based algorithm to nearly match the sample-efficiency of methods that use state-based features. Our code is open-sourced and available at https://www.github.com/MishaLaskin/curl. | Michael Laskin, Aravind Srinivas, Pieter Abbeel | null | null | 2,020 | icml |
Recht-Re Noncommutative Arithmetic-Geometric Mean Conjecture is False | null | Stochastic optimization algorithms have become indispensable in modern machine learning. An unresolved foundational question in this area is the difference between with-replacement sampling and without-replacement sampling — does the latter have superior convergence rate compared to the former? A groundbreaking result of Recht and Ré reduces the problem to a noncommutative analogue of the arithmetic-geometric mean inequality where $n$ positive numbers are replaced by $n$ positive definite matrices. If this inequality holds for all $n$, then without-replacement sampling (also known as random reshuffling) indeed outperforms with-replacement sampling in some important optimization problems. The conjectured Recht–Ré inequality has so far only been established for $n = 2$ and a special case of $n = 3$. We will show that the Recht–Ré conjecture is false for general $n$. Our approach relies on the noncommutative Positivstellensatz, which allows us to reduce the conjectured inequality to a semidefinite program and the validity of the conjecture to certain bounds for the optimum values, which we show are false as soon as $n = 5$. | Zehua Lai, Lek-Heng Lim | null | null | 2,020 | icml |
Learning with Good Feature Representations in Bandits and in RL with a Generative Model | null | The construction in the recent paper by Du et al. [2019] implies that searching for a near-optimal action in a bandit sometimes requires examining essentially all the actions, even if the learner is given linear features in R^d that approximate the rewards with a small uniform error. We use the Kiefer-Wolfowitz theorem to prove a positive result that by checking only a few actions, a learner can always find an action that is suboptimal with an error of at most O($\epsilon$$\sqrt{}$d) where $\epsilon$ is the approximation error of the features. Thus, features are useful when the approximation error is small relative to the dimensionality of the features. The idea is applied to stochastic bandits and reinforcement learning with a generative model where the learner has access to d-dimensional linear features that approximate the action-value functions for all policies to an accuracy of $\epsilon$. For linear bandits, we prove a bound on the regret of order d$\sqrt{}$(n log(k)) + $\epsilon$n$\sqrt{}$d log(n) with k the number of actions and n the horizon. For RL we show that approximate policy iteration can learn a policy that is optimal up to an additive error of order $\epsilon$$\sqrt{}$d/(1 − $\gamma$)^2 and using about d/($\epsilon$^2(1 − $\gamma$)^4) samples from the generative model. These bounds are independent of the finer details of the features. We also investigate how the structure of the feature set impacts the tradeoff between sample complexity and estimation error. | Tor Lattimore, Csaba Szepesvari, Gellert Weisz | null | null | 2,020 | icml |
Inertial Block Proximal Methods for Non-Convex Non-Smooth Optimization | null | We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order methods: (1) they allow using two different extrapolation points to evaluate the gradients and to add the inertial force (we will empirically show that it is more efficient than using a single extrapolation point), (2) they allow to randomly select the block of variables to update, and (3) they do not require a restarting step. We prove the subsequential convergence of the generated sequence under mild assumptions, prove the global convergence under some additional assumptions, and provide convergence rates. We deploy the proposed methods to solve non-negative matrix factorization (NMF) and show that they compete favorably with the state-of-the-art NMF algorithms. Additional experiments on non-negative approximate canonical polyadic decomposition, also known as nonnegative tensor factorization, are also provided. | Hien Le, Nicolas Gillis, Panagiotis Patrinos | null | null | 2,020 | icml |
Estimating Model Uncertainty of Neural Networks in Sparse Information Form | null | We present a sparse representation of model uncertainty for Deep Neural Networks (DNNs) where the parameter posterior is approximated with an inverse formulation of the Multivariate Normal Distribution (MND), also known as the information form. The key insight of our work is that the information matrix, i.e. the inverse of the covariance matrix tends to be sparse in its spectrum. Therefore, dimensionality reduction techniques such as low rank approximations (LRA) can be effectively exploited. To achieve this, we develop a novel sparsification algorithm and derive a cost-effective analytical sampler. As a result, we show that the information form can be scalably applied to represent model uncertainty in DNNs. Our exhaustive theoretical analysis and empirical evaluations on various benchmarks show the competitiveness of our approach over the current methods. | Jongseok Lee, Matthias Humt, Jianxiang Feng, Rudolph Triebel | null | null | 2,020 | icml |
Duality in RKHSs with Infinite Dimensional Outputs: Application to Robust Losses | null | Operator-Valued Kernels (OVKs) and associated vector-valued Reproducing Kernel Hilbert Spaces provide an elegant way to extend scalar kernel methods when the output space is a Hilbert space. Although primarily used in finite dimension for problems like multi-task regression, the ability of this framework to deal with infinite dimensional output spaces unlocks many more applications, such as functional regression, structured output prediction, and structured data representation. However, these sophisticated schemes crucially rely on the kernel trick in the output space, so that most of previous works have focused on the square norm loss function, completely neglecting robustness issues that may arise in such surrogate problems. To overcome this limitation, this paper develops a duality approach that allows to solve OVK machines for a wide range of loss functions. The infinite dimensional Lagrange multipliers are handled through a Double Representer Theorem, and algorithms for \epsilon-insensitive losses and the Huber loss are thoroughly detailed. Robustness benefits are emphasized by a theoretical stability analysis, as well as empirical improvements on structured data applications. | Pierre Laforgue, Alex Lambert, Luc Brogat-Motte, Florence D’Alché-Buc | null | null | 2,020 | icml |
Causal Effect Identifiability under Partial-Observability | null | Causal effect identifiability is concerned with establishing the effect of intervening on a set of variables on another set of variables from observational or interventional distributions under causal assumptions that are usually encoded in the form of a causal graph. Most of the results of this literature implicitly assume that every variable modeled in the graph is measured in the available distributions. In practice, however, the data collections of the different studies considered do not measure the same variables, consistently. In this paper, we study the causal effect identifiability problem when the available distributions encompass different sets of variables, which we refer to as identification under partial-observability. We study a number of properties of the factors that comprise a causal effect under various levels of abstraction, and then characterize the relationship between them with respect to their status relative to the identification of a targeted intervention. We establish a sufficient graphical criterion for determining whether the effects are identifiable from partially-observed distributions. Finally, building on these graphical properties, we develop an algorithm that returns a formula for a causal effect in terms of the available distributions. | Sanghack Lee, Elias Bareinboim | null | null | 2,020 | icml |
Learning Compound Tasks without Task-specific Knowledge via Imitation and Self-supervised Learning | null | Most real-world tasks are compound tasks that consist of multiple simpler sub-tasks. The main challenge of learning compound tasks is that we have no explicit supervision to learn the hierarchical structure of compound tasks. To address this challenge, previous imitation learning methods exploit task-specific knowledge, e.g., labeling demonstrations manually or specifying termination conditions for each sub-task. However, the need for task-specific knowledge makes it difficult to scale imitation learning to real-world tasks. In this paper, we propose an imitation learning method that can learn compound tasks without task-specific knowledge. The key idea behind our method is to leverage a self-supervised learning framework to learn the hierarchical structure of compound tasks. Our work also proposes a task-agnostic regularization technique to prevent unstable switching between sub-tasks, which has been a common degenerate case in previous works. We evaluate our method against several baselines on compound tasks. The results show that our method achieves state-of-the-art performance on compound tasks, outperforming prior imitation learning methods. | Sang-Hyun Lee, Seung-Woo Seo | null | null | 2,020 | icml |
Batch Reinforcement Learning with Hyperparameter Gradients | null | We consider the batch reinforcement learning problem where the agent needs to learn only from a fixed batch of data, without further interaction with the environment. In such a scenario, we want to prevent the optimized policy from deviating too much from the data collection policy since the estimation becomes highly unstable otherwise due to the off-policy nature of the problem. However, imposing this requirement too strongly will result in a policy that merely follows the data collection policy. Unlike prior work where this trade-off is controlled by hand-tuned hyperparameters, we propose a novel batch reinforcement learning approach, batch optimization of policy and hyperparameter (BOPAH), that uses a gradient-based optimization of the hyperparameter using held-out data. We show that BOPAH outperforms other batch reinforcement learning algorithms in tabular and continuous control tasks, by finding a good balance to the trade-off between adhering to the data collection policy and pursuing the possible policy improvement. | Byungjun Lee, Jongmin Lee, Peter Vrancx, Dongho Kim, Kee-Eung Kim | null | null | 2,020 | icml |
Analytic Marching: An Analytic Meshing Solution from Deep Implicit Surface Networks | null | This paper studies a problem of learning surface mesh via implicit functions in an emerging field of deep learning surface reconstruction, where implicit functions are popularly implemented as multi-layer perceptrons (MLPs) with rectified linear units (ReLU). To achieve meshing from the learned implicit functions, existing methods adopt the de-facto standard algorithm of marching cubes; while promising, they suffer from loss of precision learned in the MLPs, due to the discretization nature of marching cubes. Motivated by the knowledge that a ReLU based MLP partitions its input space into a number of linear regions, we identify from these regions analytic cells and faces that are associated with zero-level isosurface of the implicit function, and characterize the conditions under which the identified faces are guaranteed to connect and form a closed, piecewise planar surface. We propose a naturally parallelizable algorithm of analytic marching to exactly recover the mesh captured by a learned MLP. Experiments on deep learning mesh reconstruction verify the advantages of our algorithm over existing ones. | Jiabao Lei, Kui Jia | null | null | 2,020 | icml |
Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoning | null | The goal of neural-symbolic computation is to integrate the connectionist and symbolist paradigms. Prior methods learn the neural-symbolic models using reinforcement learning (RL) approaches, which ignore the error propagation in the symbolic reasoning module and thus converge slowly with sparse rewards. In this paper, we address these issues and close the loop of neural-symbolic learning by (1) introducing the grammar model as a symbolic prior to bridge neural perception and symbolic reasoning, and (2) proposing a novel back-search algorithm which mimics the top-down human-like learning procedure to propagate the error through the symbolic reasoning module efficiently. We further interpret the proposed learning framework as maximum likelihood estimation using Markov chain Monte Carlo sampling and the back-search algorithm as a Metropolis-Hastings sampler. The experiments are conducted on two weakly-supervised neural-symbolic tasks: (1) handwritten formula recognition on the newly introduced HWF dataset; (2) visual question answering on the CLEVR dataset. The results show that our approach significantly outperforms the RL methods in terms of performance, converging speed, and data efficiency. Our code and data are released at https://liqing-ustc.github.io/NGS. | Qing Li, Siyuan Huang, Yining Hong, Yixin Chen, Ying Nian Wu, Song-Chun Zhu | null | null | 2,020 | icml |
Temporal Phenotyping using Deep Predictive Clustering of Disease Progression | null | Due to the wider availability of modern electronic health records, patient care data is often being stored in the form of time-series. Clustering such time-series data is crucial for patient phenotyping, anticipating patients’ prognoses by identifying “similar” patients, and designing treatment guidelines that are tailored to homogeneous patient subgroups. In this paper, we develop a deep learning approach for clustering time-series data, where each cluster comprises patients who share similar future outcomes of interest (e.g., adverse events, the onset of comorbidities). To encourage each cluster to have homogeneous future outcomes, the clustering is carried out by learning discrete representations that best describe the future outcome distribution based on novel loss functions. Experiments on two real-world datasets show that our model achieves superior clustering performance over state-of-the-art benchmarks and identifies meaningful clusters that can be translated into actionable information for clinical decision-making. | Changhee Lee, Mihaela Van Der Schaar | null | null | 2,020 | icml |
PENNI: Pruned Kernel Sharing for Efficient CNN Inference | null | Although state-of-the-art (SOTA) CNNs achieve outstanding performance on various tasks, their high computation demand and massive number of parameters make it difficult to deploy these SOTA CNNs onto resource-constrained devices. Previous works on CNN acceleration utilize low-rank approximation of the original convolution layers to reduce computation cost. However, these methods are very difficult to conduct upon sparse models, which limits execution speedup since redundancies within the CNN model are not fully exploited. We argue that kernel granularity decomposition can be conducted with low-rank assumption while exploiting the redundancy within the remaining compact coefficients. Based on this observation, we propose PENNI, a CNN model compression framework that is able to achieve model compactness and hardware efficiency simultaneously by (1) implementing kernel sharing in convolution layers via a small number of basis kernels and (2) alternately adjusting bases and coefficients with sparse constraints. Experiments show that we can prune 97% parameters and 92% FLOPs on ResNet18 CIFAR10 with no accuracy loss, and achieve a 44% reduction in run-time memory consumption and a 53% reduction in inference latency. | Shiyu Li, Edward Hanson, Hai Li, Yiran Chen | null | null | 2,020 | icml |
ACFlow: Flow Models for Arbitrary Conditional Likelihoods | null | Understanding the dependencies among features of a dataset is at the core of most unsupervised learning tasks. However, a majority of generative modeling approaches are focused solely on the joint distribution $p(x)$ and utilize models where it is intractable to obtain the conditional distribution of some arbitrary subset of features $x_u$ given the rest of the observed covariates $x_o$: $p(x_u \mid x_o)$. Traditional conditional approaches provide a model for a \emph{fixed} set of covariates conditioned on another \emph{fixed} set of observed covariates. Instead, in this work we develop a model that is capable of yielding \emph{all} conditional distributions $p(x_u \mid x_o)$ (for arbitrary $x_u$) via tractable conditional likelihoods. We propose a novel extension of (change of variables based) flow generative models, arbitrary conditioning flow models (ACFlow). ACFlow can be conditioned on arbitrary subsets of observed covariates, which was previously infeasible. We further extend ACFlow to model the joint distributions $p(x)$ and arbitrary marginal distributions $p(x_u)$. We also apply ACFlow to the imputation of features, and develop a unified platform for both multiple and single imputation by introducing an auxiliary objective that provides a principled single “best guess” for flow models. Extensive empirical evaluations show that our model achieves state-of-the-art performance in modeling arbitrary conditional likelihoods in addition to both single and multiple imputation in synthetic and real-world datasets. | Yang Li, Shoaib Akbar, Junier Oliva | null | null | 2,020 | icml |
Neural Architecture Search in A Proxy Validation Loss Landscape | null | This paper searches for the optimal neural architecture by minimizing a proxy of validation loss. Existing neural architecture search (NAS) methods used to discover the optimal neural architecture that best fits the validation examples given the up-to-date network weights. However, back propagation with a number of validation examples could be time consuming, especially when it needs to be repeated many times in NAS. Though these intermediate validation results are invaluable, they would be wasted if we cannot use them to predict the future from the past. In this paper, we propose to approximate the validation loss landscape by learning a mapping from neural architectures to their corresponding validate losses. The optimal neural architecture thus can be easily identified as the minimum of this proxy validation loss landscape. A novel sampling strategy is further developed for an efficient approximation of the loss landscape. Theoretical analysis indicates that the validation loss estimator learnt with our sampling strategy can reach a lower error rate and a lower label complexity compared with a uniform sampling. Experimental results on benchmarks demonstrate that the architecture searched by the proposed algorithm can achieve a satisfactory accuracy with less time cost. | Yanxi Li, Minjing Dong, Yunhe Wang, Chang Xu | null | null | 2,020 | icml |
Acceleration for Compressed Gradient Descent in Distributed and Federated Optimization | null | Due to the high communication cost in distributed and federated learning problems, methods relying on compression of communicated messages are becoming increasingly popular. While in other contexts the best performing gradient-type methods invariably rely on some form of acceleration/momentum to reduce the number of iterations, there are no methods which combine the benefits of both gradient compression and acceleration. In this paper, we remedy this situation and propose the first \emph{accelerated compressed gradient descent (ACGD)} methods. In the single machine regime, we prove that ACGD enjoys the rate $O\Big((1+\omega)\sqrt{\frac{L}{\mu}}\log \frac{1}{\epsilon}\Big)$ for $\mu$-strongly convex problems and $O\Big((1+\omega)\sqrt{\frac{L}{\epsilon}}\Big)$ for convex problems, respectively, where $\omega$ is the compression parameter. Our results improve upon the existing non-accelerated rates $O\Big((1+\omega)\frac{L}{\mu}\log \frac{1}{\epsilon}\Big)$ and $O\Big((1+\omega)\frac{L}{\epsilon}\Big)$, respectively, and recover the optimal rates of accelerated gradient descent as a special case when no compression ($\omega=0$) is applied. We further propose a distributed variant of ACGD (called ADIANA) and prove the convergence rate $\widetilde{O}\Big(\omega+\sqrt{\frac{L}{\mu}}+\sqrt{\big(\frac{\omega}{n}+\sqrt{\frac{\omega}{n}}\big)\frac{\omega L}{\mu}}\Big)$, where $n$ is the number of devices/workers and $\widetilde{O}$ hides the logarithmic factor $\log \frac{1}{\epsilon}$. This improves upon the previous best result $\widetilde{O}\Big(\omega + \frac{L}{\mu}+\frac{\omega L}{n\mu} \Big)$ achieved by the DIANA method of Mishchenko et al. (2019). Finally, we conduct several experiments on real-world datasets which corroborate our theoretical results and confirm the practical superiority of our accelerated methods. | Zhize Li, Dmitry Kovalev, Xun Qian, Peter Richtarik | null | null | 2,020 | icml |
Fine-Grained Analysis of Stability and Generalization for Stochastic Gradient Descent | null | Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions on the boundedness of gradients, smoothness and convexity of loss functions. In this paper, we provide a fine-grained analysis of stability and generalization for SGD by substantially relaxing these assumptions. Firstly, we establish stability and generalization for SGD by removing the existing bounded gradient assumptions. The key idea is the introduction of a new stability measure called on-average model stability, for which we develop novel bounds controlled by the risks of SGD iterates. This yields generalization bounds depending on the behavior of the best model, and leads to the first-ever-known fast bounds in the low-noise setting using stability approach. Secondly, the smoothness assumption is relaxed by considering loss functions with Holder continuous (sub)gradients for which we show that optimal bounds are still achieved by balancing computation and stability. To our best knowledge, this gives the first-ever-known stability and generalization bounds for SGD with non-smooth loss functions (e.g., hinge loss). Finally, we study learning problems with (strongly) convex objectives but non-convex loss functions. | Yunwen Lei, Yiming Ying | null | null | 2,020 | icml |
Manifold Identification for Ultimately Communication-Efficient Distributed Optimization | null | This work proposes a progressive manifold identification approach for distributed optimization with sound theoretical justifications to greatly reduce both the rounds of communication and the bytes communicated per round for partly-smooth regularized problems such as the $\ell_1$- and group-LASSO-regularized ones. Our two-stage method first uses an inexact proximal quasi-Newton method to iteratively identify a sequence of low-dimensional manifolds in which the final solution would lie, and restricts the model update within the current manifold to gradually lower the order of the per-round communication cost from the problem dimension to the dimension of the manifold that contains a solution and makes the problem within it smooth. After identifying this manifold, we take superlinear-convergent truncated semismooth Newton steps computed by preconditioned conjugate gradient to largely reduce the communication rounds by improving the convergence rate from the existing linear or sublinear ones to a superlinear rate. Experiments show that our method can be orders of magnitudes lower in the communication cost and an order of magnitude faster in the running time than the state of the art. | Yu-Sheng Li, Wei-Lin Chiang, Ching-Pei Lee | null | null | 2,020 | icml |
Context-aware Dynamics Model for Generalization in Model-Based Reinforcement Learning | null | Model-based reinforcement learning (RL) enjoys several benefits, such as data-efficiency and planning, by learning a model of the environment’s dynamics. However, learning a global model that can generalize across different dynamics remains a challenge. To tackle this problem, we decompose the task of learning a global dynamics model into two stages: (a) learning a context latent vector that captures the local dynamics, then (b) predicting the next state conditioned on it. In order to encode dynamics-specific information into the context latent vector, we introduce a novel loss function that encourages the context latent vector to be useful for predicting both forward and backward dynamics. The proposed method achieves superior generalization ability across various simulated robotics and control tasks, compared to existing RL schemes. | Kimin Lee, Younggyo Seo, Seunghyun Lee, Honglak Lee, Jinwoo Shin | null | null | 2,020 | icml |
Implicit Euler Skip Connections: Enhancing Adversarial Robustness via Numerical Stability | null | Deep neural networks have achieved great success in various areas, but recent works have found that neural networks are vulnerable to adversarial attacks, which leads to a hot topic nowadays. Although many approaches have been proposed to enhance the robustness of neural networks, few of them explored robust architectures for neural networks. On this account, we try to address such an issue from the perspective of dynamic system in this work. By viewing ResNet as an explicit Euler discretization of an ordinary differential equation (ODE), for the first time, we find that the adversarial robustness of ResNet is connected to the numerical stability of the corresponding dynamic system, i.e., more stable numerical schemes may correspond to more robust deep networks. Furthermore, inspired by the implicit Euler method for solving numerical ODE problems, we propose Implicit Euler skip connections (IE-Skips) by modifying the original skip connection in ResNet or its variants. Then we theoretically prove its advantages under the adversarial attack and the experimental results show that our ResNet with IE-Skips can largely improve the robustness and the generalization ability under adversarial attacks when compared with the vanilla ResNet of the same parameter size. | Mingjie Li, Lingshen He, Zhouchen Lin | null | null | 2,020 | icml |
On the Relation between Quality-Diversity Evaluation and Distribution-Fitting Goal in Text Generation | null | The goal of text generation models is to fit the underlying real probability distribution of text. For performance evaluation, quality and diversity metrics are usually applied. However, it is still not clear to what extend can the quality-diversity evaluation reflect the distribution-fitting goal. In this paper, we try to reveal such relation in a theoretical approach. We prove that under certain conditions, a linear combination of quality and diversity constitutes a divergence metric between the generated distribution and the real distribution. We also show that the commonly used BLEU/Self-BLEU metric pair fails to match any divergence metric, thus propose CR/NRR as a substitute for quality/diversity metric pair. | Jianing Li, Yanyan Lan, Jiafeng Guo, Xueqi Cheng | null | null | 2,020 | icml |
Latent Space Factorisation and Manipulation via Matrix Subspace Projection | null | We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines. | Xiao Li, Chenghua Lin, Ruizhe Li, Chaozheng Wang, Frank Guerin | null | null | 2,020 | icml |
On a projective ensemble approach to two sample test for equality of distributions | null | In this work, we propose a robust test for the multivariate two-sample problem through projective ensemble, which is a generalization of the Cramer-von Mises statistic. The proposed test statistic has a simple closed-form expression without any tuning parameters involved, it is easy to implement can be computed in quadratic time. Moreover, our test is insensitive to the dimension and consistent against all fixed alternatives, it does not require the moment assumption and is robust to the presence of outliers. We study the asymptotic behaviors of the test statistic under the null and two kinds of alternative hypotheses. We also suggest a permutation procedure to approximate critical values and employ its consistency. We demonstrate the effectiveness of our test through extensive simulation studies and a real data application. | Zhimei Li, Yaowu Zhang | null | null | 2,020 | icml |
Evolutionary Topology Search for Tensor Network Decomposition | null | Tensor network (TN) decomposition is a promising framework to represent extremely high-dimensional problems with few parameters. However, it is challenging to search the (near-)optimal topological structures for TN decomposition, since the number of candidate solutions exponentially grows with increasing the order of a tensor. In this paper, we claim that the issue can be practically tackled by evolutionary algorithms in an affordable manner. We encode the complex topological structures into binary strings, and develop a simple genetic meta-algorithm to search the optimal topology on Hamming space. The experimental results by both synthetic and real-world data demonstrate that our method can effectively discover the ground-truth topology or even better structures with a small number of generations, and significantly boost the representational power of TN decomposition compared with well-known tensor-train (TT) or tensor-ring (TR) models. | Chao Li, Zhun Sun | null | null | 2,020 | icml |
Train Big, Then Compress: Rethinking Model Size for Efficient Training and Inference of Transformers | null | Since hardware resources are limited, the objective of training deep learning models is typically to maximize accuracy subject to the time and memory constraints of training and inference. We study the impact of model size in this setting, focusing on Transformer models for NLP tasks that are limited by compute: self-supervised pretraining and high-resource machine translation. We first show that even though smaller Transformer models execute faster per iteration, wider and deeper models converge in significantly fewer steps. Moreover, this acceleration in convergence typically outpaces the additional computational overhead of using larger models. Therefore, the most compute-efficient training strategy is to counterintuitively train extremely large models but stop after a small number of iterations. This leads to an apparent trade-off between the training efficiency of large Transformer models and the inference efficiency of small Transformer models. However, we show that large models are more robust to compression techniques such as quantization and pruning than small models. Consequently, one can get the best of both worlds: heavily compressed, large models achieve higher accuracy than lightly compressed, small models. | Zhuohan Li, Eric Wallace, Sheng Shen, Kevin Lin, Kurt Keutzer, Dan Klein, Joey Gonzalez | null | null | 2,020 | icml |
Learning from Irregularly-Sampled Time Series: A Missing Data Perspective | null | Irregularly-sampled time series occur in many domains including healthcare. They can be challenging to model because they do not naturally yield a fixed-dimensional representation as required by many standard machine learning models. In this paper, we consider irregular sampling from the perspective of missing data. We model observed irregularly-sampled time series data as a sequence of index-value pairs sampled from a continuous but unobserved function. We introduce an encoder-decoder framework for learning from such generic indexed sequences. We propose learning methods for this framework based on variational autoencoders and generative adversarial networks. For continuous irregularly-sampled time series, we introduce continuous convolutional layers that can efficiently interface with existing neural network architectures. Experiments show that our models are able to achieve competitive or better classification results on irregularly-sampled multivariate time series compared to recent RNN models while offering significantly faster training times. | Steven Cheng-Xian Li, Benjamin Marlin | null | null | 2,020 | icml |
Input-Sparsity Low Rank Approximation in Schatten Norm | null | We give the first input-sparsity time algorithms for the rank-$k$ low rank approximation problem in every Schatten norm. Specifically, for a given $n\times n$ matrix $A$, our algorithm computes $Y,Z\in \R^{n\times k}$, which, with high probability, satisfy $\|A-YZ^T\|_p \leq (1+\eps)\|A-A_k\|_p$, where $\|M\|_p = \left (\sum_{i=1}^n \sigma_i(M)^p \right )^{1/p}$ is the Schatten $p$-norm of a matrix $M$ with singular values $\sigma_1(M), \ldots, \sigma_n(M)$, and where $A_k$ is the best rank-$k$ approximation to $A$. Our algorithm runs in time $\tilde{O}(\nnz(A) + n^{\alpha_p}\poly(k/\eps))$, where $\alpha_p = 1$ for $p\in [1,2)$ and $\alpha_p = 1 + (\omega-1)(1-2/p)$ for $p>2$ and $\omega \approx 2.374$ is the exponent of matrix multiplication. For the important case of $p = 1$, which corresponds to the more “robust” nuclear norm, we obtain $\tilde{O}(\nnz(A) + n \cdot \poly(k/\epsilon))$ time, which was previously only known for the Frobenius norm $(p = 2)$. Moreover, since $\alpha_p < \omega$ for every $p$, our algorithm has a better dependence on $n$ than that in the singular value decomposition for every $p$. Crucial to our analysis is the use of dimensionality reduction for Ky-Fan $p$-norms. | Yi Li, David Woodruff | null | null | 2,020 | icml |
Temporal Logic Point Processes | null | We propose a modeling framework for event data and aim to answer questions such as \emph{when} and \emph{why} the next event would happen. Our proposed model excels in small data regime with the ability to incorporate domain knowledge in terms of logic rules. We model the dynamics of the event starts and ends via intensity function with the structures informed by a set of first-order temporal logic rules. Using the softened representation of temporal relations, and a weighted combination of logic rules, our probabilistic model can deal with uncertainty in events. Furthermore, many well-known point processes (e.g., Hawkes process, self-correcting point process) can be interpreted as special cases of our model given simple temporal logic rules. Our model, therefore, riches the family of point processes. We derive a maximum likelihood estimation procedure for our model and show that it can lead to accurate predictions when data are sparse and domain knowledge is critical. | Shuang Li, Lu Wang, Ruizhi Zhang, Xiaofu Chang, Xuqin Liu, Yao Xie, Yuan Qi, Le Song | null | null | 2,020 | icml |
Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation | null | Unsupervised domain adaptation (UDA) aims to leverage the knowledge learned from a labeled source dataset to solve similar tasks in a new unlabeled domain. Prior UDA methods typically require to access the source data when learning to adapt the model, making them risky and inefficient for decentralized private data. This work tackles a practical setting where only a trained source model is available and investigates how we can effectively utilize such a model without source data to solve UDA problems. We propose a simple yet generic representation learning framework, named \emph{Source HypOthesis Transfer} (SHOT). SHOT freezes the classifier module (hypothesis) of the source model and learns the target-specific feature extraction module by exploiting both information maximization and self-supervised pseudo-labeling to implicitly align representations from the target domains to the source hypothesis. To verify its versatility, we evaluate SHOT in a variety of adaptation cases including closed-set, partial-set, and open-set domain adaptation. Experiments indicate that SHOT yields state-of-the-art results among multiple domain adaptation benchmarks. | Jian Liang, Dapeng Hu, Jiashi Feng | null | null | 2,020 | icml |
RIFLE: Backpropagation in Depth for Deep Transfer Learning through Re-Initializing the Fully-connected LayEr | null | Fine-tuning the deep convolution neural network (CNN) using a pre-trained model helps transfer knowledge learned from larger datasets to the target task. While the accuracy could be largely improved even when the training dataset is small, the transfer learning outcome is similar with the pre-trained one with closed CNN weights[17], as the backpropagation here brings less updates to deeper CNN layers. In this work, we propose RIFLE - a simple yet effective strategy that deepens backpropagation in transfer learning settings, through periodically ReInitializing the Fully-connected LayEr with random scratch during the fine-tuning procedure. RIFLE brings significant perturbation to the backpropagation process and leads to deep CNN weights update, while the affects of perturbation can be easily converged throughout the overall learning procedure. The experiments show that the use of RIFLE significantly improves deep transfer learning accuracy on a wide range of datasets, outperforming known tricks for the similar purpose, such as dropout, dropconnect, stochastic depth, and cyclic learning rate, under the same settings with 0.5%-2% higher testing accuracy. Empirical cases and ablation studies further indicate RIFLE brings meaningful updates to deep CNN layers with accuracy improved. | Xingjian Li, Haoyi Xiong, Haozhe An, Cheng-Zhong Xu, Dejing Dou | null | null | 2,020 | icml |
Adaptive Droplet Routing in Digital Microfluidic Biochips Using Deep Reinforcement Learning | null | We present and investigate a novel application domain for deep reinforcement learning (RL): droplet routing on digital microfluidic biochips (DMFBs). A DMFB, composed of a two-dimensional electrode array, manipulates discrete fluid droplets to automatically execute biochemical protocols such as point-of-care clinical diagnosis. However, a major concern associated with the use of DMFBs is that electrodes in a biochip can degrade over time. Droplet-transportation operations associated with the degraded electrodes can fail, thereby compromising the integrity of the bioassay outcome. We show that casting droplet transportation as an RL problem enables the training of deep network policies to capture the underlying health conditions of electrodes and to provide reliable fluidic operations. We propose a new RL-based droplet-routing flow that can be used for various sizes of DMFBs, and demonstrate reliable execution of an epigenetic bioassay with the RL droplet router on a fabricated DMFB. To facilitate further research, we also present a simulation environment based on the OpenAI Gym Interface for RL-guided droplet-routing problems on DMFBs. | Tung-Che Liang, Zhanwei Zhong, Yaas Bigdeli, Tsung-Yi Ho, Krishnendu Chakrabarty, Richard Fair | null | null | 2,020 | icml |
On the Theoretical Properties of the Network Jackknife | null | We study the properties of a leave-node-out jackknife procedure for network data. Under the sparse graphon model, we prove an Efron-Stein-type inequality, showing that the network jackknife leads to conservative estimates of the variance (in expectation) for any network functional that is invariant to node permutation. For a general class of count functionals, we also establish consistency of the network jackknife. We complement our theoretical analysis with a range of simulated and real-data examples and show that the network jackknife offers competitive performance in cases where other resampling methods are known to be valid. In fact, for several network statistics, we see that the jackknife provides more accurate inferences compared to related methods such as subsampling. | Qiaohui Lin, Robert Lunde, Purnamrita Sarkar | null | null | 2,020 | icml |
Sparse Shrunk Additive Models | null | Most existing feature selection methods in literature are linear models, so that the nonlinear relations between features and response variables are not considered. Meanwhile, in these feature selection models, the interactions between features are often ignored or just discussed under prior structure information. To address these challenging issues, we consider the problem of sparse additive models for high-dimensional nonparametric regression with the allowance of the flexible interactions between features. A new method, called as sparse shrunk additive models (SSAM), is proposed to explore the structure information among features. This method bridges sparse kernel regression and sparse feature selection. Theoretical results on the convergence rate and sparsity characteristics of SSAM are established by the novel analysis techniques with integral operator and concentration estimate. In particular, our algorithm and theoretical analysis only require the component functions to be continuous and bounded, which are not necessary to be in reproducing kernel Hilbert spaces. Experiments on both synthetic and real-world data demonstrate the effectiveness of the proposed approach. | Guodong Liu, Hong Chen, Heng Huang | null | null | 2,020 | icml |
Peer Loss Functions: Learning from Noisy Labels without Knowing Noise Rates | null | Learning with noisy labels is a common challenge in supervised learning. Existing approaches often require practitioners to specify noise rates, i.e., a set of parameters controlling the severity of label noises in the problem, and the specifications are either assumed to be given or estimated using additional steps. In this work, we introduce a new family of loss functions that we name as peer loss functions, which enables learning from noisy labels and does not require a priori specification of the noise rates. Peer loss functions work within the standard empirical risk minimization (ERM) framework. We show that, under mild conditions, performing ERM with peer loss functions on the noisy data leads to the optimal or a near-optimal classifier as if performing ERM over the clean training data, which we do not have access to. We pair our results with an extensive set of experiments. Peer loss provides a way to simplify model development when facing potentially noisy training labels, and can be promoted as a robust candidate loss function in such situations. | Yang Liu, Hongyi Guo | null | null | 2,020 | icml |
Finite-Time Last-Iterate Convergence for Multi-Agent Learning in Games | null | In this paper, we consider multi-agent learning via online gradient descent in a class of games called $\lambda$-cocoercive games, a fairly broad class of games that admits many Nash equilibria and that properly includes unconstrained strongly monotone games. We characterize the finite-time last-iterate convergence rate for joint OGD learning on $\lambda$-cocoercive games; further, building on this result, we develop a fully adaptive OGD learning algorithm that does not require any knowledge of problem parameter (e.g. cocoercive constant $\lambda$) and show, via a novel double-stopping time technique, that this adaptive algorithm achieves same finite-time last-iterate convergence rate as non-adaptive counterpart. Subsequently, we extend OGD learning to the noisy gradient feedback case and establish last-iterate convergence results–first qualitative almost sure convergence, then quantitative finite-time convergence rates– all under non-decreasing step-sizes. To our knowledge, we provide the first set of results that fill in several gaps of the existing multi-agent online learning literature, where three aspects–finite-time convergence rates, non-decreasing step-sizes, and fully adaptive algorithms have been unexplored before. | Tianyi Lin, Zhengyuan Zhou, Panayotis Mertikopoulos, Michael Jordan | null | null | 2,020 | icml |
Understanding the Curse of Horizon in Off-Policy Evaluation via Conditional Importance Sampling | null | Off-policy policy estimators that use importance sampling (IS) can suffer from high variance in long-horizon domains, and there has been particular excitement over new IS methods that leverage the structure of Markov decision processes. We analyze the variance of the most popular approaches through the viewpoint of conditional Monte Carlo. Surprisingly, we find that in finite horizon MDPs there is no strict variance reduction of per-decision importance sampling or marginalized importance sampling, comparing with vanilla importance sampling. We then provide sufficient conditions under which the per-decision or marginalized estimators will provably reduce the variance over importance sampling with finite horizons. For the asymptotic (in terms of horizon $T$) case, we develop upper and lower bounds on the variance of those estimators which yields sufficient conditions under which there exists an exponential v.s. polynomial gap between the variance of importance sampling and that of the per-decision or stationary/marginalized estimators. These results help advance our understanding of if and when new types of IS estimators will improve the accuracy of off-policy estimation. | Yao Liu, Pierre-Luc Bacon, Emma Brunskill | null | null | 2,020 | icml |
InfoGAN-CR and ModelCentrality: Self-supervised Model Training and Selection for Disentangling GANs | null | Disentangled generative models map a latent code vector to a target space, while enforcing that a subset of the learned latent codes are interpretable and associated with distinct properties of the target distribution. Recent advances have been dominated by Variational AutoEncoder (VAE)-based methods, while training disentangled generative adversarial networks (GANs) remains challenging. In this work, we show that the dominant challenges facing disentangled GANs can be mitigated through the use of self-supervision. We make two main contributions: first, we design a novel approach for training disentangled GANs with self-supervision. We propose contrastive regularizer, which is inspired by a natural notion of disentanglement: latent traversal. This achieves higher disentanglement scores than state-of-the-art VAE- and GAN-based approaches. Second, we propose an unsupervised model selection scheme called ModelCentrality, which uses generated synthetic samples to compute the medoid (multi-dimensional generalization of median) of a collection of models. The current common practice of hyper-parameter tuning requires using ground-truths samples, each labelled with known perfect disentangled latent codes. As real datasets are not equipped with such labels, we propose an unsupervised model selection scheme and show that it finds a model close to the best one, for both VAEs and GANs. Combining contrastive regularization with ModelCentrality, we improve upon the state-of-the-art disentanglement scores significantly, without accessing the supervised data. | Zinan Lin, Kiran Thekumparampil, Giulia Fanti, Sewoong Oh | null | null | 2,020 | icml |
Sample Complexity Bounds for 1-bit Compressive Sensing and Binary Stable Embeddings with Generative Priors | null | The goal of standard 1-bit compressive sensing is to accurately recover an unknown sparse vector from binary-valued measurements, each indicating the sign of a linear function of the vector. Motivated by recent advances in compressive sensing with generative models, where a generative modeling assumption replaces the usual sparsity assumption, we study the problem of 1-bit compressive sensing with generative models. We first consider noiseless 1-bit measurements, and provide sample complexity bounds for approximate recovery under i.i.d. Gaussian measurements and a Lipschitz continuous generative prior, as well as a near-matching algorithm-independent lower bound. Moreover, we demonstrate that the Binary $\epsilon$-Stable Embedding property, which characterizes the robustness of the reconstruction to measurement errors and noise, also holds for 1-bit compressive sensing with Lipschitz continuous generative models with sufficiently many Gaussian measurements. In addition, we apply our results to neural network generative models, and provide a proof-of-concept numerical experiment demonstrating significant improvements over sparsity-based approaches. | Zhaoqiang Liu, Selwyn Gomes, Avtansh Tiwari, Jonathan Scarlett | null | null | 2,020 | icml |
Boosting Deep Neural Network Efficiency with Dual-Module Inference | null | Using deep neural networks (DNNs) in machine learning tasks is promising in delivering high-quality results but challenging to meet stringent latency requirements and energy constraints because of the memory-bound and the compute-bound execution pattern of DNNs. We propose a big-little dual-module inference to dynamically skip unnecessary memory accesses and computations to accelerate DNN inference. Leveraging the noise-resilient feature of nonlinear activation functions, we propose to use a lightweight little module that approximates the original DNN layer, termed as the big module, to compute activations of the insensitive region that are more noise-resilient. Hence, the expensive memory accesses and computations of the big module can be reduced as the results are only calculated in the sensitive region. For memory-bound models such as recurrent neural networks (RNNs), our method can reduce the overall memory accesses by 40% on average and achieve 1.54x to 1.75x speedup on a commodity CPU-based server platform with a negligible impact on model quality. In addition, our method can reduce the operations of the compute-bound models such as convolutional neural networks (CNNs) by 3.02x, with only a 0.5% accuracy drop. | Liu Liu, Lei Deng, Zhaodong Chen, Yuke Wang, Shuangchen Li, Jingwei Zhang, Yihua Yang, Zhenyu Gu, Yufei Ding, Yuan Xie | null | null | 2,020 | icml |
Learning to Encode Position for Transformer with Continuous Dynamical Model | null | We introduce a new way of learning to encode position information for non-recurrent models, such as Transformer models. Unlike RNN and LSTM, which contain inductive bias by loading the input tokens sequentially, non-recurrent models are less sensitive to position. The main reason is that position information among input units is not encoded inherently, i.e., they are permutation equivalent, this problem justifies why all of the existing models are accompanied by position encoding/embedding layer at the input. However, this solution has clear limitations: the sinusoidal position encoding is not flexible enough as it is manually designed and does not contain any learnable parameters, whereas the position embedding restricts the maximum length of input sequences. It is thus desirable to design a new position layer that contains learnable parameters to adjust to different datasets and different architectures. At the same time, we would also like it to extrapolate in accordance with the variable length of inputs. In our proposed solution, we borrow from the recent Neural ODE approach, which may be viewed as a versatile continuous version of a ResNet. This model is capable of modeling many kinds of dynamical systems. We model the evolution of encoded results along position index by such a dynamical system, thereby overcoming the above limitations of existing methods. We evaluate our new position layers on a variety of neural machine translation and language understanding tasks, the experimental results show consistent improvements over the baselines. | Xuanqing Liu, Hsiang-Fu Yu, Inderjit Dhillon, Cho-Jui Hsieh | null | null | 2,020 | icml |
Exploration Through Reward Biasing: Reward-Biased Maximum Likelihood Estimation for Stochastic Multi-Armed Bandits | null | Inspired by the Reward-Biased Maximum Likelihood Estimate method of adaptive control, we propose RBMLE – a novel family of learning algorithms for stochastic multi-armed bandits (SMABs). For a broad range of SMABs including both the parametric Exponential Family as well as the non-parametric sub-Gaussian/Exponential family, we show that RBMLE yields an index policy. To choose the bias-growth rate $\alpha(t)$ in RBMLE, we reveal the nontrivial interplay between $\alpha(t)$ and the regret bound that generally applies in both the Exponential Family as well as the sub-Gaussian/Exponential family bandits. To quantify the finite-time performance, we prove that RBMLE attains order-optimality by adaptively estimating the unknown constants in the expression of $\alpha(t)$ for Gaussian and sub-Gaussian bandits. Extensive experiments demonstrate that the proposed RBMLE achieves empirical regret performance competitive with the state-of-the-art methods, while being more computationally efficient and scalable in comparison to the best-performing ones among them. | Xi Liu, Ping-Chun Hsieh, Yu Heng Hung, Anirban Bhattacharya, P. Kumar | null | null | 2,020 | icml |
A Chance-Constrained Generative Framework for Sequence Optimization | null | Deep generative modeling has achieved many successes for continuous data generation, such as producing realistic images and controlling their properties (e.g., styles). However, the development of generative modeling techniques for optimizing discrete data, such as sequences or strings, still lags behind largely due to the challenges in modeling complex and long-range constraints, including both syntax and semantics, in discrete structures. In this paper, we formulate the sequence optimization task as a chance-constrained optimization problem. The key idea is to enforce a high probability of generating valid sequences and also optimize the property of interest. We propose a novel minimax algorithm to simultaneously tighten a bound of the valid chance and optimize the expected property. Extensive experimental results in three domains demonstrate the superiority of our approach over the existing sequence optimization methods. | Xianggen Liu, Qiang Liu, Sen Song, Jian Peng | null | null | 2,020 | icml |
Min-Max Optimization without Gradients: Convergence and Applications to Black-Box Evasion and Poisoning Attacks | null | In this paper, we study the problem of constrained min-max optimization in a black-box setting, where the desired optimizer cannot access the gradients of the objective function but may query its values. We present a principled optimization framework, integrating a zeroth-order (ZO) gradient estimator with an alternating projected stochastic gradient descent-ascent method, where the former only requires a small number of function queries and the later needs just one-step descent/ascent update. We show that the proposed framework, referred to as ZO-Min-Max, has a sublinear convergence rate under mild conditions and scales gracefully with problem size. We also explore a promising connection between black-box min-max optimization and black-box evasion and poisoning attacks in adversarial machine learning (ML). Our empirical evaluations on these use cases demonstrate the effectiveness of our approach and its scalability to dimensions that prohibit using recent black-box solvers. | Sijia Liu, Songtao Lu, Xiangyi Chen, Yao Feng, Kaidi Xu, Abdullah Al-Dujaili, Mingyi Hong, Una-May O’Reilly | null | null | 2,020 | icml |
A Generic First-Order Algorithmic Framework for Bi-Level Programming Beyond Lower-Level Singleton | null | In recent years, a variety of gradient-based bi-level optimization methods have been developed for learning tasks. However, theoretical guarantees of these existing approaches often heavily rely on the simplification that for each fixed upper-level variable, the lower-level solution must be a singleton (a.k.a., Lower-Level Singleton, LLS). In this work, by formulating bi-level models from the optimistic viewpoint and aggregating hierarchical objective information, we establish Bi-level Descent Aggregation (BDA), a flexible and modularized algorithmic framework for bi-level programming. Theoretically, we derive a new methodology to prove the convergence of BDA without the LLS condition. Furthermore, we improve the convergence properties of conventional first-order bi-level schemes (under the LLS simplification) based on our proof recipe. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed BDA for different tasks, including hyper-parameter optimization and meta learning. | Risheng Liu, Pan Mu, Xiaoming Yuan, Shangzhi Zeng, Jin Zhang | null | null | 2,020 | icml |
Too Relaxed to Be Fair | null | We address the problem of classification under fairness constraints. Given a notion of fairness, the goal is to learn a classifier that is not discriminatory against a group of individuals. In the literature, this problem is often formulated as a constrained optimization problem and solved using relaxations of the fairness constraints. We show that many existing relaxations are unsatisfactory: even if a model satisfies the relaxed constraint, it can be surprisingly unfair. We propose a principled framework to solve this problem. This new approach uses a strongly convex formulation and comes with theoretical guarantees on the fairness of its solution. In practice, we show that this method gives promising results on real data. | Michael Lohaus, Michael Perrot, Ulrike Von Luxburg | null | null | 2,020 | icml |
Differentiating through the Fréchet Mean | null | Recent advances in deep representation learning on Riemannian manifolds extend classical deep learning operations to better capture the geometry of the manifold. One possible extension is the Fr{é}chet mean, the generalization of the Euclidean mean; however, it has been difficult to apply because it lacks a closed form with an easily computable derivative. In this paper, we show how to differentiate through the Fr{é}chet mean for arbitrary Riemannian manifolds. Then, focusing on hyperbolic space, we derive explicit gradient expressions and a fast, accurate, and hyperparameter-free Fr{é}chet mean solver. This fully integrates the Fr{é}chet mean into the hyperbolic neural network pipeline. To demonstrate this integration, we present two case studies. First, we apply our Fr{é}chet mean to the existing Hyperbolic Graph Convolutional Network, replacing its projected aggregation to obtain state-of-the-art results on datasets with high hyperbolicity. Second, to demonstrate the Fr{é}chet mean’s capacity to generalize Euclidean neural network operations, we develop a hyperbolic batch normalization method that gives an improvement parallel to the one observed in the Euclidean setting. | Aaron Lou, Isay Katsman, Qingxuan Jiang, Serge Belongie, Ser-Nam Lim, Christopher De Sa | null | null | 2,020 | icml |
Improved Communication Cost in Distributed PageRank Computation – A Theoretical Study | null | PageRank is a widely used approach for measuring the importance of a node in a graph. Due to the rapid growth of the graph size in the real world, the importance of computing PageRanks in a distributed environment has been increasingly recognized. However, only a few previous works can provide a provable complexity and accuracy for distributed PageRank computation. Given a constant $d\ge 1$ and a graph of $n$ nodes, the state-of-the-art approach, Radar-Push, uses $O(\log\log{n}+\log{d})$ communication rounds to approximate the PageRanks within a relative error $\Theta(\frac{1}{\log^d{n}})$ under a generalized congested clique distributed computation model. However, Radar-Push entails as large as $O(\log^{2d+3}{n})$ bits of bandwidth (e.g., the communication cost between a pair of nodes per round). In this paper, we provide a new algorithm that uses asymptotically the same communication round complexity while using only $O(d\log^3{n})$ bits of bandwidth. | Siqiang Luo | null | null | 2,020 | icml |
Multi-Task Learning with User Preferences: Gradient Descent with Controlled Ascent in Pareto Optimization | null | Multi-Task Learning (MTL) is a well established paradigm for jointly learning models for multiple correlated tasks. Often the tasks conflict, requiring trade-offs between them during optimization. In such cases, multi-objective optimization based MTL methods can be used to find one or more Pareto optimal solutions. A common requirement in MTL applications, that cannot be addressed by these methods, is to find a solution satisfying userspecified preferences with respect to task-specific losses. We advance the state-of-the-art by developing the first gradient-based multi-objective MTL algorithm to solve this problem. Our unique approach combines multiple gradient descent with carefully controlled ascent to traverse the Pareto front in a principled manner, which also makes it robust to initialization. The scalability of our algorithm enables its use in large-scale deep networks for MTL. Assuming only differentiability of the task-specific loss functions, we provide theoretical guarantees for convergence. Our experiments show that our algorithm outperforms the best competing methods on benchmark datasets. | Debabrata Mahapatra, Vaibhav Rajan | null | null | 2,020 | icml |
How recurrent networks implement contextual processing in sentiment analysis | null | Neural networks have a remarkable capacity for contextual processing{—}using recent or nearby inputs to modify processing of current input. For example, in natural language, contextual processing is necessary to correctly interpret negation (e.g. phrases such as "not bad"). However, our ability to understand how networks process context is limited. Here, we propose general methods for reverse engineering recurrent neural networks (RNNs) to identify and elucidate contextual processing. We apply these methods to understand RNNs trained on sentiment classification. This analysis reveals inputs that induce contextual effects, quantifies the strength and timescale of these effects, and identifies sets of these inputs with similar properties. Additionally, we analyze contextual effects related to differential processing of the beginning and end of documents. Using the insights learned from the RNNs we improve baseline Bag-of-Words models with simple extensions that incorporate contextual modification, recovering greater than 90% of the RNN’s performance increase over the baseline. This work yields a new understanding of how RNNs process contextual information, and provides tools that should provide similar insight more broadly. | Niru Maheswaranathan, David Sussillo | null | null | 2,020 | icml |
Individual Fairness for k-Clustering | null | We give a local search based algorithm for $k$-median and $k$-means (and more generally for any $k$-clustering with $\ell_p$ norm cost function) from the perspective of individual fairness. More precisely, for a point $x$ in a point set $P$ of size $n$, let $r(x)$ be the minimum radius such that the ball of radius $r(x)$ centered at $x$ has at least $n/k$ points from $P$. Intuitively, if a set of $k$ random points are chosen from $P$ as centers, every point $x\in P$ expects to have a center within radius $r(x)$. In this work, we show how to get an approximately optimal such fair $k$-clustering: The $k$-median ($k$-means) cost of our solution is within a constant factor of the cost of an optimal fair $k$-clustering, and our solution approximately satisfies the fairness condition (also within a constant factor). | Sepideh Mahabadi, Ali Vakilian | null | null | 2,020 | icml |
Convex Representation Learning for Generalized Invariance in Semi-Inner-Product Space | null | Invariance (defined in a general sense) has been one of the most effective priors for representation learning. Direct factorization of parametric models is feasible only for a small range of invariances, while regularization approaches, despite improved generality, lead to nonconvex optimization. In this work, we develop a \emph{convex} representation learning algorithm for a variety of generalized invariances that can be modeled as semi-norms. Novel Euclidean embeddings are introduced for kernel representers in a semi-inner-product space, and approximation bounds are established. This allows invariant representations to be learned efficiently and effectively as confirmed in our experiments, along with accurate predictions. | Yingyi Ma, Vignesh Ganapathiraman, Yaoliang Yu, Xinhua Zhang | null | null | 2,020 | icml |
Bandits with Adversarial Scaling | null | We study "adversarial scaling", a multi-armed bandit model where rewards have a stochastic and an adversarial component. Our model captures display advertising where the "click-through-rate" can be decomposed to a (fixed across time) arm-quality component and a non-stochastic user-relevance component (fixed across arms). Despite the relative stochasticity of our model, we demonstrate two settings where most bandit algorithms suffer. On the positive side, we show that two algorithms, one from the action elimination and one from the mirror descent family are adaptive enough to be robust to adversarial scaling. Our results shed light on the robustness of adaptive parameter selection in stochastic bandits, which may be of independent interest. | Thodoris Lykouris, Vahab Mirrokni, Renato Paes Leme | null | null | 2,020 | icml |
Adversarial Nonnegative Matrix Factorization | null | Nonnegative Matrix Factorization (NMF) has become an increasingly important research topic in machine learning. Despite all the practical success, most of existing NMF models are still vulnerable to adversarial attacks. To overcome this limitation, we propose a novel Adversarial NMF (ANMF) approach in which an adversary can exercise some control over the perturbed data generation process. Different from the traditional NMF models which focus on either the regular input or certain types of noise, our model considers potential test adversaries that are beyond the pre-defined constraints, which can cope with various noises (or perturbations). We formulate the proposed model as a bilevel optimization problem and use Alternating Direction Method of Multipliers (ADMM) to solve it with convergence analysis. Theoretically, the robustness analysis of ANMF is established under mild conditions dedicating asymptotically unbiased prediction. Extensive experiments verify that ANMF is robust to a broad categories of perturbations, and achieves state-of-the-art performances on distinct real-world benchmark datasets. | Lei Luo, Yanfu Zhang, Heng Huang | null | null | 2,020 | icml |
Countering Language Drift with Seeded Iterated Learning | null | Pretraining on human corpus and then finetuning in a simulator has become a standard pipeline for training a goal-oriented dialogue agent. Nevertheless, as soon as the agents are finetuned to maximize task completion, they suffer from the so-called language drift phenomenon: they slowly lose syntactic and semantic properties of language as they only focus on solving the task. In this paper, we propose a generic approach to counter language drift called Seeded iterated learning (SIL). We periodically refine a pretrained student agent by imitating data sampled from a newly generated teacher agent. At each time step, the teacher is created by copying the student agent, before being finetuned to maximize task completion. SIL does not require external syntactic constraint nor semantic knowledge, making it a valuable task-agnostic finetuning protocol. We evaluate SIL in a toy-setting Lewis Game, and then scale it up to the translation game with natural language. In both settings, SIL helps counter language drift as well as it improves the task completion compared to baselines. | Yuchen Lu, Soumye Singhal, Florian Strub, Aaron Courville, Olivier Pietquin | null | null | 2,020 | icml |
Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraints | null | Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed with theoretical convergence guarantees for non-convex unconstrained problems, it remains a challenge to design provably efficient algorithms for problems with non-convex functional constraints. This paper proposes a class of subgradient methods for constrained optimization where the objective function and the constraint functions are weakly convex and nonsmooth. Our methods solve a sequence of strongly convex subproblems, where a quadratic regularization term is added to both the objective function and each constraint function. Each subproblem can be solved by various algorithms for strongly convex optimization. Under a uniform Slater’s condition, we establish the computation complexities of our methods for finding a nearly stationary point. | Runchao Ma, Qihang Lin, Tianbao Yang | null | null | 2,020 | icml |
Understanding the Impact of Model Incoherence on Convergence of Incremental SGD with Random Reshuffle | null | Although SGD with random reshuffle has been widely-used in machine learning applications, there is a limited understanding of how model characteristics affect the convergence of the algorithm. In this work, we introduce model incoherence to characterize the diversity of model characteristics and study its impact on convergence of SGD with random reshuffle under weak strong convexity. Specifically, minimizer incoherence measures the discrepancy between the global minimizers of a sample loss and those of the total loss and affects the convergence error of SGD with random reshuffle. In particular, we show that the variable sequence generated by SGD with random reshuffle converges to a certain global minimizer of the total loss under full minimizer coherence. The other curvature incoherence measures the quality of condition numbers of the sample losses and determines the convergence rate of SGD. With model incoherence, our results show that SGD has a faster convergence rate and smaller convergence error under random reshuffle than those under random sampling, and hence provide justifications to the superior practical performance of SGD with random reshuffle. | Shaocong Ma, Yi Zhou | null | null | 2,020 | icml |
A Mean Field Analysis Of Deep ResNet And Beyond: Towards Provably Optimization Via Overparameterization From Depth | null | Training deep neural networks with stochastic gradient descent (SGD) can often achieve zero training loss on real-world tasks although the optimization landscape is known to be highly non-convex. To understand the success of SGD for training deep neural networks, this work presents a mean-field analysis of deep residual networks, based on a line of works which interpret the continuum limit of the deep residual network as an ordinary differential equation as the the network capacity tends to infinity. Specifically, we propose a \textbf{new continuum limit} of deep residual networks, which enjoys a good landscape in the sense that \textbf{every local minimizer is global}. This characterization enables us to derive the first global convergence result for multilayer neural networks in the mean-field regime. Furthermore, our proof does not rely on the convexity of the loss landscape, but instead, an assumption on the global minimizer should achieve zero loss which can be achieved when the model shares a universal approximation property. Key to our result is the observation that a deep residual network resembles a shallow network ensemble \cite{veit2016residual}, \emph{i.e.} a two-layer network. We bound the difference between the shallow network and our ResNet model via the adjoint sensitivity method, which enables us to transfer previous mean-field analysis of two-layer networks to deep networks. Furthermore, we propose several novel training schemes based on our new continuous model, among which one new training procedure introduces the operation of switching the order of the residual blocks and results in strong empirical performance on benchmark datasets. | Yiping Lu, Chao Ma, Yulong Lu, Jianfeng Lu, Lexing Ying | null | null | 2,020 | icml |
Convergence of a Stochastic Gradient Method with Momentum for Non-Smooth Non-Convex Optimization | null | Stochastic gradient methods with momentum are widely used in applications and at the core of optimization subroutines in many popular machine learning libraries. However, their sample complexities have not been obtained for problems beyond those that are convex or smooth. This paper establishes the convergence rate of a stochastic subgradient method with a momentum term of Polyak type for a broad class of non-smooth, non-convex, and constrained optimization problems. Our key innovation is the construction of a special Lyapunov function for which the proven complexity can be achieved without any tuning of the momentum parameter. For smooth problems, we extend the known complexity bound to the constrained case and demonstrate how the unconstrained case can be analyzed under weaker assumptions than the state-of-the-art. Numerical results confirm our theoretical developments. | Vien Mai, Mikael Johansson | null | null | 2,020 | icml |
Evolutionary Reinforcement Learning for Sample-Efficient Multiagent Coordination | null | Many cooperative multiagent reinforcement learning environments provide agents with a sparse team-based reward, as well as a dense agent-specific reward that incentivizes learning basic skills. Training policies solely on the team-based reward is often difficult due to its sparsity. Also, relying solely on the agent-specific reward is sub-optimal because it usually does not capture the team coordination objective. A common approach is to use reward shaping to construct a proxy reward by combining the individual rewards. However, this requires manual tuning for each environment. We introduce Multiagent Evolutionary Reinforcement Learning (MERL), a split-level training platform that handles the two objectives separately through two optimization processes. An evolutionary algorithm maximizes the sparse team-based objective through neuroevolution on a population of teams. Concurrently, a gradient-based optimizer trains policies to only maximize the dense agent-specific rewards. The gradient-based policies are periodically added to the evolutionary population as a way of information transfer between the two optimization processes. This enables the evolutionary algorithm to use skills learned via the agent-specific rewards toward optimizing the global objective. Results demonstrate that MERL significantly outperforms state-of-the-art methods, such as MADDPG, on a number of difficult coordination benchmarks. | Somdeb Majumdar, Shauharda Khadka, Santiago Miret, Stephen Mcaleer, Kagan Tumer | null | null | 2,020 | icml |
Adaptive Adversarial Multi-task Representation Learning | null | Adversarial Multi-task Representation Learning (AMTRL) methods are able to boost the performance of Multi-task Representation Learning (MTRL) models. However, the theoretical mechanism behind AMTRL is less investigated. To fill this gap, we study the generalization error bound of AMTRL through the lens of Lagrangian duality . Based on the duality, we proposed an novel adaptive AMTRL algorithm which improves the performance of original AMTRL methods. The extensive experiments back up our theoretical analysis and validate the superiority of our proposed algorithm. | Yuren Mao, Weiwei Liu, Xuemin Lin | null | null | 2,020 | icml |
Emergence of Separable Manifolds in Deep Language Representations | null | Deep neural networks (DNNs) have shown much empirical success in solving perceptual tasks across various cognitive modalities. While they are only loosely inspired by the biological brain, recent studies report considerable similarities between representations extracted from task-optimized DNNs and neural populations in the brain. DNNs have subsequently become a popular model class to infer computational principles underlying complex cognitive functions, and in turn, they have also emerged as a natural testbed for applying methods originally developed to probe information in neural populations. In this work, we utilize mean-field theoretic manifold analysis, a recent technique from computational neuroscience that connects geometry of feature representations with linear separability of classes, to analyze language representations from large-scale contextual embedding models. We explore representations from different model families (BERT, RoBERTa, GPT, etc.) and find evidence for emergence of linguistic manifolds across layer depth (e.g., manifolds for part-of-speech tags), especially in ambiguous data (i.e, words with multiple part-of-speech tags, or part-of-speech classes including many words). In addition, we find that the emergence of linear separability in these manifolds is driven by a combined reduction of manifolds’ radius, dimensionality and inter-manifold correlations. | Jonathan Mamou, Hang Le, Miguel Del Rio, Cory Stephenson, Hanlin Tang, Yoon Kim, Sueyeon Chung | null | null | 2,020 | icml |
Adding seemingly uninformative labels helps in low data regimes | null | Evidence suggests that networks trained on large datasets generalize well not solely because of the numerous training examples, but also class diversity which encourages learning of enriched features. This raises the question of whether this remains true when data is scarce - is there an advantage to learning with additional labels in low-data regimes? In this work, we consider a task that requires difficult-to-obtain expert annotations: tumor segmentation in mammography images. We show that, in low-data settings, performance can be improved by complementing the expert annotations with seemingly uninformative labels from non-expert annotators, turning the task into a multi-class problem. We reveal that these gains increase when less expert data is available, and uncover several interesting properties through further studies. We demonstrate our findings on CSAW-S, a new dataset that we introduce here, and confirm them on two public datasets. | Christos Matsoukas, Albert Bou Hernandez, Yue Liu, Karin Dembrower, Gisele Miranda, Emir Konuk, Johan Fredin Haslum, Athanasios Zouzos, Peter Lindholm, Fredrik Strand, Kevin Smith | null | null | 2,020 | icml |
Fast and Consistent Learning of Hidden Markov Models by Incorporating Non-Consecutive Correlations | null | Can the parameters of a hidden Markov model (HMM) be estimated from a single sweep through the observations – and additionally, without being trapped at a local optimum in the likelihood surface? That is the premise of recent method of moments algorithms devised for HMMs. In these, correlations between consecutive pair- or triplet-wise observations are empirically estimated and used to compute estimates of the HMM parameters. Albeit computationally very attractive, the main drawback is that by restricting to only low-order correlations in the data, information is being neglected which results in a loss of accuracy (compared to standard maximum likelihood schemes). In this paper, we propose extending these methods (both pair- and triplet-based) by also including non-consecutive correlations in a way which does not significantly increase the computational cost (which scales linearly with the number of additional lags included). We prove strong consistency of the new methods, and demonstrate an improved performance in numerical experiments on both synthetic and real-world financial time-series datasets. | Robert Mattila, Cristian Rojas, Eric Moulines, Vikram Krishnamurthy, Bo Wahlberg | null | null | 2,020 | icml |
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