2015

Quantifying changes in climate variability and extremes: Pitfalls and their overcoming

Sippel, S., Zscheischler, J., Heimann, M., Otto, F. E. L., Peters, J., Mahecha, M. D.

Geophysical Research Letters, 42(22):9990-9998, November 2015 (article)

2015

Diversity of sharp wave-ripple LFP signatures reveals differentiated brain-wide dynamical events

Ramirez-Villegas, J. F., Logothetis, N. K., Besserve, M.

Proceedings of the National Academy of Sciences U.S.A, 112(46):E6379-E6387, November 2015 (article)

Noise masking of White’s illusion exposes the weakness of current spatial filtering models of lightness perception

Betz, T., Shapley, R. M., Wichmann, F. A., Maertens, M.

Journal of Vision, 15(14):1-17, October 2015 (article)

Shifts of Gamma Phase across Primary Visual Cortical Sites Reflect Dynamic Stimulus-Modulated Information Transfer

Besserve, M., Lowe, S. C., Logothetis, N. K., Schölkopf, B., Panzeri, S.

PLOS Biology, 13(9):e1002257, September 2015 (article)

Semi-Supervised Interpolation in an Anticausal Learning Scenario
Journal of Machine Learning Research, 16, pages: 1923-1948, September 2015 (article)

Testing the role of luminance edges in White’s illusion with contour adaptation

Betz, T., Shapley, R. M., Wichmann, F. A., Maertens, M.

Journal of Vision, 15(11):1-16, August 2015 (article)

Blind multirigid retrospective motion correction of MR images

Loktyushin, A., Nickisch, H., Pohmann, R., Schölkopf, B.

Magnetic Resonance in Medicine, 73(4):1457-1468, April 2015 (article)

A quantum advantage for inferring causal structure

Ried, K., Agnew, M., Vermeyden, L., Janzing, D., Spekkens, R. W., Resch, K. J.

Nature Physics, 11(5):414-420, March 2015 (article)

Abstract
The problem of inferring causal relations from observed correlations is relevant to a wide variety of scientific disciplines. Yet given the correlations between just two classical variables, it is impossible to determine whether they arose from a causal influence of one on the other or a common cause influencing both. Only a randomized trial can settle the issue. Here we consider the problem of causal inference for quantum variables. We show that the analogue of a randomized trial, causal tomography, yields a complete solution. We also show that, in contrast to the classical case, one can sometimes infer the causal structure from observations alone. We implement a quantum-optical experiment wherein we control the causal relation between two optical modes, and two measurement schemes—with and without randomization—that extract this relation from the observed correlations. Our results show that entanglement and quantum coherence provide an advantage for causal inference.

Positive definite matrices and the S-divergence
Proceedings of the American Mathematical Society, 2015, Published electronically: October 22, 2015 (article)

Structural Intervention Distance (SID) for Evaluating Causal Graphs

Peters, J., Bühlmann, P.

Neural Computation , 27(3):771-799, 2015 (article)

Likelihood and Consilience: On Forster’s Counterexamples to the Likelihood Theory of Evidence

Zhang, J., Zhang, K.

Philosophy of Science, Supplementary Volume 2015, 82(5):930-940, 2015 (article)

On the Intersection Property of Conditional Independence and its Application to Causal Discovery
Journal of Causal Inference, 3(1):97-108, 2015 (article)

Crowdsourced analysis of clinical trial data to predict amyotrophic lateral sclerosis progression

Küffner, R., Zach, N., Norel, R., Hawe, J., Schoenfeld, D., Wang, L., Li, G., Fang, L., Mackey, L., Hardiman, O., Cudkowicz, M., Sherman, A., Ertaylan, G., Grosse-Wentrup, M., Hothorn, T., van Ligtenberg, J., Macke, J., Meyer, T., Schölkopf, B., Tran, L., Vaughan, R., Stolovitzky, G., Leitner, M.

Nature Biotechnology, 33, pages: 51-57, 2015 (article)

Probabilistic Interpretation of Linear Solvers
SIAM Journal on Optimization, 25(1):234-260, 2015 (article)

Developing biorobotics for veterinary research into cat movements

Mariti, C., Muscolo, G., Peters, J., Puig, D., Recchiuto, C., Sighieri, C., Solanas, A., von Stryk, O.

Journal of Veterinary Behavior: Clinical Applications and Research, 10(3):248-254, 2015 (article)

Spatial statistics and attentional dynamics in scene viewing

Engbert, R., Trukenbrod, H., Barthelmé, S., Wichmann, F.

Journal of Vision, 15(1):1-17, 2015 (article)

The Randomized Causation Coefficient

Lopez-Paz, D., Muandet, K., Recht, B.

Journal of Machine Learning, 16, pages: 2901-2907, 2015 (article)

Towards denoising XMCD movies of fast magnetization dynamics using extended Kalman filter

Kopp, M., Harmeling, S., Schütz, G., Schölkopf, B., Fähnle, M.

Ultramicroscopy, 148, pages: 115-122, 2015 (article)

Abstract
The Kalman filter is a well-established approach to get information on the time-dependent state of a system from noisy observations. It was developed in the context of the Apollo project to see the deviation of the true trajectory of a rocket from the desired trajectory. Afterwards it was applied to many different systems with small numbers of components of the respective state vector (typically about 10). In all cases the equation of motion for the state vector was known exactly. The fast dissipative magnetization dynamics is often investigated by x-ray magnetic circular dichroism movies (XMCD movies), which are often very noisy. In this situation the number of components of the state vector is extremely large (about 105), and the equation of motion for the dissipative magnetization dynamics (especially the values of the material parameters of this equation) is not well known. In the present paper it is shown by theoretical considerations that – nevertheless – there is no principle problem for the use of the Kalman filter to denoise XMCD movies of fast dissipative magnetization dynamics.

Causal interpretation rules for encoding and decoding models in neuroimaging

Weichwald, S., Meyer, T., Özdenizci, O., Schölkopf, B., Ball, T., Grosse-Wentrup, M.

NeuroImage, 110, pages: 48–59, 2015 (article)

Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations
Statistics and Computing , 25(4):755-766, 2015 (article)

Artificial intelligence: Learning to see and act
Nature, News & Views, 518(7540):486-487, 2015 (article)

Context affects lightness at the level of surfaces

Maertens, M., Wichmann, F., Shapley, R.

Journal of Vision, 15(1):1-15, 2015 (article)

Genome-wide analysis of local chromatin packing in Arabidopsis thaliana

Wang, C., Liu, C., Roqueiro, D., Grimm, D., Schwab, R., Becker, C., Lanz, C., Weigel, D.

Genome Research, 25(2):246-256, 2015 (article)

Segmentation-based attenuation correction in positron emission tomography/magnetic resonance: erroneous tissue identification and its impact on positron emission tomography interpretation

Brendle, C., Schmidt, H., Oergel, A., Bezrukov, I., Mueller, M., Schraml, C., Pfannenberg, C., la Fougère, C., Nikolaou, K., Schwenzer, N.

Active Reward Learning with a Novel Acquisition Function

Daniel, C., Kroemer, O., Viering, M., Metz, J., Peters, J.

Autonomous Robots, 39(3):389-405, 2015 (article)

A systematic search for transiting planets in the K2 data

Foreman-Mackey, D., Montet, B., Hogg, D., Morton, T., Wang, D., Schölkopf, B.

The Astrophysical Journal, 806(2), 2015 (article)

Abstract
Photometry of stars from the K2 extension of NASA’s Kepler mission is afflicted by systematic effects caused by small (few-pixel) drifts in the telescope pointing and other spacecraft issues. We present a method for searching K2 light curves for evidence of exoplanets by simultaneously fitting for these systematics and the transit signals of interest. This method is more computationally expensive than standard search algorithms but we demonstrate that it can be efficiently implemented and used to discover transit signals. We apply this method to the full Campaign 1 data set and report a list of 36 planet candidates transiting 31 stars, along with an analysis of the pipeline performance and detection efficiency based on artificial signal injections and recoveries. For all planet candidates, we present posterior distributions on the properties of each system based strictly on the transit observables.

Learning Movement Primitive Attractor Goals and Sequential Skills from Kinesthetic Demonstrations

Manschitz, S., Kober, J., Gienger, M., Peters, J.

Robotics and Autonomous Systems, 74, Part A, pages: 97-107, 2015 (article)

Bayesian Optimization for Learning Gaits under Uncertainty

Calandra, R., Seyfarth, A., Peters, J., Deisenroth, M.

Annals of Mathematics and Artificial Intelligence, pages: 1-19, 2015 (article)

Assessment of murine brain tissue shrinkage caused by different histological fixatives using magnetic resonance and computed tomography imaging

Wehrl, H. F., Bezrukov, I., Wiehr, S., Lehnhoff, M., Fuchs, K., Mannheim, J. G., Quintanilla-Martinez, L., Kneilling, M., Pichler, B. J., Sauter, A. W.

Histology and Histopathology, 30(5):601-613, 2015 (article)

Improved Bayesian Information Criterion for Mixture Model Selection

Mehrjou, A., Hosseini, R., Araabi, B.

Pattern Recognition Letters, 69, pages: 22-27, 2015 (article)

Correlation matrix nearness and completion under observation uncertainty

Alaíz, C. M., Dinuzzo, F., Sra, S.

IMA Journal of Numerical Analysis, 35(1):325-340, 2015 (article)

Quantitative evaluation of segmentation- and atlas- based attenuation correction for PET/MR on pediatric patients

Bezrukov, I., Schmidt, H., Gatidis, S., Mantlik, F., Schäfer, J. F., Schwenzer, N., Pichler, B. J.

Journal of Nuclear Medicine, 56(7):1067-1074, 2015 (article)

Probabilistic numerics and uncertainty in computations

Hennig, P., Osborne, M. A., Girolami, M.

Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 471(2179), 2015 (article)

Abstract
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

Mass and galaxy distributions of four massive galaxy clusters from Dark Energy Survey Science Verification data

Melchior, P., Suchyta, E., Huff, E., Hirsch, M., Kacprzak, T., Rykoff, E., Gruen, D., Armstrong, R., Bacon, D., Bechtol, K., others,

Monthly Notices of the Royal Astronomical Society, 449(3):2219-2238, Oxford University Press, 2015 (article)

Entropic Movement Complexity Reflects Subjective Creativity Rankings of Visualized Hand Motion Trajectories

Peng, Z, Braun, DA

Frontiers in Psychology, 6(1879):1-13, December 2015 (article)

Abstract
In a previous study we have shown that human motion trajectories can be characterized by translating continuous trajectories into symbol sequences with well-defined complexity measures. Here we test the hypothesis that the motion complexity individuals generate in their movements might be correlated to the degree of creativity assigned by a human observer to the visualized motion trajectories. We asked participants to generate 55 novel hand movement patterns in virtual reality, where each pattern had to be repeated 10 times in a row to ensure reproducibility. This allowed us to estimate a probability distribution over trajectories for each pattern. We assessed motion complexity not only by the previously proposed complexity measures on symbolic sequences, but we also propose two novel complexity measures that can be directly applied to the distributions over trajectories based on the frameworks of Gaussian Processes and Probabilistic Movement Primitives. In contrast to previous studies, these new methods allow computing complexities of individual motion patterns from very few sample trajectories. We compared the different complexity measures to how a group of independent jurors rank ordered the recorded motion trajectories according to their personal creativity judgment. We found three entropic complexity measures that correlate significantly with human creativity judgment and discuss differences between the measures. We also test whether these complexity measures correlate with individual creativity in divergent thinking tasks, but do not find any consistent correlation. Our results suggest that entropic complexity measures of hand motion may reveal domain-specific individual differences in kinesthetic creativity.

Bounded rationality, abstraction and hierarchical decision-making: an information-theoretic optimality principle

Genewein, T, Leibfried, F, Grau-Moya, J, Braun, DA

Frontiers in Robotics and AI, 2(27):1-24, October 2015 (article)

Abstract
Abstraction and hierarchical information-processing are hallmarks of human and animal intelligence underlying the unrivaled flexibility of behavior in biological systems. Achieving such a flexibility in artificial systems is challenging, even with more and more computational power. Here we investigate the hypothesis that abstraction and hierarchical information-processing might in fact be the consequence of limitations in information-processing power. In particular, we study an information-theoretic framework of bounded rational decision-making that trades off utility maximization against information-processing costs. We apply the basic principle of this framework to perception-action systems with multiple information-processing nodes and derive bounded optimal solutions. We show how the formation of abstractions and decision-making hierarchies depends on information-processing costs. We illustrate the theoretical ideas with example simulations and conclude by formalizing a mathematically unifying optimization principle that could potentially be extended to more complex systems.

Signaling equilibria in sensorimotor interactions

Leibfried, F, Grau-Moya, J, Braun, DA

Cognition, 141, pages: 73-86, August 2015 (article)

Abstract
Although complex forms of communication like human language are often assumed to have evolved out of more simple forms of sensorimotor signaling, less attention has been devoted to investigate the latter. Here, we study communicative sensorimotor behavior of humans in a two-person joint motor task where each player controls one dimension of a planar motion. We designed this joint task as a game where one player (the sender) possesses private information about a hidden target the other player (the receiver) wants to know about, and where the sender's actions are costly signals that influence the receiver's control strategy. We developed a game-theoretic model within the framework of signaling games to investigate whether subjects' behavior could be adequately described by the corresponding equilibrium solutions. The model predicts both separating and pooling equilibria, in which signaling does and does not occur respectively. We observed both kinds of equilibria in subjects and found that, in line with model predictions, the propensity of signaling decreased with increasing signaling costs and decreasing uncertainty on the part of the receiver. Our study demonstrates that signaling games, which have previously been applied to economic decision-making and animal communication, provide a framework for human signaling behavior arising during sensorimotor interactions in continuous and dynamic environments.

Structure Learning in Bayesian Sensorimotor Integration

Genewein, T, Hez, E, Razzaghpanah, Z, Braun, DA

PLoS Computational Biology, 11(8):1-27, August 2015 (article)

Abstract
Previous studies have shown that sensorimotor processing can often be described by Bayesian learning, in particular the integration of prior and feedback information depending on its degree of reliability. Here we test the hypothesis that the integration process itself can be tuned to the statistical structure of the environment. We exposed human participants to a reaching task in a three-dimensional virtual reality environment where we could displace the visual feedback of their hand position in a two dimensional plane. When introducing statistical structure between the two dimensions of the displacement, we found that over the course of several days participants adapted their feedback integration process in order to exploit this structure for performance improvement. In control experiments we found that this adaptation process critically depended on performance feedback and could not be induced by verbal instructions. Our results suggest that structural learning is an important meta-learning component of Bayesian sensorimotor integration.

A Reward-Maximizing Spiking Neuron as a Bounded Rational Decision Maker

Leibfried, F, Braun, DA

Neural Computation, 27(8):1686-1720, July 2015 (article)

Abstract
Rate distortion theory describes how to communicate relevant information most efficiently over a channel with limited capacity. One of the many applications of rate distortion theory is bounded rational decision making, where decision makers are modeled as information channels that transform sensory input into motor output under the constraint that their channel capacity is limited. Such a bounded rational decision maker can be thought to optimize an objective function that trades off the decision maker's utility or cumulative reward against the information processing cost measured by the mutual information between sensory input and motor output. In this study, we interpret a spiking neuron as a bounded rational decision maker that aims to maximize its expected reward under the computational constraint that the mutual information between the neuron's input and output is upper bounded. This abstract computational constraint translates into a penalization of the deviation between the neuron's instantaneous and average firing behavior. We derive a synaptic weight update rule for such a rate distortion optimizing neuron and show in simulations that the neuron efficiently extracts reward-relevant information from the input by trading off its synaptic strengths against the collected reward.

What is epistemic value in free energy models of learning and acting? A bounded rationality perspective

Ortega, PA, Braun, DA

Cognitive Neuroscience, 6(4):215-216, December 2015 (article)

Abstract
Free energy models of learning and acting do not only care about utility or extrinsic value, but also about intrinsic value, that is, the information value stemming from probability distributions that represent beliefs or strategies. While these intrinsic values can be interpreted as epistemic values or exploration bonuses under certain conditions, the framework of bounded rationality offers a complementary interpretation in terms of information-processing costs that we discuss here.

2010

Causal relationships between frequency bands of extracellular signals in visual cortex revealed by an information theoretic analysis

Besserve, M., Schölkopf, B., Logothetis, N., Panzeri, S.

Journal of Computational Neuroscience, 29(3):547-566, December 2010 (article)

2010

Tackling Box-Constrained Optimization via a New Projected Quasi-Newton Approach

Kim, D., Sra, S., Dhillon, I.

SIAM Journal on Scientific Computing, 32(6):3548-3563 , December 2010 (article)

Abstract
Numerous scientific applications across a variety of fields depend on box-constrained convex optimization. Box-constrained problems therefore continue to attract research interest. We address box-constrained (strictly convex) problems by deriving two new quasi-Newton algorithms. Our algorithms are positioned between the projected-gradient [J. B. Rosen, J. SIAM, 8 (1960), pp. 181–217] and projected-Newton [D. P. Bertsekas, SIAM J. Control Optim., 20 (1982), pp. 221–246] methods. We also prove their convergence under a simple Armijo step-size rule. We provide experimental results for two particular box-constrained problems: nonnegative least squares (NNLS), and nonnegative Kullback–Leibler (NNKL) minimization. For both NNLS and NNKL our algorithms perform competitively as compared to well-established methods on medium-sized problems; for larger problems our approach frequently outperforms the competition.

Algorithmen zum Automatischen Erlernen von Motorfähigkeiten
at - Automatisierungstechnik, 58(12):688-694, December 2010 (article)

Abstract
Robot learning methods which allow autonomous robots to adapt to novel situations have been a long standing vision of robotics, artificial intelligence, and cognitive sciences. However, to date, learning techniques have yet to fulfill this promise as only few methods manage to scale into the high-dimensional domains of manipulator robotics, or even the new upcoming trend of humanoid robotics. If possible, scaling was usually only achieved in precisely pre-structured domains. In this paper, we investigate the ingredients for a general approach policy learning with the goal of an application to motor skill refinement in order to get one step closer towards human-like performance. For doing so, we study two major components for such an approach, i. e., firstly, we study policy learning algorithms which can be applied in the general setting of motor skill learning, and, secondly, we study a theoretically well-founded general approach to representing the required control structures for task representation and execution.

PAC-Bayesian Analysis of Co-clustering and Beyond

Seldin, Y., Tishby, N.

Journal of Machine Learning Research, 11, pages: 3595-3646, December 2010 (article)

Gaussian Processes for Machine Learning (GPML) Toolbox

Rasmussen, C., Nickisch, H.

Journal of Machine Learning Research, 11, pages: 3011-3015, November 2010 (article)

Abstract
The GPML toolbox provides a wide range of functionality for Gaussian process (GP) inference and prediction. GPs are specified by mean and covariance functions; we offer a library of simple mean and covariance functions and mechanisms to compose more complex ones. Several likelihood functions are supported including Gaussian and heavy-tailed for regression as well as others suitable for classification. Finally, a range of inference methods is provided, including exact and variational inference, Expectation Propagation, and Laplace's method dealing with non-Gaussian likelihoods and FITC for dealing with large regression tasks.

Cryo-EM structure and rRNA model of a translating eukaryotic 80S ribosome at 5.5-Å resolution

Armache, J-P., Jarasch, A., Anger, AM., Villa, E., Becker, T., Bhushan, S., Jossinet, F., Habeck, M., Dindar, G., Franckenberg, S., Marquez, V., Mielke, T., Thomm, M., Berninghausen, O., Beatrix, B., Söding, J., Westhof, E., Wilson, DN., Beckmann, R.

Proceedings of the National Academy of Sciences of the United States of America, 107(46):19748-19753, November 2010 (article)

Abstract
Protein biosynthesis, the translation of the genetic code into polypeptides, occurs on ribonucleoprotein particles called ribosomes. Although X-ray structures of bacterial ribosomes are available, high-resolution structures of eukaryotic 80S ribosomes are lacking. Using cryoelectron microscopy and single-particle reconstruction, we have determined the structure of a translating plant (Triticum aestivum) 80S ribosome at 5.5-Å resolution. This map, together with a 6.1-Å map of a Saccharomyces cerevisiae 80S ribosome, has enabled us to model ∼98% of the rRNA. Accurate assignment of the rRNA expansion segments (ES) and variable regions has revealed unique ES–ES and r-protein–ES interactions, providing insight into the structure and evolution of the eukaryotic ribosome.

Scholarpedia, 5(11):3698, November 2010 (article)

Abstract
Policy gradient methods are a type of reinforcement learning techniques that rely upon optimizing parametrized policies with respect to the expected return (long-term cumulative reward) by gradient descent. They do not suffer from many of the problems that have been marring traditional reinforcement learning approaches such as the lack of guarantees of a value function, the intractability problem resulting from uncertain state information and the complexity arising from continuous states & actions.

Localization of eukaryote-specific ribosomal proteins in a 5.5-Å cryo-EM map of the 80S eukaryotic ribosome

Armache, J-P., Jarasch, A., Anger, AM., Villa, E., Becker, T., Bhushan, S., Jossinet, F., Habeck, M., Dindar, G., Franckenberg, S., Marquez, V., Mielke, T., Thomm, M., Berninghausen, O., Beatrix, B., Söding, J., Westhof, E., Wilson, DN., Beckmann, R.

Proceedings of the National Academy of Sciences of the United States of America, 107(46):19754-19759, November 2010 (article)

Abstract
Protein synthesis in all living organisms occurs on ribonucleoprotein particles, called ribosomes. Despite the universality of this process, eukaryotic ribosomes are significantly larger in size than their bacterial counterparts due in part to the presence of 80 r proteins rather than 54 in bacteria. Using cryoelectron microscopy reconstructions of a translating plant (Triticum aestivum) 80S ribosome at 5.5-Å resolution, together with a 6.1-Å map of a translating Saccharomyces cerevisiae 80S ribosome, we have localized and modeled 74/80 (92.5%) of the ribosomal proteins, encompassing 12 archaeal/eukaryote-specific small subunit proteins as well as the complete complement of the ribosomal proteins of the eukaryotic large subunit. Near-complete atomic models of the 80S ribosome provide insights into the structure, function, and evolution of the eukaryotic translational apparatus.

Spatio-Spectral Remote Sensing Image Classification With Graph Kernels
IEEE Geoscience and Remote Sensing Letters, 7(4):741-745, October 2010 (article)

Abstract
This letter presents a graph kernel for spatio-spectral remote sensing image classification with support vector machines (SVMs). The method considers higher order relations in the neighborhood (beyond pairwise spatial relations) to iteratively compute a kernel matrix for SVM learning. The proposed kernel is easy to compute and constitutes a powerful alternative to existing approaches. The capabilities of the method are illustrated in several multi- and hyperspectral remote sensing images acquired over both urban and agricultural areas.

Causal Inference Using the Algorithmic Markov Condition
IEEE Transactions on Information Theory, 56(10):5168-5194, October 2010 (article)

Abstract
Inferring the causal structure that links $n$ observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when the sample size is one. We develop a theory how to generate causal graphs explaining similarities between single objects. To this end, we replace the notion of conditional stochastic independence in the causal Markov condition with the vanishing of conditional algorithmic mutual information and describe the corresponding causal inference rules. We explain why a consistent reformulation of causal inference in terms of algorithmic complexity implies a new inference principle that takes into account also the complexity of conditional probability densities, making it possible to select among Markov equivalent causal graphs. This insight provides a theoretical foundation of a heuristic principle proposed in earlier work. We also sketch some ideas on how to replace Kolmogorov complexity with decidable complexity criteria. This can be seen as an algorithmic analog of replacing the empirically undecidable question of statistical independence with practical independence tests that are based on implicit or explicit assumptions on the underlying distribution.
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