Self-paced learning (SPL) is a recently raised methodology designed through simulating the learning principle of humans animals. A variety of SPL realization schemes have been designed for different computer vision and pattern recognition tasks, and empirically substantiated to be effective in these applications. However, the investigation on its theoretical insight is still a blank. To this issue, this study attempts to provide some new theoretical understanding under the SPL scheme. Specifically, we prove that the solving strategy on SPL accords with a majorization minimization algorithm implemented on a latent objective function. Furthermore, we find that the loss function contained in this latent objective has a similar configuration with non-convex regularized penalty (NSPR) known in statistics and machine learning. Such connection inspires us discovering more intrinsic relationship between SPL regimes and NSPR forms, like SCAD, LOG and EXP. The robustness insight under SPL can then be finely explained. We also analyze the capability of SPL on its easy loss prior embedding property, and provide an insightful interpretation to the effectiveness mechanism under previous SPL variations. Besides, we design a group-partial-order loss prior, which is especially useful to weakly labeled large-scale data processing tasks. Through applying SPL with this loss prior to the FCVID dataset, which is currently one of the biggest manually annotated video dataset, our method achieves state-of-the-art performance beyond previous methods, which further helps supports the proposed theoretical arguments.
@cite_5: Motivated by the recent developments of nonconvex penalties in sparsity modeling, we propose a nonconvex optimization model for handing the low-rank matrix recovery problem. Different from the famous robust principal component analysis (RPCA), we suggest recovering low-rank and sparse matrices via a nonconvex loss function and a nonconvex penalty. The advantage of the nonconvex approach lies in its stronger robustness. To solve the model, we devise a majorization-minimization augmented Lagrange multiplier (MM-ALM) algorithm which finds the local optimal solutions of the proposed nonconvex model. We also provide an efficient strategy to speedup MM-ALM, which makes the running time comparable with the state-of-the-art algorithm of solving RPCA. Finally, empirical results demonstrate the superiority of our nonconvex approach over RPCA in terms of matrix recovery accuracy.
@cite_17: In recent applications with massive but less reliable data (e.g., labels obtained by a semi-supervised learning method or crowdsourcing), non-robustness of the support vector machine (SVM) often causes considerable performance deterioration. Although improving the robustness of SVM has been investigated for long time, robust SVM (RSVM) learning still poses two major challenges: obtaining a good (local) solution from a non-convex optimization problem and optimally controlling the robustness-efficiency trade-off. In this paper, we address these two issues simultaneously in an integrated way by introducing a novel homotopy approach to RSVM learning. Based on theoretical investigation of the geometry of RSVM solutions, we show that a path of local RSVM solutions can be computed efficiently when the influence of outliers is gradually suppressed as simulated annealing. We experimentally demonstrate that our algorithm tends to produce better local solutions than the alternative approach based on the concave-convex procedure, with the ability of stable and efficient model selection for controlling the influence of outliers.
Albeit possessing elegant statistic properties and empirically verified to be effective in specific applications through finely designed solving strategy, involving such NCPR terms brings non-convexity to the model. This inclines to result in the issue that the algorithm easily get stuck to an undesired local minima of the problem @cite_5 @cite_17 .