Multimodal Multipart Learning for Action Recognition in Depth Videos

The articulated and complex nature of human actions makes the task of action recognition difficult. One approach to handle this complexity is dividing it to the kinetics of body parts and analyzing the actions based on these partial descriptors. We propose a joint sparse regression based learning method which utilizes the structured sparsity to model each action as a combination of multimodal features from a sparse set of body parts. To represent dynamics and appearance of parts, we employ a heterogeneous set of depth and skeleton based features. The proper structure of multimodal multipart features are formulated into the learning framework via the proposed hierarchical mixed norm, to regularize the structured features of each part and to apply sparsity between them, in favor of a group feature selection. Our experimental results expose the effectiveness of the proposed learning method in which it outperforms other methods in all three tested datasets while saturating one of them by achieving perfect accuracy

Optimistic Robust Optimization With Applications To Machine Learning

Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this paper, we explore an optimistic, or best-case view of uncertainty and show that it can be a fruitful approach. We show that these techniques can be used to address a wide variety of problems. First, we apply our methods in the context of robust linear programming, providing a method for reducing conservatism in intuitive ways that encode economically realistic modeling assumptions. Second, we look at problems in machine learning and find that this approach is strongly connected to the existing literature. Specifically, we provide a new interpretation for popular sparsity inducing non-convex regularization schemes. Additionally, we show that successful approaches for dealing with outliers and noise can be interpreted as optimistic robust optimization problems. Although many of the problems resulting from our approach are non-convex, we find that DCA or DCA-like optimization approaches can be intuitive and efficient

Optimization with Sparsity-Inducing Penalties

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate non-smooth norms. The goal of this paper is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted $\ell_2$-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view