Unsupervised Feature Learning by Deep Sparse Coding

In this paper, we propose a new unsupervised feature learning framework, namely Deep Sparse Coding (DeepSC), that extends sparse coding to a multi-layer architecture for visual object recognition tasks. The main innovation of the framework is that it connects the sparse-encoders from different layers by a sparse-to-dense module. The sparse-to-dense module is a composition of a local spatial pooling step and a low-dimensional embedding process, which takes advantage of the spatial smoothness information in the image. As a result, the new method is able to learn several levels of sparse representation of the image which capture features at a variety of abstraction levels and simultaneously preserve the spatial smoothness between the neighboring image patches. Combining the feature representations from multiple layers, DeepSC achieves the state-of-the-art performance on multiple object recognition tasks.Comment: 9 pages, submitted to ICL

Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization

We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficients are estimated in alternate steps, keeping the other fixed. Typically, the coefficients are estimated via $\ell_1$ minimization, keeping the dictionary fixed, and the dictionary is estimated through least squares, keeping the coefficients fixed. In this paper, we establish local linear convergence for this variant of alternating minimization and establish that the basin of attraction for the global optimum (corresponding to the true dictionary and the coefficients) is \order{1/s^2}, where $s$ is the sparsity level in each sample and the dictionary satisfies RIP. Combined with the recent results of approximate dictionary estimation, this yields provable guarantees for exact recovery of both the dictionary elements and the coefficients, when the dictionary elements are incoherent.Comment: Local linear convergence now holds under RIP and also more general restricted eigenvalue condition

Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization

We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficients are estimated in alternate steps, keeping the other fixed. Typically, the coefficients are estimated via ℓ_1 minimization, keeping the dictionary fixed, and the dictionary is estimated through least squares, keeping the coefficients fixed. In this paper, we establish local linear convergence for this variant of alternating minimization and establish that the basin of attraction for the global optimum (corresponding to the true dictionary and the coefficients) is O(1/s^2), where s is the sparsity level in each sample and the dictionary satisfies restricted isometry property. Combined with the recent results of approximate dictionary estimation, this yields provable guarantees for exact recovery of both the dictionary elements and the coefficients, when the dictionary elements are incoherent

Scaling Up Large-scale Sparse Learning and Its Application to Medical Imaging

abstract: Large-scale $\ell_1$-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. In many applications, it remains challenging to apply the sparse learning model to large-scale problems that have massive data samples with high-dimensional features. One popular and promising strategy is to scaling up the optimization problem in parallel. Parallel solvers run multiple cores on a shared memory system or a distributed environment to speed up the computation, while the practical usage is limited by the huge dimension in the feature space and synchronization problems. In this dissertation, I carry out the research along the direction with particular focuses on scaling up the optimization of sparse learning for supervised and unsupervised learning problems. For the supervised learning, I firstly propose an asynchronous parallel solver to optimize the large-scale sparse learning model in a multithreading environment. Moreover, I propose a distributed framework to conduct the learning process when the dataset is distributed stored among different machines. Then the proposed model is further extended to the studies of risk genetic factors for Alzheimer's Disease (AD) among different research institutions, integrating a group feature selection framework to rank the top risk SNPs for AD. For the unsupervised learning problem, I propose a highly efficient solver, termed Stochastic Coordinate Coding (SCC), scaling up the optimization of dictionary learning and sparse coding problems. The common issue for the medical imaging research is that the longitudinal features of patients among different time points are beneficial to study together. To further improve the dictionary learning model, I propose a multi-task dictionary learning method, learning the different task simultaneously and utilizing shared and individual dictionary to encode both consistent and changing imaging features.Dissertation/ThesisDoctoral Dissertation Computer Science 201

Sparse, hierarchical and shared-factors priors for representation learning

La représentation en caractéristiques est une préoccupation centrale des systèmes d’apprentissage automatique d’aujourd’hui. Une représentation adéquate peut faciliter une tâche d’apprentissage complexe. C’est le cas lorsque par exemple cette représentation est de faible dimensionnalité et est constituée de caractéristiques de haut niveau. Mais comment déterminer si une représentation est adéquate pour une tâche d’apprentissage ? Les récents travaux suggèrent qu’il est préférable de voir le choix de la représentation comme un problème d’apprentissage en soi. C’est ce que l’on nomme l’apprentissage de représentation. Cette thèse présente une série de contributions visant à améliorer la qualité des représentations apprises. La première contribution élabore une étude comparative des approches par dictionnaire parcimonieux sur le problème de la localisation de points de prises (pour la saisie robotisée) et fournit une analyse empirique de leurs avantages et leurs inconvénients. La deuxième contribution propose une architecture réseau de neurones à convolution (CNN) pour la détection de points de prise et la compare aux approches d’apprentissage par dictionnaire. Ensuite, la troisième contribution élabore une nouvelle fonction d’activation paramétrique et la valide expérimentalement. Finalement, la quatrième contribution détaille un nouveau mécanisme de partage souple de paramètres dans un cadre d’apprentissage multitâche.Feature representation is a central concern of today’s machine learning systems. A proper representation can facilitate a complex learning task. This is the case when for instance the representation has low dimensionality and consists of high-level characteristics. But how can we determine if a representation is adequate for a learning task? Recent work suggests that it is better to see the choice of representation as a learning problem in itself. This is called Representation Learning. This thesis presents a series of contributions aimed at improving the quality of the learned representations. The first contribution elaborates a comparative study of Sparse Dictionary Learning (SDL) approaches on the problem of grasp detection (for robotic grasping) and provides an empirical analysis of their advantages and disadvantages. The second contribution proposes a Convolutional Neural Network (CNN) architecture for grasp detection and compares it to SDL. Then, the third contribution elaborates a new parametric activation function and validates it experimentally. Finally, the fourth contribution details a new soft parameter sharing mechanism for multitasking learning