In many learning tasks with structural properties, structured sparse modeling usually leads to better interpretability and higher generalization performance. While great efforts have focused on the convex regularization, recent studies show that nonconvex regularizers can outperform their convex counterparts in many situations. However, the resulting nonconvex optimization problems are still challenging, especially for the structured sparsity-inducing regularizers. In this paper, we propose a splitting method for solving nonconvex structured sparsity optimization problems. The proposed method alternates between a gradient step and an easily solvable proximal step, and thus enjoys low per-iteration computational complexity. We prove that the whole sequence generated by the proposed method converges to a critical point with at least sublinear convergence rate, relying on the Kurdyka-Łojasiewicz inequality. Experiments on both simulated and real-world data sets demonstrate the efficiency and efficacy of the proposed method.

Many randomized heuristic derivative-free optimization methods share a framework that iteratively learns a model for promising search areas and samples solutions from the model. This paper studies a particular setting of such framework, where the model is implemented by a classification model discriminating good solutions from bad ones. This setting allows a general theoretical characterization, where critical factors to the optimization are discovered. We also prove that optimization problems with Local Lipschitz continuity can be solved in polynomial time by proper configurations of this framework. Following the critical factors, we propose the randomized coordinate shrinking classification algorithm to learn the model, forming the RACOS algorithm, for optimization in continuous and discrete domains. Experiments on the testing functions as well as on the machine learning tasks including spectral clustering and classification with Ramp loss demonstrate the effectiveness of RACOS.

Many real world applications in medicine, biology, communication networks, web mining, and economics, among others, involve modeling and learning structured stochastic processes that evolve over continuous time. Existing approaches, however, have focused on propositional domains only. Without extensive feature engineering, it is difficult-if not impossible-to apply them within relational domains where we may have varying number of objects and relations among them. We therefore develop the first relational representation called Relational Continuous-Time Bayesian Networks (RCTBNs) that can address this challenge. It features a nonparametric learning method that allows for efficiently learning the complex dependencies and their strengths simultaneously from sequence data. Our experimental results demonstrate that RCTBNs can learn as effectively as state-of-the-art approaches for propositional tasks while modeling relational tasks faithfully.

There are two classes of average reward reinforcement learning (RL) algorithms: model-based ones that explicitly maintain MDP models and model-free ones that do not learn such models. Though model-free algorithms are known to be more efficient, they often cannot converge to optimal policies due to the perturbation of parameters. In this paper, a novel model-free algorithm is proposed, which makes use of constant shifting values (CSVs) estimated from prior knowledge. To encourage exploration during the learning process, the algorithm constantly subtracts the CSV from the rewards. A terminating condition is proposed to handle the unboundedness of Q-values caused by such substraction. The convergence of the proposed algorithm is proved under very mild assumptions. Furthermore, linear function approximation is investigated to generalize our method to handle large-scale tasks. Extensive experiments on representative MDPs and the popular game Tetris show that the proposed algorithms significantly outperform the state-of-the-art ones.

Dictionary learning has played an important role in the success of sparse representation. Although synthesis dictionary learning for sparse representation has been well studied for universality representation (i.e., the dictionary is universal to all classes) and particularity representation (i.e., the dictionary is class-particular), jointly learning an analysis dictionary and a synthesis dictionary is still in its infant stage. Universality-particularity representation can well match the intrinsic characteristics of data (i.e., different classes share commonality and distinctness), while analysis-synthesis dictionary can give a more complete view of data representation (i.e., analysis dictionary is a dual-viewpoint of synthesis dictionary). In this paper, we proposed a novel model of analysis-synthesis dictionary learning for universality-particularity (ASDL-UP) representation based classification. The discrimination of universality and particularity representation is jointly exploited by simultaneously learning a pair of analysis dictionary and synthesis dictionary. More specifically, we impose a label preserving term to analysis coding coefficients for universality representation. Fisher-like regularizations for analysis coding coefficients and the subsequent synthesis representation are introduced to particularity representation. Compared with other state-of-the-art dictionary learning methods, ASDL-UP has shown better or competitive performance in various classification tasks.

Although many handle missing labels and class imbalance jointly. We formulate multi-label learning methods have been proposed in recent the problem as a transductive learning problem that years, a main challenge remains for this problem, i.e., the include five components that are label consistency, instancelevel lack of completely labeled training instances. This is important and class-level label smoothness, and two types of class because in many real life applications, most training cardinality (lower and upper) bounds. The first three components instances are only partially labeled, while other labels are are used to propagate the label information from the not provided or missing. One such example is image annotation, provided labels to missing labels, and the latter two components a human labeler can only feasibly annotates each are included to handle two types of the class imbalance training image with a subset of tags, especially when the problem. We first formulate a unified model that combines number of classes/tags is large. Learning from such partially these components as a constrained submodular minimization labeled instances is referred to as the multi-label learning problem (CSM). However, due to the class cardinality with missing labels (MLML) problem (Wu et al. 2014; constraint, it is a NPhard problem.

In the past decade, social and information networks have become prevalent, and research on the network data has attracted much attention. Besides the link structure, network data are often equipped with the content information (i.e, node attributes) that is usually noisy and characterized by high dimensionality. As the curse of dimensionality could hamper the performance of many machine learning tasks on networks (e.g., community detection and link prediction), feature selection can be a useful technique for alleviating such issue. In this paper, we investigate the problem of unsupervised feature selection on networks. Most existing feature selection methods fail to incorporate the linkage information, and the state-of-the-art approaches usually rely on pseudo labels generated from clustering. Such cluster labels may be far from accurate and can mislead the feature selection process. To address these issues, we propose a generative point of view for unsupervised features selection on networks that can seamlessly exploit the linkage and content information in a more effective manner. We assume that the link structures and node content are generated from a succinct set of high-quality features, and we find these features through maximizing the likelihood of the generation process. Experimental results on three real-world datasets show that our approach can select more discriminative features than state-of-the-art methods.

Feature extraction is an important task in machine learning. In this paper, we present a simple and efficient method, named max-margin data shifting (MMDS), to process the data before feature extraction. By relying on a large-margin classifier, MMDS is helpful to enhance the discriminative ability of subsequent feature extractors. The kernel trick can be applied to extract nonlinear features from input data. We further analyze in detail the example of principal component analysis (PCA). The empirical results on multiple linear and nonlinear models demonstrate that MMDS can efficiently improve the performance of unsupervised extractors.

This paper proposes a set of new error criteria and a learning approach, called Adaptive Normalized Risk-Averting Training (ANRAT) to attack the non-convex optimization problem in training deep neural networks without pretraining. Theoretically, we demonstrate its effectiveness based on the expansion of the convexity region. By analyzing the gradient on the convexity index $\lambda$, we explain the reason why our learning method using gradient descent works. In practice, we show how this training method is successfully applied for improved training of deep neural networks to solve visual recognition tasks on the MNIST and CIFAR-10 datasets. Using simple experimental settings without pretraining and other tricks, we obtain results comparable or superior to those reported in recent literature on the same tasks using standard ConvNets + MSE/cross entropy. Performance on deep/shallow multilayer perceptron and Denoised Auto-encoder is also explored. ANRAT can be combined with other quasi-Newton training methods, innovative network variants, regularization techniques and other common tricks in DNNs. Other than unsupervised pretraining, it provides a new perspective to address the non-convex optimization strategy in training DNNs.

Despite its nonconvex nature, ℓ 0 sparse approximation is desirable in many theoretical and application cases. We study the ℓ 0 sparse approximation problem with the tool of deep learning, by proposing Deep ℓ 0 Encoders. Two typical forms, the ℓ 0 regularized problem and the M-sparse problem, are investigated. Based on solid iterative algorithms, we model them as feed-forward neural networks, through introducing novel neurons and pooling functions. Enforcing such structural priors acts as an effective network regularization. The deep encoders also enjoy faster inference, larger learning capacity, and better scalability compared to conventional sparse coding solutions. Furthermore, under task-driven losses, the models can be conveniently optimized from end to end. Numerical results demonstrate the impressive performances of the proposed encoders.