Deep Belief Networks (DBN) have been successfully applied on popular machine learning tasks. Specifically, when applied on hand-written digit recognition, DBNs have achieved approximate accuracy rates of 98.8%. In an effort to optimize the data representation achieved by the DBN and maximize their descriptive power, recent advances have focused on inducing sparse constraints at each layer of the DBN. In this paper we present a theoretical approach for sparse constraints in the DBN using the mixed norm for both non-overlapping and overlapping groups. We explore how these constraints affect the classification accuracy for digit recognition in three different datasets (MNIST, USPS, RIMES) and provide initial estimations of their usefulness by altering different parameters such as the group size and overlap percentage.

We consider the minimum error entropy (MEE) criterion and an empirical risk minimization learning algorithm in a regression setting. A learning theory approach is presented for this MEE algorithm and explicit error bounds are provided in terms of the approximation ability and capacity of the involved hypothesis space when the MEE scaling parameter is large. Novel asymptotic analysis is conducted for the generalization error associated with Renyi's entropy and a Parzen window function, to overcome technical difficulties arisen from the essential differences between the classical least squares problems and the MEE setting. A semi-norm and the involved symmetrized least squares error are introduced, which is related to some ranking algorithms.

In this article supervised learning problems are solved using soft rule ensembles. We first review the importance sampling learning ensembles (ISLE) approach that is useful for generating hard rules. The soft rules are then obtained with logistic regression from the corresponding hard rules. In order to deal with the perfect separation problem related to the logistic regression, Firth's bias corrected likelihood is used. Various examples and simulation results show that soft rule ensembles can improve predictive performance over hard rule ensembles.

We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure updating of such a set of measures upon acquiring new information is well-known to suffer from problems; agents are not always able to learn appropriately. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and a natural approach to determining the weights. We then show how this representation can be used in decision-making, by modifying a standard approach to decision making -- minimizing expected regret -- to obtain minimax weighted expected regret (MWER). We provide an axiomatization that characterizes preferences induced by MWER both in the static and dynamic case.

Signal processing tasks as fundamental as sampling, reconstruction, minimum mean-square error interpolation and prediction can be viewed under the prism of reproducing kernel Hilbert spaces. Endowing this vantage point with contemporary advances in sparsity-aware modeling and processing, promotes the nonparametric basis pursuit advocated in this paper as the overarching framework for the confluence of kernel-based learning (KBL) approaches leveraging sparse linear regression, nuclear-norm regularization, and dictionary learning. The novel sparse KBL toolbox goes beyond translating sparse parametric approaches to their nonparametric counterparts, to incorporate new possibilities such as multi-kernel selection and matrix smoothing. The impact of sparse KBL to signal processing applications is illustrated through test cases from cognitive radio sensing, microarray data imputation, and network traffic prediction.

Anomaly detection is being regarded as an unsupervised learning task as anomalies stem from adversarial or unlikely events with unknown distributions. However, the predictive performance of purely unsupervised anomaly detection often fails to match the required detection rates in many tasks and there exists a need for labeled data to guide the model generation. Our first contribution shows that classical semi-supervised approaches, originating from a supervised classifier, are inappropriate and hardly detect new and unknown anomalies. We argue that semi-supervised anomaly detection needs to ground on the unsupervised learning paradigm and devise a novel algorithm that meets this requirement. Although being intrinsically non-convex, we further show that the optimization problem has a convex equivalent under relatively mild assumptions. Additionally, we propose an active learning strategy to automatically filter candidates for labeling. In an empirical study on network intrusion detection data, we observe that the proposed learning methodology requires much less labeled data than the state-of-the-art, while achieving higher detection accuracies.

Semantic parsing, i.e., the automatic derivation of meaning representation such as an instantiated predicate-argument structure for a sentence, plays a critical role in deep processing of natural language. Unlike all other top systems of semantic dependency parsing that have to rely on a pipeline framework to chain up a series of submodels each specialized for a specific subtask, the one presented in this article integrates everything into one model, in hopes of achieving desirable integrity and practicality for real applications while maintaining a competitive performance. This integrative approach tackles semantic parsing as a word pair classification problem using a maximum entropy classifier. We leverage adaptive pruning of argument candidates and large-scale feature selection engineering to allow the largest feature space ever in use so far in this field, it achieves a state-of-the-art performance on the evaluation data set for CoNLL-2008 shared task, on top of all but one top pipeline system, confirming its feasibility and effectiveness.

Researchers and scientists increasingly find themselves in the position of having to quickly understand large amounts of technical material. Our goal is to effectively serve this need by using bibliometric text mining and summarization techniques to generate summaries of scientific literature. We show how we can use citations to produce automatically generated, readily consumable, technical extractive summaries. We first propose C-LexRank, a model for summarizing single scientific articles based on citations, which employs community detection and extracts salient information-rich sentences. Next, we further extend our experiments to summarize a set of papers, which cover the same scientific topic. We generate extractive summaries of a set of Question Answering (QA) and Dependency Parsing (DP) papers, their abstracts, and their citation sentences and show that citations have unique information amenable to creating a summary.

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations lie on a lower-dimensional manifold of high probability. It has been more difficult, however, to exploit this insight to build explicit, tractable density models for high-dimensional data. In this paper, we introduce the deep density model (DDM), a new approach to density estimation. We exploit insights from deep learning to construct a bijective map to a representation space, under which the transformation of the distribution of the data is approximately factorized and has identical and known marginal densities. The simplicity of the latent distribution under the model allows us to feasibly explore it, and the invertibility of the map to characterize contraction of measure across it. This enables us to compute normalized densities for out-of-sample data. This combination of tractability and flexibility allows us to tackle a variety of probabilistic tasks on high-dimensional datasets, including: rapid computation of normalized densities at test-time without evaluating a partition function; generation of samples without MCMC; and characterization of the joint entropy of the data.

When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated by a single Gaussian. In this paper we abandon the normality assumption and instead use statistical methods for nonparametric density estimation. For a naive Bayesian classifier, we present experimental results on a variety of natural and artificial domains, comparing two methods of density estimation: assuming normality and modeling each conditional distribution with a single Gaussian; and using nonparametric kernel density estimation. We observe large reductions in error on several natural and artificial data sets, which suggests that kernel estimation is a useful tool for learning Bayesian models.