Principal component analysis (PCA) is an unsupervised method for learning low-dimensional features with orthogonal projections. Multilinear PCA methods extend PCA to deal with multidimensional data (tensors) directly via tensor-to-tensor projection or tensor-to-vector projection (TVP). However, under the TVP setting, it is difficult to develop an effective multilinear PCA method with the orthogonality constraint. This paper tackles this problem by proposing a novel Semi-Orthogonal Multilinear PCA (SO-MPCA) approach. SO-MPCA learns low-dimensional features directly from tensors via TVP by imposing the orthogonality constraint in only one mode. This formulation results in more captured variance and more learned features than full orthogonality. For better generalization, we further introduce a relaxed start (RS) strategy to get SO-MPCA-RS by fixing the starting projection vectors, which increases the bias and reduces the variance of the learning model. Experiments on both face (2D) and gait (3D) data demonstrate that SO-MPCA-RS outperforms other competing algorithms on the whole, and the relaxed start strategy is also effective for other TVP-based PCA methods.

Large sparse datasets are common in many real-world applications. Linear SVM has been shown to be very efficient for classifying such datasets. However, it is still unknown how data sparseness would affect its convergence behavior. To study this problem in a systematic manner, we propose a novel approach to generate large and sparse data from real-world datasets, using statistical inference and the data sampling process in the PAC framework. We first study the convergence behavior of linear SVM experimentally, and make several observations, useful for real-world applications. We then offer theoretical proofs for our observations by studying the Bayes risk and PAC bound. Our experiment and theoretic results are valuable for learning large sparse datasets with linear SVM.

The adoption of a generic contrariness notion in ASPIC+ substantially enhances its expressiveness with respect to other formalisms for structured argumentation. In particular, it opens the way to novel investigation directions, like the use of multivalued logics in the construction of arguments. This paper points out however that in the current version of ASPIC+ a serious technical difficulty related with generic contrariness is present. With the aim of preserving the same level of generality, the paper provides a solution based on a novel notion of closure of the contrariness relation at the level of sets of formulas and an abstract representation of conflicts between sets of arguments. The proposed solution is shown to satisfy the same rationality postulates as ASPIC+ and represents a starting point for further technical and conceptual developments in structured argumentation.

In this paper we focus on the greedy matrix completion problem. A simple atom selection strategy is proposed building upon an alternating minimization procedure. Based on this per-iteration strategy, we devise a greedy algorithm OAMC and establish an upper bound of the approximation error. To evaluate different weight refinement methods, several variants of OAMC are designed. We prove that OAMC and three of its variants have the property of linear convergence. Experiments of Recommendation and Image Recovery are conducted to make empirical evaluation. Results are promising. We report that our algorithm takes only 700 seconds to process Yahoo Music dataset in PC, yet achieves a root mean square error 24.5 on test set.

User interest inference from social networks is a fundamental problem to many applications. It usually exhibits dual-heterogeneities: a user's interests are complementarily and comprehensively reflected by multiple social networks; interests are inter-correlated in a nonuniform way rather than independent to each other. Although great success has been achieved by previous approaches, few of them consider these dual-heterogeneities simultaneously. In this work, we propose a structure-constrained multi-source multi-task learning scheme to co-regularize the source consistency and the tree-guided task relatedness. Meanwhile, it is able to jointly learn the task-sharing and task-specific features. Comprehensive experiments on a real-world dataset validated our scheme. In addition, we have released our dataset to facilitate the research communities.

The semantic class (i.e., type) of an entity plays a vital role in many natural language processing tasks, such as question answering. However, most of existing type classification systems extensively rely on hand-crafted features. This paper introduces a hybrid neural model which classifies entity mentions to a wide-coverage set of 22 types derived from DBpedia. It consists of two parts. The mention model uses recurrent neural networks to recursively obtain the vector representation of an entity mention from the words it contains. The context model, on the other hand, employs multilayer perceptrons to obtain the hidden representation for contextual information of a mention. Representations obtained by the two parts are used together to predict the type distribution. Using automatically generated data, these two parts are jointly learned. Experimental studies illustrate that the proposed approach outperforms baseline methods. Moreover, when type information provided by our method is used in a question answering system, we observe a 14.7% relative improvement for the top-1 accuracy of answers.

Monte-Carlo Tree Search (MCTS) algorithms such as UCT are an attractive online framework for solving planning under uncertainty problems modeled as a Markov Decision Process. However, MCTS search trees are constructed in flat state and action spaces, which can lead to poor policies for large problems. In a separate research thread, domain abstraction techniques compute symmetries to reduce the original MDP. This can lead to significant savings in computation, but these have been predominantly implemented for offline planning. This paper makes two contributions. First, we define the ASAP (Abstraction of State-Action Pairs) framework, which extends and unifies past work on domain abstractions by holistically aggregating both states and state-action pairs — ASAP uncovers a much larger number of symmetries in a given domain. Second, we propose ASAP-UCT, which implements ASAP-style abstractions within a UCT framework combining strengths of online planning with domain abstractions. Experimental evaluation on several benchmark domains shows up to 26% improvement in the quality of policies obtained over existing algorithms.

A consequence of a logic program is a consistent set of literals that are satisfied by every answer set. The well-founded model is a consequence that can be used to simplify the logic program. In this paper, we extend the notion of well-founded models to consequences for simplifying disjunctive logic programs (DLPs) in a general manner. Specifically, we provide two main notions, strong reliable set and weak reliable set, and show that a DLP is strongly equivalent to the simplified program if and only if the consequence is a strong reliable set, and they have the same answer sets if and only if the consequence is a weak reliable set. Then we provide computational complexity on identifying both notions. In addition, we provide an algorithm to compute some strong reliable sets and show that the approach is an extension of the well-founded model in simplifying logic programs.

Pareto optimization solves a constrained optimization task by reformulating the task as a bi-objective problem. Pareto optimization has been shown quite effective in applications; however, it has little theoretical support. This work theoretically compares Pareto optimization with a penalty approach, which is a common method transforming a constrained optimization into an unconstrained optimization. We prove that on two large classes of constrained Boolean optimization problems, minimum matroid optimization (P-solvable) and minimum cost coverage (NP-hard), Pareto optimization is more efficient than the penalty function method for obtaining the optimal and approximate solutions, respectively. Furthermore, on a minimum cost coverage instance, we also show the advantage of Pareto optimization over a greedy algorithm.

In repeated stochastic games (RSGs), an agent must quickly adapt to the behavior of previously unknown associates, who may themselves be learning. This machine-learning problem is particularly challenging due, in part, to the presence of multiple (even infinite) equilibria and inherently large strategy spaces. In this paper, we introduce a method to reduce the strategy space of two-player general-sum RSGs to a handful of expert strategies. This process, called mega, effectually reduces an RSG to a bandit problem. We show that the resulting strategy space preserves several important properties of the original RSG, thus enabling a learner to produce robust strategies within a reasonably small number of interactions. To better establish strengths and weaknesses of this approach, we empirically evaluate the resulting learning system against other algorithms in three different RSGs.