Multi-label classification is a challenging and appealing supervised learning problem where a subset of labels, rather than a single label seen in traditional classification problems, is assigned to a single test instance. Classifier chains based methods are a promising strategy to tackle multi-label classification problems as they model label correlations at acceptable complexity. However, these methods are difficult to approximate the underlying dependency in the label space, and suffer from the problems of poorly ordered chain and error propagation. In this paper, we propose a novel polytree-augmented classifier chains method to remedy these problems. A polytree is used to model reasonable conditional dependence between labels over attributes, under which the directional relationship between labels within causal basins could be appropriately determined. In addition, based on the max-sum algorithm, exact inference would be performed on polytrees at reasonable cost, preventing from error propagation. The experiments performed on both artificial and benchmark multi-label data sets demonstrated that the proposed method is competitive with the state-of-the-art multi-label classification methods.

Mixed occlusions commonly consist in real-world face images and bring with it great challenges for automatic face recognition. The existing methods usually utilize the same reconstruction error to code the occluded test image with respect to the labeled training set and simultaneously to estimate the occlusion/feature support. However, this error coding model might not be applicable for face recognition with mixed occlusions. For mixed occlusions, the error used to code the test image, called the discriminative error, and the error used to estimate the occlusion support, called the structural error, might have totally different behaviors. By combining the two various errors with the occlusion support, we present an extended error coding model, dubbed Mixed Error Coding (MEC). To further enhance discriminability and feature selection ability, we also incorporate into MEC the hidden feature selection technology of the subspace learning methods in the domain of the image gradient orientations. Experiments demonstrate the effectiveness and robustness of the proposed MEC model in dealing with mixed occlusions.

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both basis dictionary elements — eigenfunctions of a GP prior — and prior precisions in a sparse finite model. It is well known that, among all orthogonal basis functions, eigenfunctions can provide the most compact representation. Unlike other sparse Bayesian finite models where the basis function has a fixed form, our eigenfunctions live in a reproducing kernel Hilbert space as a finite linear combination of kernel functions. We learn the dictionary elements — eigenfunctions — and the prior precisions over these elements as well as all the other hyperparameters from data by maximizing the model marginal likelihood. We explore computational linear algebra to simplify the gradient computation significantly. Our experimental results demonstrate improved predictive performance of EigenGP over alternative sparse GP methods as well as relevance vector machines.

Justification logic originated from the study of the logic of proofs.  However, in a more general setting, it may be regarded as a kind of explicit epistemic logic. In such logic, the reasons why a fact is believed are explicitly represented as justification terms.  Traditionally, the modeling of uncertain beliefs is crucially important for epistemic reasoning. While graded modal logics interpreted with possibility theory semantics have been successfully applied to the representation and reasoning of uncertain beliefs, they cannot keep track of the reasons why an agent believes a fact. The objective of this paper is to extend the graded modal logics with explicit justifications. We introduce a possibilistic justification logic,  present its syntax and semantics, and investigate its meta-properties, such as soundness, completeness, and realizability.

Probabilistic sentential decision diagrams (PSDDs) are a tractable representation of structured probability spaces, which are characterized by complex logical constraints on what constitutes a possible world. We develop general-purpose techniques for probabilistic reasoning and learning with PSDDs, allowing one to compute the probabilities of arbitrary logical formulas and to learn PSDDs from incomplete data. We illustrate the effectiveness of these techniques in the context of learning preference distributions, to which considerable work has been devoted in the past. We show, analytically and empirically, that our proposed framework is general enough to support diverse and complex data and query types. In particular, we show that it can learn maximum-likelihood models from partial rankings, pairwise preferences, and arbitrary preference constraints. Moreover, we show that it can efficiently answer many queries exactly, from expected and most likely rankings, to the probability of pairwise preferences, and diversified recommendations. This case study illustrates the effectiveness and flexibility of the developed PSDD framework as a domain-independent tool for learning and reasoning with structured probability spaces.

Distributed constraint optimization (DCOP) is an important framework for coordinated multiagent decision making. We address a practically useful variant of DCOP, called resource-constrained DCOP (RC-DCOP), which takes into account agents' consumption of shared limited resources. We present a promising new class of algorithm for RC-DCOPs by translating the underlying coordination problem to probabilistic inference. Using inference techniques such as expectation-maximization and convex optimization machinery, we develop a novel convergent message-passing algorithm for RC-DCOPs. Experiments on standard benchmarks show that our approach provides better quality than previous best DCOP algorithms and has much lower failure rate. Comparisons against an efficient centralized solver show that our approach provides near-optimal solutions, and is significantly faster on larger instances.

Interval-based possibilistic logic is a flexible setting extending standard possibilistic logic such that each logical expression is associated with a sub-interval of [0,1]. This paper focuses on the fundamental issue of conditioning in the interval-based possibilistic setting. The first part of the paper first proposes a set of natural properties that an interval-based conditioning operator should satisfy. We then give a natural and safe definition for conditioning an interval-based possibility distribution. This definition is based on applying standard min-based or product-based conditioning on the set of all associated compatible possibility distributions. We analyze the obtained posterior distributions and provide a precise characterization of lower and upper endpoints of the intervals associated with interpretations. The second part of the paper provides an equivalent syntactic computation of interval-based conditioning when interval-based distributions are compactly encoded by means of interval-based possibilistic knowledge bases. We show that interval-based conditioning is achieved without extra computational cost comparing to conditioning standard possibilistic knowledge bases.

Differentiation is an important inference method in Bayesian networks and intervention is a basic notion in causal Bayesian networks. In this paper, we reveal the connection between differentiation and intervention in Bayesian networks. We first encode an intervention as changing a conditional probabilistic table into a partial intervention table. We next introduce a jointree algorithm to compute the full atomic interventions of all nodes with respect to evidence in a Bayesian network. We further discover that an intervention has differential semantics if the intervention variables can reach the evidence in Bayesian networks and the output of the state-of-the-art algorithm is not the differentiation but the intervention of a Bayesian network if the differential nodes cannot reach any one of the evidence nodes. Finally, we present experimental results to demonstrate the efficiency of our algorithm to infer the causal effect in Bayesian networks.

The recent surge of interest in reasoning about probabilistic graphical models has led to the development of various techniques for probabilistic reasoning. Of these, techniques based on weighted model counting are particularly interesting since they can potentially leverage recent advances in unweighted model counting and in propositional satisfiability solving. In this paper, we present a new approach to weighted model counting via reduction to unweighted model counting. Our reduction, which is polynomial-time and preserves the normal form (CNF/DNF) of the input formula, allows us to exploit advances in unweighted model counting to solve weighted model counting instances. Experiments with weighted model counters built using our reduction indicate that these counters performs much better than a state-of-the-art weighted model counter

In natural language processing and information retrieval, the bag of words representation is used to implicitly represent the meaning of the text. Implicit semantics, however, are insufficient in supporting text or natural language based interfaces, which are adopted by an increasing number of applications. Indeed, in applications ranging from automatic ontology construction to question answering, explicit representation of semantics is starting to play a more prominent role. In this paper, we introduce the task of conceptual labeling (CL), which aims at generating a minimum set of conceptual labels that best summarize a bag of words. We draw the labels from a data driven semantic network that contains millions of highly connected concepts. The semantic network provides meaning to the concepts, and in turn, it provides meaning to the bag of words through the conceptual labels we generate. To achieve our goal, we use an information theoretic approach to trade-off the semantic coverage of a bag of words against the minimality of the output labels. Specifically, we use Minimum Description Length (MDL) as the criteria in selecting the best concepts. Our extensive experimental results demonstrate the effectiveness of our approach in representing the explicit semantics of a bag of words.