Several heuristic search algorithms such as A* and breadth-first branch and bound have been developed for learning Bayesian network structures that optimize a scoring function. These algorithms rely on a lower bound function called k-cycle conflict heuristic in guiding the search to explore the most promising search spaces. The heuristic takes as input a partition of the random variables of a data set; the importance of the partition opens up opportunities for further research. This work introduces a new partition method based on information extracted from the potential optimal parent sets (POPS) of the variables. Empirical results show that the new partition can significantly improve the efficiency and scalability of heuristic search-based structure learning algorithms.

The global financial crisis occurred in 2008 and its contagion to other regions, as well as the long-lasting impact on different markets, show that it is increasingly important to understand the complicated coupling relationships across financial markets. This is indeed very difficult as complex hidden coupling relationships exist between different financial markets in various countries, which are very hard to model. The couplings involve interactions between homogeneous markets from various countries (we call intra-market coupling), interactions between heterogeneous markets (inter-market coupling) and interactions between current and past market behaviors (temporal coupling). Very limited work has been done towards modeling such complex couplings, whereas some existing methods predict market movement by simply aggregating indicators from various markets but ignoring the inbuilt couplings. As a result, these methods are highly sensitive to observations, and may often fail when financial indicators change slightly. In this paper, a coupled deep belief network is designed to accommodate the above three types of couplings across financial markets. With a deep-architecture model to capture the high-level coupled features, the proposed approach can infer market trends. Experimental results on data of stock and currency markets from three countries show that our approach outperforms other baselines, from both technical and business perspectives.

Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning Multivariate Time Series (MTS). However, in general, it is difficult to set the dimension of an LDS's hidden state space. A small number of hidden states may not be able to model the complexities of a MTS, while a large number of hidden states can lead to overfitting. In this paper, we study learning methods that impose various regularization penalties on the transition matrix of the LDS model and propose a regularized LDS learning framework (rLDS) which aims to (1) automatically shut down LDSs' spurious and unnecessary dimensions, and consequently, address the problem of choosing the optimal number of hidden states; (2) prevent the overfitting problem given a small amount of MTS data; and (3) support accurate MTS forecasting. To learn the regularized LDS from data we incorporate a second order cone program and a generalized gradient descent method into the Maximum a Posteriori framework and use Expectation Maximization to obtain a low-rank transition matrix of the LDS model. We propose two priors for modeling the matrix which lead to two instances of our rLDS. We show that our rLDS is able to recover well the intrinsic dimensionality of the time series dynamics and it improves the predictive performance when compared to baselines on both synthetic and real-world MTS datasets.

Restricted Boltzmann Machines (RBMs) are an important class of latent variable models for representing vector data. An under-explored area is multimode data, where each data point is a matrix or a tensor. Standard RBMs applying to such data would require vectorizing matrices and tensors, thus resulting in unnecessarily high dimensionality and at the same time, destroying the inherent higher-order interaction structures. This paper introduces Tensor-variate Restricted Boltzmann Machines (TvRBMs) which generalize RBMs to capture the multiplicative interaction between data modes and the latent variables. TvRBMs are highly compact in that the number of free parameters grows only linear with the number of modes. We demonstrate the capacity of TvRBMs on three real-world applications: handwritten digit classification, face recognition and EEG-based alcoholic diagnosis. The learnt features of the model are more discriminative than the rivals, resulting in better classification performance.

This paper is concerned with model-based clustering of discrete data. Latent class models (LCMs) are usually used for the task. An LCM consists of a latent variable and a number of attributes. It makes the overly restrictive assumption that the attributes are mutually independent given the latent variable. We propose a novel method to relax the assumption. The key idea is to partition the attributes into groups such that correlations among the attributes in each group can be properly modeled by using one single latent variable. The latent variables for the attribute groups are then used to build a number of models and one of them is chosen to produce the clustering results. Extensive empirical studies have been conducted to compare the new method with LCM and several other methods (K-means, kernel K-means and spectral clustering) that are not model-based. The new method outperforms the alternative methods in most cases and the differences are often large.

Many real-world Bayesian inference problems such as preference learning or trader valuation modeling in financial markets naturally use piecewise likelihoods. Unfortunately, exact closed-form inference in the underlying Bayesian graphical models is intractable in the general case and existing approximation techniques provide few guarantees on both approximation quality and efficiency. While (Markov Chain) Monte Carlo methods provide an attractive asymptotically unbiased approximation approach, rejection sampling and Metropolis-Hastings both prove inefficient in practice, and analytical derivation of Gibbs samplers require exponential space and time in the amount of data. In this work, we show how to transform problematic piecewise likelihoods into equivalent mixture models and then provide a blocked Gibbs sampling approach for this transformed model that achieves an exponential-to-linear reduction in space and time compared to a conventional Gibbs sampler. This enables fast, asymptotically unbiased Bayesian inference in a new expressive class of piecewise graphical models and empirically requires orders of magnitude less time than rejection, Metropolis-Hastings, and conventional Gibbs sampling methods to achieve the same level of accuracy.

Microblog sentiment classification is an important research topic which has wide applications in both academia and industry. Because microblog messages are short, noisy and contain masses of acronyms and informal words, microblog sentiment classification is a very challenging task. Fortunately, collectively the contextual information about these idiosyncratic words provide knowledge about their sentiment orientations. In this paper, we propose to use the microblogs' contextual knowledge mined from a large amount of unlabeled data to help improve microblog sentiment classification. We define two kinds of contextual knowledge: word-word association and word-sentiment association. The contextual knowledge is formulated as regularization terms in supervised learning algorithms. An efficient optimization procedure is proposed to learn the model. Experimental results on benchmark datasets show that our method can consistently and significantly outperform the state-of-the-art methods.

Most Relevant Explanation (MRE) is a new inference task in Bayesian networks that finds the most relevant partial instantiation of target variables as an explanation for given evidence by maximizing the Generalized Bayes Factor (GBF). No exact algorithm has been developed for solving MRE previously. This paper fills the void and introduces a breadth-first branch-and-bound MRE algorithm based on a novel upper bound on GBF. The bound is calculated by decomposing the computation of the score to a set of Markov blankets of subsets of evidence variables. Our empirical evaluations show that the proposed algorithm scales up exact MRE inference significantly.

Individual mood is important for physical and emotional well-being, creativity and working memory. However, due to the lack of long-term real tracking daily data in individual level, most current works focus their efforts on population level and short-term small group. An ignored yet important task is to find the sentiment spreading mechanism in individual level from their daily behavior data. This paper studies this task by raising the following fundamental and summarization question, being not sufficiently answered by the literature so far:Given a social network, how the sentiment spread? The current individual-level network spreading models always assume one can infect others only when he/she has been infected. Considering the negative emotion spreading characters in individual level, we loose this assumption, and give an individual negative emotion spreading model. In this paper, we propose a Graph-Coupled Hidden Markov Sentiment Model for modeling the propagation of infectious negative sentiment locally within a social network. Taking the MIT Social Evolution dataset as an example, the experimental results verify the efficacy of our techniques on real-world data.

Planning in large partially observable Markov decision processes (POMDPs) is challenging especially when a long planning horizon is required. A few recent algorithms successfully tackle this case but at the expense of a weaker information-gathering capacity. In this paper, we propose Information Gathering and Reward Exploitation of Subgoals (IGRES), a randomized POMDP planning algorithm that leverages information in the state space to automatically generate "macro-actions" to tackle tasks with long planning horizons, while locally exploring the belief space to allow effective information gathering. Experimental results show that IGRES is an effective multi-purpose POMDP solver, providing state-of-the-art performance for both long horizon planning tasks and information-gathering tasks on benchmark domains. Additional experiments with an ecological adaptive management problem indicate that IGRES is a promising tool for POMDP planning in real-world settings.