Markov networks (MNs) are a powerful way to compactly represent a joint probability distribution, but most MN structure learning methods are very slow, due to the high cost of evaluating candidates structures. Dependency networks (DNs) represent a probability distribution as a set of conditional probability distributions. DNs are very fast to learn, but the conditional distributions may be inconsistent with each other and few inference algorithms support DNs. In this paper, we present a closed-form method for converting a DN into an MN, allowing us to enjoy both the efficiency of DN learning and the convenience of the MN representation. When the DN is consistent, this conversion is exact. For inconsistent DNs, we present averaging methods that significantly improve the approximation. In experiments on 12 standard datasets, our methods are orders of magnitude faster than and often more accurate than combining conditional distributions using weight learning.

Latent variable models are an elegant framework for capturing rich probabilistic dependencies in many applications. However, current approaches typically parametrize these models using conditional probability tables, and learning relies predominantly on local search heuristics such as Expectation Maximization. Using tensor algebra, we propose an alternative parameterization of latent variable models (where the model structures are junction trees) that still allows for computation of marginals among observed variables. While this novel representation leads to a moderate increase in the number of parameters for junction trees of low treewidth, it lets us design a local-minimum-free algorithm for learning this parameterization. The main computation of the algorithm involves only tensor operations and SVDs which can be orders of magnitude faster than EM algorithms for large datasets. To our knowledge, this is the first provably consistent parameter learning technique for a large class of low-treewidth latent graphical models beyond trees. We demonstrate the advantages of our method on synthetic and real datasets.

Recently two search algorithms, A* and breadth-first branch and bound (BFBnB), were developed based on a simple admissible heuristic for learning Bayesian network structures that optimize a scoring function. The heuristic represents a relaxation of the learning problem such that each variable chooses optimal parents independently. As a result, the heuristic may contain many directed cycles and result in a loose bound. This paper introduces an improved admissible heuristic that tries to avoid directed cycles within small groups of variables. A sparse representation is also introduced to store only the unique optimal parent choices. Empirical results show that the new techniques significantly improved the efficiency and scalability of A* and BFBnB on most of datasets tested in this paper.

Multi-modal data collections, such as corpora of paired images and text snippets, require analysis methods beyond single-view component and topic models. For continuous observations the current dominant approach is based on extensions of canonical correlation analysis, factorizing the variation into components shared by the different modalities and those private to each of them. For count data, multiple variants of topic models attempting to tie the modalities together have been presented. All of these, however, lack the ability to learn components private to one modality, and consequently will try to force dependencies even between minimally correlating modalities. In this work we combine the two approaches by presenting a novel HDP-based topic model that automatically learns both shared and private topics. The model is shown to be especially useful for querying the contents of one domain given samples of the other.

Understanding the adaptation process of plants to drought stress is essential in improving management practices, breeding strategies as well as engineering viable crops for a sustainable agriculture in the coming decades. Hyper-spectral imaging provides a particularly promising approach to gain such understanding since it allows to discover non-destructively spectral characteristics of plants governed primarily by scattering and absorption characteristics of the leaf internal structure and biochemical constituents. Several drought stress indices have been derived using hyper-spectral imaging. However, they are typically based on few hyper-spectral images only, rely on interpretations of experts, and consider few wavelengths only. In this study, we present the first data-driven approach to discovering spectral drought stress indices, treating it as an unsupervised labeling problem at massive scale. To make use of short range dependencies of spectral wavelengths, we develop an online variational Bayes algorithm for latent Dirichlet allocation with convolved Dirichlet regularizer. This approach scales to massive datasets and, hence, provides a more objective complement to plant physiological practices. The spectral topics found conform to plant physiological knowledge and can be computed in a fraction of the time compared to existing LDA approaches.

We describe theoretical bounds and a practical algorithm for teaching a model by demonstration in a sequential decision making environment. Unlike previous efforts that have optimized learners that watch a teacher demonstrate a static policy, we focus on the teacher as a decision maker who can dynamically choose different policies to teach different parts of the environment. We develop several teaching frameworks based on previously defined supervised protocols, such as Teaching Dimension, extending them to handle noise and sequences of inputs encountered in an MDP. We provide theoretical bounds on the learnability of several important model classes in this setting and suggest a practical algorithm for dynamic teaching.

In practical machine learning systems, graph based data representation has been widely used in various learning paradigms, ranging from unsupervised clustering to supervised classification. Besides those applications with natural graph or network structure data, such as social network analysis and relational learning, many other applications often involve a critical step in converting data vectors to an adjacency graph. In particular, a sparse subgraph extracted from the original graph is often required due to both theoretic and practical needs. Previous study clearly shows that the performance of different learning algorithms, e.g., clustering and classification, benefits from such sparse subgraphs with balanced node connectivity. However, the existing graph construction methods are either computationally expensive or with unsatisfactory performance. In this paper, we utilize a scalable method called auction algorithm and its parallel extension to recover a sparse yet nearly balanced subgraph with significantly reduced computational cost. Empirical study and comparison with the stateof-art approaches clearly demonstrate the superiority of the proposed method in both efficiency and accuracy.

Many latent (factorized) models have been proposed for recommendation tasks like collaborative filtering and for ranking tasks like document or image retrieval and annotation. Common to all those methods is that during inference the items are scored independently by their similarity to the query in the latent embedding space. The structure of the ranked list (i.e. considering the set of items returned as a whole) is not taken into account. This can be a problem because the set of top predictions can be either too diverse (contain results that contradict each other) or are not diverse enough. In this paper we introduce a method for learning latent structured rankings that improves over existing methods by providing the right blend of predictions at the top of the ranked list. Particular emphasis is put on making this method scalable. Empirical results on large scale image annotation and music recommendation tasks show improvements over existing approaches.

EDML is a recently proposed algorithm for learning MAP parameters in Bayesian networks. In this paper, we present a number of new advances and insights on the EDML algorithm. First, we provide the multivalued extension of EDML, originally proposed for Bayesian networks over binary variables. Next, we identify a simplified characterization of EDML that further implies a simple fixed-point algorithm for the convex optimization problem that underlies it. This characterization further reveals a connection between EDML and EM: a fixed point of EDML is a fixed point of EM, and vice versa. We thus identify also a new characterization of EM fixed points, but in the semantics of EDML. Finally, we propose a hybrid EDML/EM algorithm that takes advantage of the improved empirical convergence behavior of EDML, while maintaining the monotonic improvement property of EM.

Active Learning (AL) is increasingly important in a broad range of applications. Two main AL principles to obtain accurate classification with few labeled data are refinement of the current decision boundary and exploration of poorly sampled regions. In this paper we derive a novel AL scheme that balances these two principles in a natural way. In contrast to many AL strategies, which are based on an estimated class conditional probability ^p(y|x), a key component of our approach is to view this quantity as a random variable, hence explicitly considering the uncertainty in its estimated value. Our main contribution is a novel mathematical framework for uncertainty-based AL, and a corresponding AL scheme, where the uncertainty in ^p(y|x) is modeled by a second-order distribution. On the practical side, we show how to approximate such second-order distributions for kernel density classification. Finally, we find that over a large number of UCI, USPS and Caltech4 datasets, our AL scheme achieves significantly better learning curves than popular AL methods such as uncertainty sampling and error reduction sampling, when all use the same kernel density classifier.