The paper presents an iterative version of join-tree clustering that applies the message passing of join-tree clustering algorithm to join-graphs rather than to join-trees, iteratively. It is inspired by the success of Pearl's belief propagation algorithm as an iterative approximation scheme on one hand, and by a recently introduced mini-clustering i. success as an anytime approximation method, on the other. The proposed Iterative Join-graph Propagation IJGP belongs to the class of generalized belief propagation methods, recently proposed using analogy with algorithms in statistical physics. Empirical evaluation of this approach on a number of problem classes demonstrates that even the most time-efficient variant is almost always superior to IBP and MC i, and is sometimes more accurate by as much as several orders of magnitude.

Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such models can be very computationally expensive when there are many datapoints and many continuous variables with complex nonlinear relationships, particularly when no good ways of decomposing the joint distribution are known a priori. In such situations, previous research has generally focused on the use of discretization techniques in which each continuous variable has a single discretization that is used throughout the entire network. \ In this paper, we present and compare a wide variety of tree-based algorithms for learning and evaluating conditional density estimates over continuous variables. These trees can be thought of as discretizations that vary according to the particular interactions being modeled; however, the density within a given leaf of the tree need not be assumed constant, and we show that such nonuniform leaf densities lead to more accurate density estimation. We have developed Bayesian network structure-learning algorithms that employ these tree-based conditional density representations, and we show that they can be used to practically learn complex joint probability models over dozens of continuous variables from thousands of datapoints. We focus on finding models that are simultaneously accurate, fast to learn, and fast to evaluate once they are learned.

The problem of learning Markov equivalence classes of Bayesian network structures may be solved by searching for the maximum of a scoring metric in a space of these classes. This paper deals with the definition and analysis of one such search space. We use a theoretically motivated neighbourhood, the inclusion boundary, and represent equivalence classes by essential graphs. We show that this search space is connected and that the score of the neighbours can be evaluated incrementally. We devise a practical way of building this neighbourhood for an essential graph that is purely graphical and does not explicitely refer to the underlying independences. We find that its size can be intractable, depending on the complexity of the essential graph of the equivalence class. The emphasis is put on the potential use of this space with greedy hill -climbing search

We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this paper, we pose it as a combinatorial optimization problem, which is then relaxed to a convex optimization problem that involves searching over the forest and hyperforest polytopes with special structures, independently. A supergradient method is used to solve the dual problem, with a run-time complexity of $O(k^3 n^{k+2} \log n)$ for each iteration, where $n$ is the number of variables and $k$ is a bound on the treewidth. We compare our approach to state-of-the-art methods on synthetic datasets and classical benchmarks, showing the gains of the novel convex approach.

In machine learning, Domain Adaptation (DA) arises when the distribution gen- erating the test (target) data differs from the one generating the learning (source) data. It is well known that DA is an hard task even under strong assumptions, among which the covariate-shift where the source and target distributions diverge only in their marginals, i.e. they have the same labeling function. Another popular approach is to consider an hypothesis class that moves closer the two distributions while implying a low-error for both tasks. This is a VC-dim approach that restricts the complexity of an hypothesis class in order to get good generalization. Instead, we propose a PAC-Bayesian approach that seeks for suitable weights to be given to each hypothesis in order to build a majority vote. We prove a new DA bound in the PAC-Bayesian context. This leads us to design the first DA-PAC-Bayesian algorithm based on the minimization of the proposed bound. Doing so, we seek for a \rho-weighted majority vote that takes into account a trade-off between three quantities. The first two quantities being, as usual in the PAC-Bayesian approach, (a) the complexity of the majority vote (measured by a Kullback-Leibler divergence) and (b) its empirical risk (measured by the \rho-average errors on the source sample). The third quantity is (c) the capacity of the majority vote to distinguish some structural difference between the source and target samples.

Machine Learning manuscript No. (will be inserted by the editor) Abstract This paper considers the challenge of evaluating a set of classifiers, as done in shared task evaluations like the KDD Cup or NIST TREC, without expert labels. While expert labels provide the traditional cornerstone for evaluating statistical learners, limited or expensive access to experts represents a practical bottleneck. Instead, we seek methodology for estimating performance of the classifiers (relative and absolute) which is more scalable than expert labeling yet preserves high correlation with evaluation based on expert labels. We consider both: 1) using only labels automatically generated by the classifiers themselves (blind evaluation); and 2) using labels obtained via crowdsourcing. While crowdsourcing methods are lauded for scalability, using such data for evaluation raises serious concerns given the prevalence of label noise. In regard to blind evaluation, two broad strategies are investigated: combine & score and score & combine. Combine & Score methods infer a single "pseudo-gold" label set by aggregating classifier labels; classifiers are then evaluated based on this single pseudo-gold label set. On the other hand, score & combine methods: i) sample multiple label sets from classifier outputs, ii) evaluate classifiers on each label set, and iii) average classifier performance across label sets. When additional crowd labels are also collected, we investigate two alternative avenues for exploiting them: 1) direct evaluation of classifiers; or 2) supervision of combine-and-score methods. To assess generality of our techniques, classifier performance is measured using four common classification metrics, with statistical significance tests establishing relative performance of the classifiers for each metric. Finally, we measure both score and rank correlations between estimated classifier performance vs. actual performance according to expert judgments. Rigorous evaluation of classifiers from the TREC 2011 Crowdsourcing Track shows reliable evaluation can be achieved without reliance on expert labels.

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters. Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter estimation problems arising in detailed combustion kinetics.

We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the structure of a Markov decision process. Adopting a Bayesian approach to inference, we show how latent variables of the model can be estimated, and how predictions about actions can be made, in a unified framework. A new Markov chain Monte Carlo (MCMC) sampler is devised for simulation from the posterior distribution. This step includes a parameter expansion step, which is shown to be essential for good convergence properties of the MCMC sampler. As an illustration, the method is applied to learning a human controller.

We apply the spike-and-slab Restricted Boltzmann Machine (ssRBM) to texture modeling. The ssRBM with tiled-convolution weight sharing (TssRBM) achieves or surpasses the state-of-the-art on texture synthesis and inpainting by parametric models. We also develop a novel RBM model with a spike-and-slab visible layer and binary variables in the hidden layer. This model is designed to be stacked on top of the TssRBM. We show the resulting deep belief network (DBN) is a powerful generative model that improves on single-layer models and is capable of modeling not only single high-resolution and challenging textures but also multiple textures.

Structure learning of Bayesian networks is an important problem that arises in numerous machine learning applications. In this work, we present a novel approach for learning the structure of Bayesian networks using the solution of an appropriately constructed traveling salesman problem. In our approach, one computes an optimal ordering (partially ordered set) of random variables using methods for the traveling salesman problem. This ordering significantly reduces the search space for the subsequent greedy optimization that computes the final structure of the Bayesian network. We demonstrate our approach of learning Bayesian networks on real world census and weather datasets. In both cases, we demonstrate that the approach very accurately captures dependencies between random variables. We check the accuracy of the predictions based on independent studies in both application domains.