Recent work in the field of probabilistic inference demonstrated the efficiency of weighted model counting (WMC) enginesfor exact inference in propositional and, very recently, first order models. To date, these methods have not been applied to decision making models, propositional or first order, such as influence diagrams, and Markov decision networks (MDN). In this paper we show how this technique can be applied to such models. First, we show how WMC can be used to solve (propositional) MDNs. Then, we show how this can be extended to handle a first-order model — the Markov Logic Decision Network (MLDN). WMC offers two central benefits: it is a very simple and very efficient technique. This is particularly true for the first-order case, where the WMC approach is simpler conceptually, and, in many cases, more effective computationally than the existing methods for solving MLDNs via first-order variable elimination, or via propositionalization. We demonstrate the above empirically.

Sound source localization and separation with permutation resolution are essential for achieving a computational auditory scene analysis system that can extract useful information from a mixture of various sounds. Because existing methods cope separately with these problems despite their mutual dependence, the overall result with these approaches can be degraded by any failure in one of these components. This paper presents a unified Bayesian framework to solve these problems simultaneously where localization and separation are regarded as a clustering problem. Experimental results confirm that our method outperforms state-of-the-art methods in terms of the separation quality with various setups including practical reverberant environments.

A key problem in climate science is how to combine the predictions of the multi-model ensemble of global climate models. Recent work in machine learning (Monteleoni et al. 2011) showed the promise of an algorithm for online learning with experts for this task.We extend the Tracking Climate Models (TCM) approach to (1) take into account climate model predictions at higher spatial resolutions and (2) to model geospatial neighborhood influence between regions. Our algorithm enables neighborhood influence by modifying the transition dynamics of the Hidden Markov Model used by TCM, allowing the performance of spatial neighbors to influence the temporal switching probabilities for the best expert (climate model) at a given location. In experiments on historical data at a variety of spatial resolutions, our algorithm demonstrates improvements over TCM, when tracking global temperature anomalies.

Common spatial patterns (CSP) is a popular feature extraction method for discriminating between positive andnegative classes in electroencephalography (EEG) data.Two probabilistic models for CSP were recently developed: probabilistic CSP (PCSP), which is trained by expectation maximization (EM), and variational BayesianCSP (VBCSP) which is learned by variational approx-imation. Parameter expansion methods use auxiliaryparameters to speed up the convergence of EM or thedeterministic approximation of the target distributionin variational inference. In this paper, we describethe development of parameter-expanded algorithms forPCSP and VBCSP, leading to PCSP-PX and VBCSP-PX, whose convergence speed-up and high performanceare emphasized. The convergence speed-up in PCSP-PX and VBCSP-PX is a direct consequence of parame-ter expansion methods. The contribution of this study is the performance improvement in the case of CSP,which is a novel development. Numerical experimentson the BCI competition datasets, III IV a and IV 2ademonstrate the high performance and fast convergenceof PCSP-PX and VBCSP-PX, as compared to PCSP andVBCSP.

Inferring probabilistic networks from data is a notoriously difficult task. Under various goodness-of-fit measures, finding an optimal network is NP-hard, even if restricted to polytrees of bounded in-degree. Polynomial-time algorithms are known only for rare special cases, perhaps most notably for branchings, that is, polytrees in which the in-degree of every node is at most one. Here, we study the complexity of finding an optimal polytree that can be turned into a branching by deleting some number of arcs or nodes, treated as a parameter. We show that the problem can be solved via a matroid intersection formulation in polynomial time if the number of deleted arcs is bounded by a constant. The order of the polynomial time bound depends on this constant, hence the algorithm does not establish fixed-parameter tractability when parameterized by the number of deleted arcs. We show that a restricted version of the problem allows fixed-parameter tractability and hence scales well with the parameter. We contrast this positive result by showing that if we parameterize by the number of deleted nodes, a somewhat more powerful parameter, the problem is not fixed-parameter tractable, subject to a complexity-theoretic assumption.

We study the marginal-MAP problem on graphical models, and present a novel approximation method based on direct approximation of the sum operation. A primary difficulty of marginal-MAP problems lies in the non-commutativity of the sum and max operations, so that even in highly structured models, marginalization may produce a densely connected graph over the variables to be maximized, resulting in an intractable potential function with exponential size. We propose a chain decomposition approach for summing over the marginalized variables, in which we produce a structured approximation to the MAP component of the problem consisting of only pairwise potentials. We show that this approach is equivalent to the maximization of a specific variational free energy, and it provides an upper bound of the optimal probability. Finally, experimental results demonstrate that our method performs favorably compared to previous methods.

Many models of interest in the natural and social sciences have no closed-form likelihood function, which means that they cannot be treated using the usual techniques of statistical inference. In the case where such models can be efficiently simulated, Bayesian inference is still possible thanks to the Approximate Bayesian Computation (ABC) algorithm. Although many refinements have been suggested, ABC inference is still far from routine. ABC is often excruciatingly slow due to very low acceptance rates. In addition, ABC requires introducing a vector of "summary statistics", the choice of which is relatively arbitrary, and often require some trial and error, making the whole process quite laborious for the user. We introduce in this work the EP-ABC algorithm, which is an adaptation to the likelihood-free context of the variational approximation algorithm known as Expectation Propagation (Minka, 2001). The main advantage of EP-ABC is that it is faster by a few orders of magnitude than standard algorithms, while producing an overall approximation error which is typically negligible. A second advantage of EP-ABC is that it replaces the usual global ABC constraint on the vector of summary statistics computed on the whole dataset, by n local constraints of the form that apply separately to each data-point. As a consequence, it is often possible to do away with summary statistics entirely. In that case, EP-ABC approximates directly the evidence (marginal likelihood) of the model. Comparisons are performed in three real-world applications which are typical of likelihood-free inference, including one application in neuroscience which is novel, and possibly too challenging for standard ABC techniques.

We consider probabilistic multinomial probit classification using Gaussian process (GP) priors. The challenges with the multiclass GP classification are the integration over the non-Gaussian posterior distribution, and the increase of the number of unknown latent variables as the number of target classes grows. Expectation propagation (EP) has proven to be a very accurate method for approximate inference but the existing EP approaches for the multinomial probit GP classification rely on numerical quadratures or independence assumptions between the latent values from different classes to facilitate the computations. In this paper, we propose a novel nested EP approach which does not require numerical quadratures, and approximates accurately all between-class posterior dependencies of the latent values, but still scales linearly in the number of classes. The predictive accuracy of the nested EP approach is compared to Laplace, variational Bayes, and Markov chain Monte Carlo (MCMC) approximations with various benchmark data sets. In the experiments nested EP was the most consistent method with respect to MCMC sampling, but the differences between the compared methods were small if only the classification accuracy is concerned.

Images obtained with coherent illumination, as is the case of sonar, ultrasound-B, laser and Synthetic Aperture Radar -- SAR, are affected by speckle noise which reduces the ability to extract information from the data. Specialized techniques are required to deal with such imagery, which has been modeled by the G0 distribution and under which regions with different degrees of roughness and mean brightness can be characterized by two parameters; a third parameter, the number of looks, is related to the overall signal-to-noise ratio. Assessing distances between samples is an important step in image analysis; they provide grounds of the separability and, therefore, of the performance of classification procedures. This work derives and compares eight stochastic distances and assesses the performance of hypothesis tests that employ them and maximum likelihood estimation. We conclude that tests based on the triangular distance have the closest empirical size to the theoretical one, while those based on the arithmetic-geometric distances have the best power. Since the power of tests based on the triangular distance is close to optimum, we conclude that the safest choice is using this distance for hypothesis testing, even when compared with classical distances as Kullback-Leibler and Bhattacharyya.

Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization for representing continuous chance variables in influence diagrams. Also, MTE potentials can be used to approximate utility functions. This paper introduces MTE influence diagrams, which can represent decision problems without restrictions on the relationships between continuous and discrete chance variables, without limitations on the distributions of continuous chance variables, and without limitations on the nature of the utility functions. In MTE influence diagrams, all probability distributions and the joint utility function (or its multiplicative factors) are represented by MTE potentials and decision nodes are assumed to have discrete state spaces. MTE influence diagrams are solved by variable elimination using a fusion algorithm.