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.

The flourishing of online labor markets such as Amazon Mechanical Turk (MTurk) makes it easy to recruit many workers for solving small tasks. We study whether information elicitation and aggregation over a combinatorial space can be achieved by integrating small pieces of potentially imprecise information, gathered from a large number of workers through simple, one-shot interactions in an online labor market. We consider the setting of predicting the ranking of $n$ competing candidates, each having a hidden underlying strength parameter. At each step, our method estimates the strength parameters from the collected pairwise comparison data and adaptively chooses another pairwise comparison question for the next recruited worker. Through an MTurk experiment, we show that the adaptive method effectively elicits and aggregates information, outperforming a naive method using a random pairwise comparison question at each step.

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.

Tractable subsets of first-order logic are a central topic in AI research. Several of these formalisms have been used as the basis for first-order probabilistic languages. However, these are intractable, losing the original motivation. Here we propose the first non-trivially tractable first-order probabilistic language. It is a subset of Markov logic, and uses probabilistic class and part hierarchies to control complexity. We call it TML (Tractable Markov Logic). We show that TML knowledge bases allow for efficient inference even when the corresponding graphical models have very high treewidth. We also show how probabilistic inheritance, default reasoning, and other inference patterns can be carried out in TML. TML opens up the prospect of efficient large-scale first-order probabilistic inference.

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 present the concept of Bayesian Tool Affordances as a solution to estimate the suitable action for the given tool to realize the given novel effects to the robot. We define Tool affordances as the “awareness within robot about the different kind of effects it can create in the environment using a tool”. It incorporates understanding the bi-directional association of executed Action, functionally relevant features of the Tool and the resulting effects. We propose Bayesian leaning of Tool Affordances for prediction, inference and planning capabilities while dealing with uncertainty, redundancy and irrelevant information using limited learning samples. The estimation results are presented in this paper to validate the proposed concept of Bayesian Tool Affordances.

This paper presents a theoretical advance by which factored POSGs can be decomposed into local models. We formalize the interface between such local models as the influence agents can exert on one another; and we prove that this interface is sufficient for decoupling them. The resulting influence-based abstraction substantially generalizes previous work on exploiting weakly-coupled agent interaction structures. Therein lie several important contributions. First, our general formulation sheds new light on the theoretical relationships among previous approaches, and promotes future empirical comparisons that could come by extending them beyond the more specific problem contexts for which they were developed. More importantly, the influence-based approaches that we generalize have shown promising improvements in the scalability of planning for more restrictive models. Thus, our theoretical result here serves as the foundation for practical algorithms that we anticipate will bring similar improvements to more general planning contexts, and also into other domains such as approximate planning, decision-making in adversarial domains, and online learning.

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.