This paper presents a sound and completecalculus for causal relevance, based onPearl's functional models semantics.The calculus consists of axioms and rulesof inference for reasoning about causalrelevance relationships.We extend the set of known axioms for causalrelevance with three new axioms, andintroduce two new rules of inference forreasoning about specific subclasses ofmodels.These subclasses give a more refinedcharacterization of causal models than the one given in Halpern's axiomatizationof counterfactual reasoning.Finally, we show how the calculus for causalrelevance can be used in the task ofidentifying causal structure from non-observational data.

This article deals with plausible reasoning from incomplete knowledge about large-scale spatial properties. The availableinformation, consisting of a set of pointwise observations,is extrapolated to neighbour points. We make use of belief functions to represent the influence of the knowledge at a given point to another point; the quantitative strength of this influence decreases when the distance between both points increases. These influences arethen aggregated using a variant of Dempster's rule of combination which takes into account the relative dependence between observations.

Automatic continuous speech recognition (CSR) is sufficiently mature that a variety of real world applications are now possible including large vocabulary transcription and interactive spoken dialogues. This paper reviews the evolution of the statistical modelling techniques which underlie current-day systems, specifically hidden Markov models (HMMs) and N-grams. Starting from a description of the speech signal and its parameterisation, the various modelling assumptions and their consequences are discussed. It then describes various techniques by which the effects of these assumptions can be mitigated. Despite the progress that has been made, the limitations of current modelling techniques are still evident. The paper therefore concludes with a brief review of some of the more fundamental modelling work now in progress.

This paper presents a new deterministic approximation technique in Bayesian networks. This method, "Expectation Propagation", unifies two previous techniques: assumed-density filtering, an extension of the Kalman filter, and loopy belief propagation, an extension of belief propagation in Bayesian networks. All three algorithms try to recover an approximate distribution which is close in KL divergence to the true distribution. Loopy belief propagation, because it propagates exact belief states, is useful for a limited class of belief networks, such as those which are purely discrete. Expectation Propagation approximates the belief states by only retaining certain expectations, such as mean and variance, and iterates until these expectations are consistent throughout the network. This makes it applicable to hybrid networks with discrete and continuous nodes. Expectation Propagation also extends belief propagation in the opposite direction - it can propagate richer belief states that incorporate correlations between nodes. Experiments with Gaussian mixture models show Expectation Propagation to be convincingly better than methods with similar computational cost: Laplace's method, variational Bayes, and Monte Carlo. Expectation Propagation also provides an efficient algorithm for training Bayes point machine classifiers.

An instrument is a random variable thatallows the identification of parameters inlinear models when the error terms arenot uncorrelated.It is a popular method used in economicsand the social sciences that reduces theproblem of identification to the problemof finding the appropriate instruments.Few years ago, Pearl introduced a necessarytest for instruments that allows the researcher to discard those candidatesthat fail the test.In this paper, we make a detailed study of Pearl's test and the general model forinstruments. The results of this studyinclude a novel interpretation of Pearl'stest, a general theory of instrumentaltests, and an affirmative answer to aprevious conjecture. We also presentnew instrumentality tests for the casesof discrete and continuous variables.

This volume contains the papers presented at the fifth workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP 2012) held on September 4th, 2012 in Budapest, co-located with the 28th International Conference on Logic Programming (ICLP 2012). It thus continues a series of previous events co-located with ICLP, aiming at facilitating the discussion about crossing the boundaries of current ASP techniques in theory, solving, and applications, in combination with or inspired by other computing paradigms.

Chow and Liu (1968) studied the problem of learning a maximumlikelihood Markov tree. We generalize their work to more complexMarkov networks by considering the problem of learning a maximumlikelihood Markov network of bounded complexity. We discuss howtree-width is in many ways the appropriate measure of complexity andthus analyze the problem of learning a maximum likelihood Markovnetwork of bounded tree-width.Similar to the work of Chow and Liu, we are able to formalize thelearning problem as a combinatorial optimization problem on graphs. Weshow that learning a maximum likelihood Markov network of boundedtree-width is equivalent to finding a maximum weight hypertree. Thisequivalence gives rise to global, integer-programming based,approximation algorithms with provable performance guarantees, for thelearning problem. This contrasts with heuristic local-searchalgorithms which were previously suggested (e.g. by Malvestuto 1991).The equivalence also allows us to study the computational hardness ofthe learning problem. We show that learning a maximum likelihoodMarkov network of bounded tree-width is NP-hard, and discuss thehardness of approximation.

Planning problems are hard, motion planning, for example, isPSPACE-hard. Such problems are even more difficult in the presence of uncertainty. Although, Markov Decision Processes (MDPs) provide a formal framework for such problems, finding solutions to high dimensional continuous MDPs is usually difficult, especially when the actions and time measurements are continuous. Fortunately, problem-specific knowledge allows us to design controllers that are good locally, though having no global guarantees. We propose a method of nonparametrically combining local controllers to obtain globally good solutions. We apply this formulation to two types of problems : motion planning (stochastic shortest path) and discounted MDPs. For motion planning, we argue that usual MDP optimality criterion (expected cost) may not be practically relevant. Wepropose an alternative: finding the minimum cost path,subject to the constraint that the robot must reach the goal withhigh probability. For this problem, we prove that a polynomial number of samples is sufficient to obtain a high probability path. For discounted MDPs, we propose a formulation that explicitly deals with model uncertainty, i.e., the problem introduced when transition probabilities are not known exactly. We formulate the problem as a robust linear program which directly incorporates this type of uncertainty.

In this paper we present a method ofcomputing the posterior probability ofconditional independence of two or morecontinuous variables from data,examined at several resolutions. Ourapproach is motivated by theobservation that the appearance ofcontinuous data varies widely atvarious resolutions, producing verydifferent independence estimatesbetween the variablesinvolved. Therefore, it is difficultto ascertain independence withoutexamining data at several carefullyselected resolutions. In our paper, weaccomplish this using the exactcomputation of the posteriorprobability of independence, calculatedanalytically given a resolution. Ateach examined resolution, we assume amultinomial distribution with Dirichletpriors for the discretized tableparameters, and compute the posteriorusing Bayesian integration. Acrossresolutions, we use a search procedureto approximate the Bayesian integral ofprobability over an exponential numberof possible histograms. Our methodgeneralizes to an arbitrary numbervariables in a straightforward manner.The test is suitable for Bayesiannetwork learning algorithms that useindependence tests to infer the networkstructure, in domains that contain anymix of continuous, ordinal andcategorical variables.

We treat collaborative filtering as a univariate time series estimation problem: given a user's previous votes, predict the next vote. We describe two families of methods for transforming data to encode time order in ways amenable to off-the-shelf classification and density estimation tools, and examine the results of using these approaches on several real-world data sets. The improvements in predictive accuracy we realize recommend the use of other predictive algorithms that exploit the temporal order of data.