The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises log marginal likelihood (BDe score). Integer programming, specifically the SCIP framework, is used to solve this optimisation problem. Acyclicity constraints are added to the integer program (IP) during solving in the form of cutting planes. Finding good cutting planes is the key to the success of the approach -the search for such cutting planes is effected using a sub-IP. Results show that this is a particularly fast method for exact BN learning.

We propose a method called EDML for learning MAP parameters in binary Bayesian networks under incomplete data. The method assumes Beta priors and can be used to learn maximum likelihood parameters when the priors are uninformative. EDML exhibits interesting behaviors, especially when compared to EM. We introduce EDML, explain its origin, and study some of its properties both analytically and empirically.

Hierarchical problem abstraction, when applicable, may offer exponential reductions in computational complexity. Previous work on coarse-to-fine dynamic programming (CFDP) has demonstrated this possibility using state abstraction to speed up the Viterbi algorithm. In this paper, we show how to apply temporal abstraction to the Viterbi problem. Our algorithm uses bounds derived from analysis of coarse timescales to prune large parts of the state trellis at finer timescales. We demonstrate improvements of several orders of magnitude over the standard Viterbi algorithm, as well as significant speedups over CFDP, for problems whose state variables evolve at widely differing rates.

Potential games and decentralised partially observable MDPs (Dec-POMDPs) are two commonly used models of multi-agent interaction, for static optimisation and sequential decisionmaking settings, respectively. In this paper we introduce filtered fictitious play for solving repeated potential games in which each player's observations of others' actions are perturbed by random noise, and use this algorithm to construct an online learning method for solving Dec-POMDPs. Specifically, we prove that noise in observations prevents standard fictitious play from converging to Nash equilibrium in potential games, which also makes fictitious play impractical for solving Dec-POMDPs. To combat this, we derive filtered fictitious play, and provide conditions under which it converges to a Nash equilibrium in potential games with noisy observations. We then use filtered fictitious play to construct a solver for Dec-POMDPs, and demonstrate our new algorithm's performance in a box pushing problem. Our results show that we consistently outperform the state-of-the-art Dec-POMDP solver by an average of 100% across the range of noise in the observation function.

We consider filtering for a continuous-time, or asynchronous, stochastic system where the full distribution over states is too large to be stored or calculated. We assume that the rate matrix of the system can be compactly represented and that the belief distribution is to be approximated as a product of marginals. The essential computation is the matrix exponential. We look at two different methods for its computation: ODE integration and uniformization of the Taylor expansion. For both we consider approximations in which only a factored belief state is maintained. For factored uniformization we demonstrate that the KL-divergence of the filtering is bounded. Our experimental results confirm our factored uniformization performs better than previously suggested uniformization methods and the mean field algorithm.

Bayes-optimal behavior, while well-defined, is often difficult to achieve. Recent advances in the use of Monte-Carlo tree search (MCTS) have shown that it is possible to act near-optimally in Markov Decision Processes (MDPs) with very large or infinite state spaces. Bayes-optimal behavior in an unknown MDP is equivalent to optimal behavior in the known belief-space MDP, although the size of this belief-space MDP grows exponentially with the amount of history retained, and is potentially infinite. We show how an agent can use one particular MCTS algorithm, Forward Search Sparse Sampling (FSSS), in an efficient way to act nearly Bayes-optimally for all but a polynomial number of steps, assuming that FSSS can be used to act efficiently in any possible underlying MDP.

Concept Relation Discovery and Innovation Enabling Technology (CORDIET), is a toolbox for gaining new knowledge from unstructured text data. At the core of CORDIET is the C-K theory which captures the essential elements of innovation. The tool uses Formal Concept Analysis (FCA), Emergent Self Organizing Maps (ESOM) and Hidden Markov Models (HMM) as main artifacts in the analysis process. The user can define temporal, text mining and compound attributes. The text mining attributes are used to analyze the unstructured text in documents, the temporal attributes use these document's timestamps for analysis. The compound attributes are XML rules based on text mining and temporal attributes. The user can cluster objects with object-cluster rules and can chop the data in pieces with segmentation rules. The artifacts are optimized for efficient data analysis; object labels in the FCA lattice and ESOM map contain an URL on which the user can click to open the selected document.

Successful analysis of video data requires an integration of techniques from KR, Computer Vision, and Machine Learning. Being able to detect and to track objects as well as extracting their changing spatial relations with other objects is one approach to describing and detecting events. Different kinds of spatial relations are important, including topology, direction, size, and distance between objects as well as changes of those relations over time. Typically these kinds of relations are treated separately, which makes it difficult to integrate all the extracted spatial information. We present a uniform and comprehensive spatial representation of moving objects that includes all the above spatial/temporal aspects, analyse different properties of this representation and demonstrate that it is suitable for video analysis.

This paper presents an axiomatic framework for influence diagram computation, which allows reasoning with partially ordered values of utility. We show how an algorithm based on sequential variable elimination can be used to compute the set of maximal values of expected utility (up to an equivalence relation). Formalisms subsumed by the framework include decision making under uncertainty based on multi-objective utility, or on interval-valued utilities, as well as a more qualitative decision theory based on order-of-magnitude probabilities and utilities.

We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that produce the largest reduction in empirical conditional entropy; it is greedy in the sense that the choice of addition is based only on the reduction achieved at that iteration. Its sequential nature gives it a lower computational complexity as compared to other existing comparison-based techniques, all of which involve exhaustive searches over every node set of a certain size. Our main result characterizes the sample complexity of this procedure, as a function of node degrees, graph size and girth in factor-graph representation. We subsequently specialize this result to the case of Ising models, where we provide a simple transparent characterization of sample complexity as a function of model and graph parameters. For tree graphs, our algorithm is the same as the classical Chow-Liu algorithm, and in that sense can be considered the extension of the same to graphs with cycles.