We propose to solve the combinatorial problem of finding the highest scoring Bayesian network structure from data. This structure learning problem can be viewed as an inference problem where the variables specify the choice of parents for each node in the graph. The key combinatorial difficulty arises from the global constraint that the graph structure has to be acyclic. We cast the structure learning problem as a linear program over the polytope defined by valid acyclic structures. In relaxing this problem, we maintain an outer bound approximation to the polytope and iteratively tighten it by searching over a new class of valid constraints. If an integral solution is found, it is guaranteed to be the optimal Bayesian network. When the relaxation is not tight, the fast dual algorithms we develop remain useful in combination with a branch and bound method. Empirical results suggest that the method is competitive or faster than alternative exact methods based on dynamic programming. 1

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In recent years, advances in science and low-cost permanent storage have resulted in the availability of massive data sets. Together with advances in machine learning, this data has the potential to lead to many new breakthroughs. For example, high-throughput genomic and proteomic experiments can be used to enable personalized medicine. Large data sets of search queries can be used to improve information retrieval. Historical climate data can be used to understand global warming and to better predict weather. However, to take full advantage of this data, we need models that are capable of explaining the data, and algorithms that can use the models to make predictions about the future. The goal of my research is to develop theory and practical algorithms for learning and probabilistic inference in very large statistical models. My research focuses on a class of statistical models called graphical models that describe multivariate probability distributions. 1 Graphical models provide a useful abstraction for quantifying uncertainty, describing complex dependencies in data while making the model’s structure explicit so that it can be exploited by algorithms. These models have been widely applied across diverse fields such as statistical machine learning, computational biology, statistical physics, communication theory, and information retrieval.

Bayesian networks have been widely used for diagnostics. These models can be extended to POMDPs to select the best action. This allows modeling partial observability due to causes and the utility of executing various tests. We describe the problem of refining diagnostic POMDPs when user feedback is available. We propose utilizing user feedback to pose constraints on the model, i.e., the transition, observation and reward functions. These constraints can then be used to efficiently learn the POMDP model and incorporate expert knowledge about the problem.

This paper formulates learning optimal Bayesian network as a shortest path finding problem. An A* search algorithm is introduced to solve the problem. With the guidance of a consistent heuristic, the algorithm learns an optimal Bayesian network by only searching the most promising parts of the solution space. Empirical results show that the A* search algorithm significantly improves the time and space efficiency of existing methods on a set of benchmark datasets. 1