Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose transition model is a function of its parents. We address the problem of learning parameters and structure of a CTBN from fully observed data. We define a conjugate prior for CTBNs, and show how it can be used both for Bayesian parameter estimation and as the basis of a Bayesian score for structure learning. Because acyclicity is not a constraint in CTBNs, we can show that the structure learning problem is significantly easier, both in theory and in practice, than structure learning for dynamic Bayesian networks (DBNs). Furthermore, as CTBNs can tailor the parameters and dependency structure to the different time granularities of the evolution of different variables, they can provide a better fit to continuous-time processes than DBNs with a fixed time granularity.

Frequently, acquiring training data has an associated cost. We consider the situation where the learner may purchase data during training, subject TO a budget. IN particular, we examine the CASE WHERE each feature label has an associated cost, AND the total cost OF ALL feature labels acquired during training must NOT exceed the budget.This paper compares methods FOR choosing which feature label TO purchase next, given the budget AND the CURRENT belief state OF naive Bayes model parameters.Whereas active learning has traditionally focused ON myopic(greedy) strategies FOR query selection, this paper presents a tractable method FOR incorporating knowledge OF the budget INTO the decision making process, which improves performance.

Bayesian networks are now being used in enormous fields, for example, diagnosis of a system, data mining, clustering and so on. In spite of their wide range of applications, the statistical properties have not yet been clarified, because the models are nonidentifiable and non-regular. In a Bayesian network, the set of its parameter for a smaller model is an analytic set with singularities in the space of large ones. Because of these singularities, the Fisher information matrices are not positive definite. In other words, the mathematical foundation for learning was not constructed. In recent years, however, we have developed a method to analyze non-regular models using algebraic geometry. This method revealed the relation between the models singularities and its statistical properties. In this paper, applying this method to Bayesian networks with latent variables, we clarify the order of the stochastic complexities.Our result claims that the upper bound of those is smaller than the dimension of the parameter space. This means that the Bayesian generalization error is also far smaller than that of regular model, and that Schwarzs model selection criterion BIC needs to be improved for Bayesian networks.

The mean field methods, which entail approximating intractable probability distributions variationally with distributions from a tractable family, enjoy high efficiency, guaranteed convergence, and provide lower bounds on the true likelihood. But due to requirement for model-specific derivation of the optimization equations and unclear inference quality in various models, it is not widely used as a generic approximate inference algorithm. In this paper, we discuss a generalized mean field theory on variational approximation to a broad class of intractable distributions using a rich set of tractable distributions via constrained optimization over distribution spaces. We present a class of generalized mean field (GMF) algorithms for approximate inference in complex exponential family models, which entails limiting the optimization over the class of cluster-factorizable distributions. GMF is a generic method requiring no model-specific derivations. It factors a complex model into a set of disjoint variable clusters, and uses a set of canonical fix-point equations to iteratively update the cluster distributions, and converge to locally optimal cluster marginals that preserve the original dependency structure within each cluster, hence, fully decomposed the overall inference problem. We empirically analyzed the effect of different tractable family (clusters of different granularity) on inference quality, and compared GMF with BP on several canonical models. Possible extension to higher-order MF approximation is also discussed.

Conditional Random Fields (CRFs) are undirected graphical models, a special case of which correspond to conditionally-trained finite state machines. A key advantage of these models is their great flexibility to include a wide array of overlapping, multi-granularity, non-independent features of the input. In face of this freedom, an important question that remains is, what features should be used? This paper presents a feature induction method for CRFs. Founded on the principle of constructing only those feature conjunctions that significantly increase log-likelihood, the approach is based on that of Della Pietra et al [1997], but altered to work with conditional rather than joint probabilities, and with additional modifications for providing tractability specifically for a sequence model. In comparison with traditional approaches, automated feature induction offers both improved accuracy and more than an order of magnitude reduction in feature count; it enables the use of richer, higher-order Markov models, and offers more freedom to liberally guess about which atomic features may be relevant to a task. The induction method applies to linear-chain CRFs, as well as to more arbitrary CRF structures, also known as Relational Markov Networks [Taskar & Koller, 2002]. We present experimental results on a named entity extraction task.

Many practitioners who use the EM algorithm complain that it is sometimes slow. When does this happen, and what can be done about it? In this paper, we study the general class of bound optimization algorithms - including Expectation-Maximization, Iterative Scaling and CCCP - and their relationship to direct optimization algorithms such as gradient-based methods for parameter learning. We derive a general relationship between the updates performed by bound optimization methods and those of gradient and second-order methods and identify analytic conditions under which bound optimization algorithms exhibit quasi-Newton behavior, and conditions under which they possess poor, first-order convergence. Based on this analysis, we consider several specific algorithms, interpret and analyze their convergence properties and provide some recipes for preprocessing input to these algorithms to yield faster convergence behavior. We report empirical results supporting our analysis and showing that simple data preprocessing can result in dramatically improved performance of bound optimizers in practice.

Here we propose a novel model family with the objective of learning to disentangle the factors of variation in data. Our approach is based on the spike-and-slab restricted Boltzmann machine which we generalize to include higher-order interactions among multiple latent variables. Seen from a generative perspective, the multiplicative interactions emulates the entangling of factors of variation. Inference in the model can be seen as disentangling these generative factors. Unlike previous attempts at disentangling latent factors, the proposed model is trained using no supervised information regarding the latent factors. We apply our model to the task of facial expression classification.

MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network given some evidence. Unlike computing posterior probabilities, or MPE (a special case of MAP), the time and space complexity of structural solutions for MAP are not only exponential in the network treewidth, but in a larger parameter known as the "constrained" treewidth. In practice, this means that computing MAP can be orders of magnitude more expensive than computing posterior probabilities or MPE. This paper introduces a new, simple upper bound on the probability of a MAP solution, which admits a tradeoff between the bound quality and the time needed to compute it. The bound is shown to be generally much tighter than those of other methods of comparable complexity. We use this proposed upper bound to develop a branch-and-bound search algorithm for solving MAP exactly. Experimental results demonstrate that the search algorithm is able to solve many problems that are far beyond the reach of any structure-based method for MAP. For example, we show that the proposed algorithm can compute MAP exactly and efficiently for some networks whose constrained treewidth is more than 40.

We present the language {m P}{cal C}+ for probabilistic reasoning about actions, which is a generalization of the action language {cal C}+ that allows to deal with probabilistic as well as nondeterministic effects of actions. We define a formal semantics of {m P}{cal C}+ in terms of probabilistic transitions between sets of states. Using a concept of a history and its belief state, we then show how several important problems in reasoning about actions can be concisely formulated in our formalism.

Precision achieved by stochastic sampling algorithms for Bayesian networks typically deteriorates in face of extremely unlikely evidence. To address this problem, we propose the Evidence Pre-propagation Importance Sampling algorithm (EPIS-BN), an importance sampling algorithm that computes an approximate importance function by the heuristic methods: loopy belief Propagation and e-cutoff. We tested the performance of e-cutoff on three large real Bayesian networks: ANDES, CPCS, and PATHFINDER. We observed that on each of these networks the EPIS-BN algorithm gives us a considerable improvement over the current state of the art algorithm, the AIS-BN algorithm. In addition, it avoids the costly learning stage of the AIS-BN algorithm.