Stochastic sampling algorithms, while an attractive alternative to exact algorithms in very large Bayesian network models, have been observed to perform poorly in evidential reasoning with extremely unlikely evidence. To address this problem, we propose an adaptive importance sampling algorithm, AIS-BN, that shows promising convergence rates even under extreme conditions and seems to outperform the existing sampling algorithms consistently. Three sources of this performance improvement are (1) two heuristics for initialization of the importance function that are based on the theoretical properties of importance sampling in finite-dimensional integrals and the structural advantages of Bayesian networks, (2) a smooth learning method for the importance function, and (3) a dynamic weighting function for combining samples from different stages of the algorithm. We tested the performance of the AIS-BN algorithm along with two state of the art general purpose sampling algorithms, likelihood weighting (Fung and Chang, 1989; Shachter and Peot, 1989) and self-importance sampling (Shachter and Peot, 1989). We used in our tests three large real Bayesian network models available to the scientific community: the CPCS network (Pradhan et al., 1994), the PathFinder network (Heckerman, Horvitz, and Nathwani, 1990), and the ANDES network (Conati, Gertner, VanLehn, and Druzdzel, 1997), with evidence as unlikely as 10^-41. While the AIS-BN algorithm always performed better than the other two algorithms, in the majority of the test cases it achieved orders of magnitude improvement in precision of the results. Improvement in speed given a desired precision is even more dramatic, although we are unable to report numerical results here, as the other algorithms almost never achieved the precision reached even by the first few iterations of the AIS-BN algorithm.

We show how to find a minimum weight loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in the method of conditioning for inference. Our randomized algorithm for finding a loop cutset outputs a minimum loop cutset after O(c 6^k kn) steps with probability at least 1 - (1 - 1/(6^k))^c6^k, where c > 1 is a constant specified by the user, k is the minimal size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this algorithm often finds a loop cutset that is closer to the minimum weight loop cutset than the ones found by the best deterministic algorithms known.

In many real-world learning tasks, it is expensive to acquire a sufficient number of labeled examples for training. This paper investigates methods for reducing annotation cost by `sample selection'. In this approach, during training the learning program examines many unlabeled examples and selects for labeling only those that are most informative at each stage. This avoids redundantly labeling examples that contribute little new information. Our work follows on previous research on Query By Committee, extending the committee-based paradigm to the context of probabilistic classification. We describe a family of empirical methods for committee-based sample selection in probabilistic classification models, which evaluate the informativeness of an example by measuring the degree of disagreement between several model variants. These variants (the committee) are drawn randomly from a probability distribution conditioned by the training set labeled so far. The method was applied to the real-world natural language processing task of stochastic part-of-speech tagging. We find that all variants of the method achieve a significant reduction in annotation cost, although their computational efficiency differs. In particular, the simplest variant, a two member committee with no parameters to tune, gives excellent results. We also show that sample selection yields a significant reduction in the size of the model used by the tagger.

A major problem in machine learning is that of inductive bias: how to choose a learner's hypothesis space so that it is large enough to contain a solution to the problem being learnt, yet small enough to ensure reliable generalization from reasonably-sized training sets. Typically such bias is supplied by hand through the skill and insights of experts. In this paper a model for automatically learning bias is investigated. The central assumption of the model is that the learner is embedded within an environment of related learning tasks. Within such an environment the learner can sample from multiple tasks, and hence it can search for a hypothesis space that contains good solutions to many of the problems in the environment. Under certain restrictions on the set of all hypothesis spaces available to the learner, we show that a hypothesis space that performs well on a sufficiently large number of training tasks will also perform well when learning novel tasks in the same environment. Explicit bounds are also derived demonstrating that learning multiple tasks within an environment of related tasks can potentially give much better generalization than learning a single task.

We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the conditioning variable and maintaining a different model for each set within a cover. Inference remains tractable by specifying the probabilistic model in terms of a random walk within the sequence of covers. We demonstrate the approach on problems of conditional density estimation, which, to our knowledge is the first closed-form, non-parametric Bayesian approach to this problem.

We address the cost-sensitive feature acquisition problem, where misclassifying an instance is costly but the expected misclassification cost can be reduced by acquiring the values of the missing features. Because acquiring the features is costly as well, the objective is to acquire the right set of features so that the sum of the feature acquisition cost and misclassification cost is minimized. We describe the Value of Information Lattice (VOILA), an optimal and efficient feature subset acquisition framework. Unlike the common practice, which is to acquire features greedily, VOILA can reason with subsets of features. VOILA efficiently searches the space of possible feature subsets by discovering and exploiting conditional independence properties between the features and it reuses probabilistic inference computations to further speed up the process. Through empirical evaluation on five medical datasets, we show that the greedy strategy is often reluctant to acquire features, as it cannot forecast the benefit of acquiring multiple features in combination.

We describe a variational approximation method for efficient inference in large-scale probabilistic models. Variational methods are deterministic procedures that provide approximations to marginal and conditional probabilities of interest. They provide alternatives to approximate inference methods based on stochastic sampling or search. We describe a variational approach to the problem of diagnostic inference in the `Quick Medical Reference' (QMR) network. The QMR network is a large-scale probabilistic graphical model built on statistical and expert knowledge. Exact probabilistic inference is infeasible in this model for all but a small set of cases. We evaluate our variational inference algorithm on a large set of diagnostic test cases, comparing the algorithm to a state-of-the-art stochastic sampling method.

Under the Defense Advanced Research Project Agency's (DARPA) Integrated Crisis Early Warning System (ICEWS), Innovative Decisions, Inc. (IDI) constructed a Bayesian network to combine forecasts produced by a set of social science models. We used Bayesian network structure learning with political science variables to produce meaningful priors. We employed a naive Bayes structure to aggregate the forecasts. In both cases, IDI improved classification by intelligently discretizing continuous variables. The resulting network not only met performance criteria set by DARPA, but also out-performed each of the social science models across all types of forecasted events. We describe the construction of the aggregator as well as a set of experiments performed to explore the nature of the Bayesian EOI Aggregator's performance.

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both the joint probability density of the variables and the likelihood function of the (objective or subjective) observation are approximated by a special mixture model, in such a way that any desired conditional distribution can be directly obtained without numerical integration. We have developed an extended version of the expectation maximization (EM) algorithm to estimate the parameters of mixture models from uncertain training examples (indirect observations). As a consequence, any piece of exact or uncertain information about both input and output values is consistently handled in the inference and learning stages. This ability, extremely useful in certain situations, is not found in most alternative methods. The proposed framework is formally justified from standard probabilistic principles and illustrative examples are provided in the fields of nonparametric pattern classification, nonlinear regression and pattern completion. Finally, experiments on a real application and comparative results over standard databases provide empirical evidence of the utility of the method in a wide range of applications.

We consider a binary unsupervised classification problem where each observation is associated with an unobserved label that we want to retrieve. More precisely, we assume that there are two groups of observation: normal and abnormal. The `normal' observations are coming from a known distribution whereas the distribution of the `abnormal' observations is unknown. Several models have been developed to fit this unknown distribution. In this paper, we propose an alternative based on a mixture of Gaussian distributions. The inference is done within a variational Bayesian framework and our aim is to infer the posterior probability of belonging to the class of interest. To this end, it makes no sense to estimate the mixture component number since each mixture model provides more or less relevant information to the posterior probability estimation. By computing a weighted average (named aggregated estimator) over the model collection, Bayesian Model Averaging (BMA) is one way of combining models in order to account for information provided by each model. The aim is then the estimation of the weights and the posterior probability for one specific model. In this work, we derive optimal approximations of these quantities from the variational theory and propose other approximations of the weights. To perform our method, we consider that the data are dependent (Markovian dependency) and hence we consider a Hidden Markov Model. A simulation study is carried out to evaluate the accuracy of the estimates in terms of classification. We also present an application to the analysis of public health surveillance systems.