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.

In this paper, we present a new algorithm that integrates recent advances in solving continuous bandit problems with sample-based rollout methods for planning in Markov Decision Processes (MDPs). Our algorithm, Hierarchical Optimistic Optimization applied to Trees (HOOT) addresses planning in continuous-action MDPs. Empirical results are given that show that the performance of our algorithm meets or exceeds that of a similar discrete action planner by eliminating the problem of manual discretization of the action space.

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.

Feature selection is an important pre-processing step for many pattern classification tasks. Traditionally, feature selection methods are designed to obtain a feature subset that can lead to high classification accuracy. However, classification accuracy has recently been shown to be an inappropriate performance metric of classification systems in many cases. Instead, the Area Under the receiver operating characteristic Curve (AUC) and its multi-class extension, MAUC, have been proved to be better alternatives. Hence, the target of classification system design is gradually shifting from seeking a system with the maximum classification accuracy to obtaining a system with the maximum AUC/MAUC. Previous investigations have shown that traditional feature selection methods need to be modified to cope with this new objective. These methods most often are restricted to binary classification problems only. In this study, a filter feature selection method, namely MAUC Decomposition based Feature Selection (MDFS), is proposed for multi-class classification problems. To the best of our knowledge, MDFS is the first method specifically designed to select features for building classification systems with maximum MAUC. Extensive empirical results demonstrate the advantage of MDFS over several compared feature selection methods.

We consider the smoothing probabilities of hidden Markov model (HMM). We show that under fairly general conditions for HMM, the exponential forgetting still holds, and the smoothing probabilities can be well approximated with the ones of double sided HMM. This makes it possible to use ergodic theorems. As an applications we consider the pointwise maximum a posteriori segmentation, and show that the corresponding risks converge.

While loopy belief propagation (LBP) performs reasonably well for inference in some Gaussian graphical models with cycles, its performance is unsatisfactory for many others. In particular for some models LBP does not converge, and in general when it does converge, the computed variances are incorrect (except for cycle-free graphs for which belief propagation (BP) is non-iterative and exact). In this paper we propose {\em feedback message passing} (FMP), a message-passing algorithm that makes use of a special set of vertices (called a {\em feedback vertex set} or {\em FVS}) whose removal results in a cycle-free graph. In FMP, standard BP is employed several times on the cycle-free subgraph excluding the FVS while a special message-passing scheme is used for the nodes in the FVS. The computational complexity of exact inference is $O(k^2n)$, where $k$ is the number of feedback nodes, and $n$ is the total number of nodes. When the size of the FVS is very large, FMP is intractable. Hence we propose {\em approximate FMP}, where a pseudo-FVS is used instead of an FVS, and where inference in the non-cycle-free graph obtained by removing the pseudo-FVS is carried out approximately using LBP. We show that, when approximate FMP converges, it yields exact means and variances on the pseudo-FVS and exact means throughout the remainder of the graph. We also provide theoretical results on the convergence and accuracy of approximate FMP. In particular, we prove error bounds on variance computation. Based on these theoretical results, we design efficient algorithms to select a pseudo-FVS of bounded size. The choice of the pseudo-FVS allows us to explicitly trade off between efficiency and accuracy. Experimental results show that using a pseudo-FVS of size no larger than $\log(n)$, this procedure converges much more often, more quickly, and provides more accurate results than LBP on the entire graph.

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.

We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size and the average network degree grows at least poly-logarithmically in this size. We also establish finite-sample confidence bounds on maximum-likelihood blockmodel parameter estimates from data comprising independent Bernoulli random variates; these results hold uniformly over class assignment. We provide simulations verifying the conditions sufficient for our results, and conclude by fitting a logit parameterization of a stochastic blockmodel with covariates to a network data example comprising a collection of Facebook profiles, resulting in block estimates that reveal residual structure.

We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is NP-hard for some cases, and strongly NP-hard for others. We finally offer pseudopolynomial exact and approximation algorithms.

This book presents a methodology and philosophy of empirical science based on large scale lossless data compression. In this view a theory is scientific if it can be used to build a data compression program, and it is valuable if it can compress a standard benchmark database to a small size, taking into account the length of the compressor itself. This methodology therefore includes an Occam principle as well as a solution to the problem of demarcation. Because of the fundamental difficulty of lossless compression, this type of research must be empirical in nature: compression can only be achieved by discovering and characterizing empirical regularities in the data. Because of this, the philosophy provides a way to reformulate fields such as computer vision and computational linguistics as empirical sciences: the former by attempting to compress databases of natural images, the latter by attempting to compress large text databases. The book argues that the rigor and objectivity of the compression principle should set the stage for systematic progress in these fields. The argument is especially strong in the context of computer vision, which is plagued by chronic problems of evaluation. The book also considers the field of machine learning. Here the traditional approach requires that the models proposed to solve learning problems be extremely simple, in order to avoid overfitting. However, the world may contain intrinsically complex phenomena, which would require complex models to understand. The compression philosophy can justify complex models because of the large quantity of data being modeled (if the target database is 100 Gb, it is easy to justify a 10 Mb model). The complex models and abstractions learned on the basis of the raw data (images, language, etc) can then be reused to solve any specific learning problem, such as face recognition or machine translation.