A fundamental issue in real-world systems, such as sensor networks, is the selection of observations which most effectively reduce uncertainty. More specifically, we address the long standing problem of nonmyopically selecting the most informative subset of variables in a graphical model. We present the first efficient randomized algorithm providing a constant factor (1 − 1/e − ε) approximation guarantee for any ε> 0 with high confidence. The algorithm leverages the theory of submodular functions, in combination with a polynomial bound on sample complexity. We furthermore prove that no polynomial time algorithm can provide a constant factor approximation better than (1 − 1/e) unless P = NP. Finally, we provide extensive evidence of the effectiveness of our method on two complex real-world datasets. 1

Many real-world decision making tasks require us to choose among several expensive observations. In a sensor network, for example, it is important to select the subset of sensors that is expected to provide the strongest reduction in uncertainty. It has been general practice to use heuristic-guided procedures for selecting observations. In this paper, we present the first efficient optimal algorithms for selecting observations for a class of graphical models containing Hidden Markov Models (HMMs). We provide results for both selecting the optimal subset of observations, and for obtaining an optimal conditional observation plan. For both problems, we present algorithms for the filtering case, where only observations made in the past are taken into account, and the smoothing case, where all observations are utilized. Furthermore we prove a surprising result: In most graphical models tasks, if one designs an efficient algorithm for chain graphs, such as HMMs, this procedure can be generalized to polytrees. We prove that the value of information problem is NP PP-hard even for discrete polytrees. It also follows from our results that even computing conditional entropies, which are widely used to measure value of information, is a #P-complete problem on polytrees. Finally, we demonstrate the effectiveness of our approach on several real-world datasets. 1

Intensive computations required for sensing and processing perceptual information can impose significant burdens on personal computer systems. We explore several policies for selective perception in SEER, a multimodal system for recognizing o#ce activity that relies on a layered Hidden Markov Model representation. We review our e#orts to employ expected-value-of-information (EVI) computations to limit sensing and analysis in a context-sensitive manner. We discuss an implementation of a one-step myopic EVI analysis and compare the results of using the myopic EVI with a heuristic sensing policy that makes observations at di#erent frequencies. Both policies are then compared to a random perception policy, where sensors are selected at random. Finally, we discuss the sensitivity of ideal perceptual actions to preferences encoded in utility models about information value and the cost of sensing.

Many real-world decision making tasks require us to choose among several expensive observations. In a sensor network, for example, it is important to select the subset of sensors that is expected to provide the strongest reduction in uncertainty. In medical decision making tasks, one needs to select which tests to administer before deciding on the most effective treatment. It has been general practice to use heuristic-guided procedures for selecting observations. In this paper, we present the first efficient optimal algorithms for selecting observations for a class of probabilistic graphical models. For example, our algorithms allow to optimally label hidden variables in Hidden Markov Models (HMMs). We provide results for both selecting the optimal subset of observations, and for obtaining an optimal conditional observation plan. Furthermore we prove a surprising result: In most graphical models tasks, if one designs an efficient algorithm for chain graphs, such as HMMs, this procedure can be generalized to polytree graphical models. We prove that the optimizing value of information is NP PP-hard even for polytrees. It also follows from our results that just computing decision theoretic value of information objective functions, which are commonly used in practice, is a #P-complete problem even on Naive Bayes models (a simple special case of polytrees). In addition, we consider several extensions, such as using our algorithms for scheduling observation selection for multiple sensors. We demonstrate the effectiveness of our approach on several real-world datasets, including a prototype sensor network deployment for energy conservation in buildings. 1.

We address the problem of efficient feature-value acquisition for classification in domains in which there are varying costs associated with both feature acquisition and misclassification. The objective is to minimize the sum of the information acquisition cost and misclassification cost. Any decision theoretic strategy tackling this problem needs to compute value of information for sets of features. Having calculated this information, different acquisition strategies are possible (acquiring one feature at time, acquiring features in sets, etc.). However, because the value of information calculation for arbitrary subsets of features is computationally intractable, most traditional approaches have been greedy, computing values of features one at a time. We make the problem of value of information calculation tractable in practice by introducing a novel data structure called the Value of Information Lattice (VOILA). VOILA exploits dependencies between missing features and makes sharing of information value computations between different feature subsets possible. To the best of our knowledge, performance differences between greedy acquisition, acquiring features in sets, and a mixed strategy have not been investigated empirically in the past, due to inherit intractability of the problem. With the help of VOILA, we are able to evaluate these strategies on five real world datasets under various cost assumptions. We show that VOILA reduces computation time dramatically. We also show that the mixed strategy outperforms both greedy acquisition and acquisition in sets.

In artificial intelligence research, the belief network framework for automated reasoning with uncertainty is rapidly gaining in popularity. The framework provides a powerful formalism for representing a joint probability distribution on a set of statistical variables.

This paper studies the problem of learning diagnostic policies from training examples. A diagnostic policy is a complete description of the decision-making actions of a diagnostician (i.e., tests followed by a diagnostic decision) for all possible combinations of test results. An optimal diagnostic policy is one that minimizes the expected total cost, which isthe sum of measurement costs and misdiagnosis costs. In most diagnostic settings, there is a tradeo between these two kinds of costs. This paper formalizes diagnostic decision making as a Markov Decision Process (MDP). The paper introduces a new family of systematic search algorithms based on the AO algorithm to solve this MDP.To makeAO e cient, the paper describes an admissible heuristic that enables AO to prune large parts of the search space. The paper also introduces several greedy algorithms including some improvements over previously-published methods. The paper then addresses the question of learning diagnostic policies from examples. When the probabilities of diseases and test results are computed from training data, there is a great danger of over tting. To reduce over tting, regularizers are integrated into the search algorithms. Finally, the paper compares the proposed methods on ve benchmark diagnostic data sets. The studies show that in most cases the systematic search methods produce better diagnostic policies than the greedy methods. In addition, the studies show that for training sets of realistic size, the systematic search algorithms are practical on today's desktop computers. 1.

The belief network framework is becoming increasingly popular for building diagnostic knowledge -based systems. The framework is especially suited for the task of diagnosis because it provides for modelling and dealing with multiple interacting disorders. However, this ability often is exploited insufficiently due to the computational complexity involved. In this paper, we present a method for multiple-disorder diagnosis with a belief network that derives its efficiency from focusing on small sets of related disorders which are constructed by taking advantage of the independencies portrayed by the graphical part of the network. 1 Introduction Although diagnosing multiple disorders has been a long-standing concern of knowledge-based systems research, it is only recently that fundamental paradigms for dealing with multiple disorders have begun to arise. The paradigms of model-based reasoning [ Reiter, 1987 ] and abductive reasoning [ Peng and Reggia, 1990 ] especially are tuned to mult...

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Formal diagnostic methods are emerging from the machine-learning research community and beginning to find application in Intel. In this paper we give an overview of these methods and the potential they show for improving diagnostic procedures in operational environments. We present an historical overview of Bayes networks and discuss how they can be applied to diagnosis. We then give an illustration of how they can model the faults in a vacuum subsystem of a manufacturing tool.