In cancer diagnosis, classification of the different tumor types is of great importance. An accurate prediction of different tumor types provides better treatment and toxicity minimization on patients. Traditional methods of tackling this situation are primarily based on morphological characteristics of tumorous tissue [1]. These conventional methods are reported to have several diagnosis limitations. In order to analyze the problem of cancer classification using gene expression data, more systematic approaches have been developed [2]. Pioneering work in cancer classification by gene expression using DNA microarray showed the possibility to help the diagnosis by means of Machine Learning or more generally Data Mining methods [3], which are now extensively used for this task [4]. However, in this setting gene expression data analysis entails a heavy computational consumption of resources, due to the extreme sparseness compared to standard data sets in classification tasks [5]. Typically, a gene expression data set may consist of dozens of observations but with thousands or even tens of thousands of genes.

Social networks are increasingly being used to conduct polls. We introduce a simple model of such social polling. We suppose agents vote sequentially, but the order in which agents choose to vote is not necessarily fixed. We also suppose that an agent's vote is influenced by the votes of their friends who have already voted. Despite its simplicity, this model provides useful insights into a number of areas including social polling, sequential voting, and manipulation. We prove that the number of candidates and the network structure affect the computational complexity of computing which candidate necessarily or possibly can win in such a social poll. For social networks with bounded treewidth and a bounded number of candidates, we provide polynomial algorithms for both problems. In other cases, we prove that computing which candidates necessarily or possibly win are computationally intractable.

This paper re-examines the problem of parameter estimation in Bayesian networks with missing values and hidden variables from the perspective of recent work in on-line learning [Kivinen & Warmuth, 1994]. We provide a unified framework for parameter estimation that encompasses both on-line learning, where the model is continuously adapted to new data cases as they arrive, and the more traditional batch learning, where a pre-accumulated set of samples is used in a one-time model selection process. In the batch case, our framework encompasses both the gradient projection algorithm and the EM algorithm for Bayesian networks. The framework also leads to new on-line and batch parameter update schemes, including a parameterized version of EM. We provide both empirical and theoretical results indicating that parameterized EM allows faster convergence to the maximum likelihood parameters than does standard EM.

Mauricio Sadinle is a Ph.D. student, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213 (email: msadinle@stat.cmu.edu); and Stephen E. Fienberg is Maurice Falk University Professor of Statistics and Social Science in the Department of Statistics, the Machine Learning Department, and the Heinz College, Carnegie Mellon University (email: fien-berg@stat.cmu.edu). This research was partially supported by NSF Grants BCS-0941518 and SES-1130706 to Carnegie Mellon University, and by the Singapore National Research Foundation under its International Research Centre @ Singapore Funding Initiative and administered by the IDM Programme Office. The authors thank Rob Hall, Kristian Lum, Michael Larsen, the Associate Editor and two referees for helpful comments and suggestions on earlier versions of this paper, and Jorge A. Restrepo for providing the Colombian homicide data. An early version of this paper was written by the first author when he was affiliated to the Conflict Analysis Resource Center (CERAC) and the National University of Colombia at Bogot a. Abstract We present a probabilistic method for linking multiple datafiles. This task is not trivial in the absence of unique identifiers for the individuals recorded. This is a common scenario when linking census data to coverage measurement surveys for census coverage evaluation, and in general when multiple record-systems need to be integrated for posterior analysis. The goal of multiple record linkage is to classify the recordK -tuples coming fromK datafiles according to the different matching patterns. We use a mixture model to fit matching probabilities via maximum likelihood using the EM algorithm. We present a method to decide the recordK -tuples membership to the subsets of matching patterns and we prove its optimality. We apply our method to the integration of the three Colombian homicide record systems and perform a simulation study to explore the performance of the method under measurement error and different scenarios. The proposed method works well and opens new directions for future research. Key words and phrases: Bell number; Census undercount; Data linkage; Data matching; EM algorithm; Mixture model; Multiple systems estimation; Partially ordered set. 1 INTRODUCTION Record linkage is a widely-used technique for identifying records that refer to the same individual across different datafiles. This task is not trivial when unique identifiers are not available, and many authors have proposed probabilistic methods to deal with this problem building upon the seminal work of Newcombe et al. (1959) and Fellegi and Sunter (1969).

We consider the problem of belief aggregation: given a group of individual agents with probabilistic beliefs over a set of uncertain events, formulate a sensible consensus or aggregate probability distribution over these events. Researchers have proposed many aggregation methods, although on the question of which is best the general consensus is that there is no consensus. We develop a market-based approach to this problem, where agents bet on uncertain events by buying or selling securities contingent on their outcomes. Each agent acts in the market so as to maximize expected utility at given securities prices, limited in its activity only by its own risk aversion. The equilibrium prices of goods in this market represent aggregate beliefs. For agents with constant risk aversion, we demonstrate that the aggregate probability exhibits several desirable properties, and is related to independently motivated techniques. We argue that the market-based approach provides a plausible mechanism for belief aggregation in multiagent systems, as it directly addresses self-motivated agent incentives for participation and for truthfulness, and can provide a decision-theoretic foundation for the "expert weights" often employed in centralized pooling techniques.

A submarine's sonar team is responsible for detecting, localising and classifying targets using information provided by the platform's sensor suite. The information used to make these assessments is typically uncertain and/or incomplete and is likely to require a measure of confidence in its reliability. Moreover, improvements in sensor and communication technology are resulting in increased amounts of on-platform and off-platform information available for evaluation. This proliferation of imprecise information increases the risk of overwhelming the operator. To assist the task of localisation and classification a concept demonstration decision aid (Horizon), based on evidential reasoning, has been developed. Horizon is an information fusion software package for representing and fusing imprecise information about the state of the world, expressed across suitable frames of reference. The Horizon software is currently at prototype stage.

In most current applications of belief networks, domain knowledge is represented by a single belief network that applies to all problem instances in the domain. In more complex domains, problem-specific models must be constructed from a knowledge base encoding probabilistic relationships in the domain. Most work in knowledge-based model construction takes the rule as the basic unit of knowledge. We present a knowledge representation framework that permits the knowledge base designer to specify knowledge in larger semantically meaningful units which we call network fragments. Our framework provides for representation of asymmetric independence and canonical intercausal interaction. We discuss the combination of network fragments to form problem-specific models to reason about particular problem instances. The framework is illustrated using examples from the domain of military situation awareness.

The efficiency of inference in both the Hugin and, most notably, the Shafer-Shenoy architectures can be improved by exploiting the independence relations induced by the incoming messages of a clique. That is, the message to be sent from a clique can be computed via a factorization of the clique potential in the form of a junction tree. In this paper we show that by exploiting such nested junction trees in the computation of messages both space and time costs of the conventional propagation methods may be reduced. The paper presents a structured way of exploiting the nested junction trees technique to achieve such reductions. The usefulness of the method is emphasized through a thorough empirical evaluation involving ten large real-world Bayesian networks and the Hugin inference algorithm.

A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is directly represented by a Bayesian network. By using a powerful way of specifying conditional probability distributions in these networks, the resulting formalism is more expressive than the previous ones. Particularly, it provides for constraints on equalities of events, and it allows to define complex, nested combination functions.

We review the problem of time-critical action and discuss a reformulation that shifts knowledge acquisition from the assessment of complex temporal probabilistic dependencies to the direct assessment of time-dependent utilities over key outcomes of interest. We dwell on a class of decision problems characterized by the centrality of diagnosing and reacting in a timely manner to pathological processes. We motivate key ideas in the context of trauma-care triage and transportation decisions.