We describe a probabilistic (generative) view of affinity matrices along with inference algorithms for a subclass of problems associated with data clustering. This probabilistic view is helpful in understanding different models and algorithms that are based on affinity functions OF the data. IN particular, we show how(greedy) inference FOR a specific probabilistic model IS equivalent TO the spectral clustering algorithm.It also provides a framework FOR developing new algorithms AND extended models. AS one CASE, we present new generative data clustering models that allow us TO infer the underlying distance measure suitable for the clustering problem at hand. These models seem to perform well in a larger class of problems for which other clustering algorithms (including spectral clustering) usually fail. Experimental evaluation was performed in a variety point data sets, showing excellent performance.

Collaborative filtering (CF) allows the preferences of multiple users to be pooled to make recommendations regarding unseen products. We consider in this paper the problem of online and interactive CF: given the current ratings associated with a user, what queries (new ratings) would most improve the quality of the recommendations made? We cast this terms of expected value of information (EVOI); but the online computational cost of computing optimal queries is prohibitive. We show how offline prototyping and computation of bounds on EVOI can be used to dramatically reduce the required online computation. The framework we develop is general, but we focus on derivations and empirical study in the specific case of the multiple-cause vector quantization model.

Group elevator scheduling is an NP-hard sequential decision-making problem with unbounded state spaces and substantial uncertainty. Decision-theoretic reasoning plays a surprisingly limited role in fielded systems. A new opportunity for probabilistic methods has opened with the recent discovery of a tractable solution for the expected waiting times of all passengers in the building, marginalized over all possible passenger itineraries. Though commercially competitive, this solution does not contemplate future passengers. Yet in up-peak traffic, the effects of future passengers arriving at the lobby and entering elevator cars can dominate all waiting times. We develop a probabilistic model of how these arrivals affect the behavior of elevator cars at the lobby, and demonstrate how this model can be used to very significantly reduce the average waiting time of all passengers.

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.

Constraint-based (CB) learning is a formalism for learning a causal network with a database D by performing a series of conditional-independence tests to infer structural information. This paper considers a new test of independence that combines ideas from Bayesian learning, Bayesian network inference, and classical hypothesis testing to produce a more reliable and robust test. The new test can be calculated in the same asymptotic time and space required for the standard tests such as the chi-squared test, but it allows the specification of a prior distribution over parameters and can be used when the database is incomplete. We prove that the test is correct, and we demonstrate empirically that, when used with a CB causal discovery algorithm with noninformative priors, it recovers structural features more reliably and it produces networks with smaller KL-Divergence, especially as the number of nodes increases or the number of records decreases. Another benefit is the dramatic reduction in the probability that a CB algorithm will stall during the search, providing a remedy for an annoying problem plaguing CB learning when the database is small.

Symbolic representations have been used successfully in off-line planning algorithms for Markov decision processes. We show that they can also improve the performance of on-line planners. In addition to reducing computation time, symbolic generalization can reduce the amount of costly real-world interactions required for convergence. We introduce Symbolic Real-Time Dynamic Programming (or sRTDP), an extension of RTDP. After each step of on-line interaction with an environment, sRTDP uses symbolic model-checking techniques to generalizes its experience by updating a group of states rather than a single state. We examine two heuristic approaches to dynamic grouping of states and show that they accelerate the planning process significantly in terms of both CPU time and the number of steps of interaction with the environment.

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.

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.

We present CLP(BN), a novel approach that aims at expressing Bayesian networks through the constraint logic programming framework. Arguably, an important limitation of traditional Bayesian networks is that they are propositional, and thus cannot represent relations between multiple similar objects in multiple contexts. Several researchers have thus proposed first-order languages to describe such networks. Namely, one very successful example of this approach are the Probabilistic Relational Models (PRMs), that combine Bayesian networks with relational database technology. The key difficulty that we had to address when designing CLP(cal{BN}) is that logic based representations use ground terms to denote objects. With probabilitic data, we need to be able to uniquely represent an object whose value we are not sure about. We use {sl Skolem functions} as unique new symbols that uniquely represent objects with unknown value. The semantics of CLP(cal{BN}) programs then naturally follow from the general framework of constraint logic programming, as applied to a specific domain where we have probabilistic data. This paper introduces and defines CLP(cal{BN}), and it describes an implementation and initial experiments. The paper also shows how CLP(cal{BN}) relates to Probabilistic Relational Models (PRMs), Ngo and Haddawys Probabilistic Logic Programs, AND Kersting AND De Raedts Bayesian Logic Programs.

Published experiments on spidering the Web suggest that, given training data in the form of a (relatively small) subgraph of the Web containing a subset of a selected class of target pages, it is possible to conduct a directed search and find additional target pages significantly faster (with fewer page retrievals) than by performing a blind or uninformed random or systematic search, e.g., breadth-first search. If true, this claim motivates a number of practical applications. Unfortunately, these experiments were carried out in specialized domains or under conditions that are difficult to replicate. We present and apply an experimental framework designed to reexamine and resolve the basic claims of the earlier work, so that the supporting experiments can be replicated and built upon. We provide high-performance tools for building experimental spiders, make use of the ground truth and static nature of the WT10g TREC Web corpus, and rely on simple well understand machine learning techniques to conduct our experiments. In this paper, we describe the basic framework, motivate the experimental design, and report on our findings supporting and qualifying the conclusions of the earlier research.