Medical diagnosis process vary in the degree to which they attempt to deal with different complicating aspects of diagnosis such as relative importance of symptoms, varied symptom pattern and the relation between diseases them selves. Based on decision theory, in the past many mathematical models such as crisp set, probability distribution, fuzzy set, intuitionistic fuzzy set were developed to deal with complicating aspects of diagnosis. But, many such models are failed to include important aspects of the expert decisions. Therefore, an effort has been made to process inconsistencies in data being considered by Pawlak with the introduction of rough set theory. Though rough set has major advantages over the other methods, but it generates too many rules that create many difficulties while taking decisions. Therefore, it is essential to minimize the decision rules. In this paper, we use two processes such as pre process and post process to mine suitable rules and to explore the relationship among the attributes. In pre process we use rough set theory to mine suitable rules, whereas in post process we use formal concept analysis from these suitable rules to explore better knowledge and most important factors affecting the decision making.

Many applications require that we learn the parameters of a model from data. EM is a method used to learn the parameters of probabilistic models for which the data for some of the variables in the models is either missing or hidden. There are instances in which this method is slow to converge. Therefore, several accelerations have been proposed to improve the method. None of the proposed acceleration methods are theoretically dominant and experimental comparisons are lacking. In this paper, we present the different proposed accelerations and try to compare them experimentally. From the results of the experiments, we argue that some acceleration of EM is always possible, but that which acceleration is superior depends on properties of the problem.

Recently, researchers have demonstrated that loopy belief propagation - the use of Pearls polytree algorithm IN a Bayesian network WITH loops OF error- correcting codes.The most dramatic instance OF this IS the near Shannon - limit performance OF Turbo Codes codes whose decoding algorithm IS equivalent TO loopy belief propagation IN a chain - structured Bayesian network. IN this paper we ask : IS there something special about the error - correcting code context, OR does loopy propagation WORK AS an approximate inference schemeIN a more general setting? We compare the marginals computed using loopy propagation TO the exact ones IN four Bayesian network architectures, including two real - world networks : ALARM AND QMR.We find that the loopy beliefs often converge AND WHEN they do, they give a good approximation TO the correct marginals.However,ON the QMR network, the loopy beliefs oscillated AND had no obvious relationship TO the correct posteriors. We present SOME initial investigations INTO the cause OF these oscillations, AND show that SOME simple methods OF preventing them lead TO the wrong results.

Given a set of possible models (e.g., Bayesian network structures) and a data sample, in the unsupervised model selection problem the task is to choose the most accurate model with respect to the domain joint probability distribution. In contrast to this, in supervised model selection it is a priori known that the chosen model will be used in the future for prediction tasks involving more ``focused' predictive distributions. Although focused predictive distributions can be produced from the joint probability distribution by marginalization, in practice the best model in the unsupervised sense does not necessarily perform well in supervised domains. In particular, the standard marginal likelihood score is a criterion for the unsupervised task, and, although frequently used for supervised model selection also, does not perform well in such tasks. In this paper we study the performance of the marginal likelihood score empirically in supervised Bayesian network selection tasks by using a large number of publicly available classification data sets, and compare the results to those obtained by alternative model selection criteria, including empirical crossvalidation methods, an approximation of a supervised marginal likelihood measure, and a supervised version of Dawids prequential(predictive sequential) principle.The results demonstrate that the marginal likelihood score does NOT perform well FOR supervised model selection, WHILE the best results are obtained BY using Dawids prequential r napproach.

We consider on-line density estimation with a parameterized density from the exponential family. The on-line algorithm receives one example at a time and maintains a parameter that is essentially an average of the past examples. After receiving an example the algorithm incurs a loss which is the negative log-likelihood of the example w.r.t. the past parameter of the algorithm. An off-line algorithm can choose the best parameter based on all the examples. We prove bounds on the additional total loss of the on-line algorithm over the total loss of the off-line algorithm. These relative loss bounds hold for an arbitrary sequence of examples. The goal is to design algorithms with the best possible relative loss bounds. We use a certain divergence to derive and analyze the algorithms. This divergence is a relative entropy between two exponential distributions.

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance, carrying out the Bayesian program of computing the full posterior distributions over the parameters remains a difficult problem. Moreover, learning the structure of models with latent variables, for which the Bayesian approach is crucial, is yet a harder problem. In this paper I present the Variational Bayes framework, which provides a solution to these problems. This approach approximates full posterior distributions over model parameters and structures, as well as latent variables, in an analytical manner without resorting to sampling methods. Unlike in the Laplace approximation, these posteriors are generally non-Gaussian and no Hessian needs to be computed. The resulting algorithm generalizes the standard Expectation Maximization algorithm, and its convergence is guaranteed. I demonstrate that this algorithm can be applied to a large class of models in several domains, including unsupervised clustering and blind source separation.

In this paper we extend the work of Smith and Papamichail (1999) and present fast approximate Bayesian algorithms for learning in complex scenarios where at any time frame, the relationships between explanatory state space variables can be described by a Bayesian network that evolve dynamically over time and the observations taken are not necessarily Gaussian. It uses recent developments in approximate Bayesian forecasting methods in combination with more familiar Gaussian propagation algorithms on junction trees. The procedure for learning state parameters from data is given explicitly for common sampling distributions and the methodology is illustrated through a real application. The efficiency of the dynamic approximation is explored by using the Hellinger divergence measure and theoretical bounds for the efficacy of such a procedure are discussed.

Probabilistic Latent Semantic Analysis is a novel statistical technique for the analysis of two-mode and co-occurrence data, which has applications in information retrieval and filtering, natural language processing, machine learning from text, and in related areas. Compared to standard Latent Semantic Analysis which stems from linear algebra and performs a Singular Value Decomposition of co-occurrence tables, the proposed method is based on a mixture decomposition derived from a latent class model. This results in a more principled approach which has a solid foundation in statistics. In order to avoid overfitting, we propose a widely applicable generalization of maximum likelihood model fitting by tempered EM. Our approach yields substantial and consistent improvements over Latent Semantic Analysis in a number of experiments.

Inference networks have a variety of important uses and are constructed by persons having quite different standpoints. Discussed in this paper are three different but complementary methods for generating and analyzing probabilistic inference networks. The first method, though over eighty years old, is very useful for knowledge representation in the task of constructing probabilistic arguments. It is also useful as a heuristic device in generating new forms of evidence. The other two methods are formally equivalent ways for combining probabilities in the analysis of inference networks. The use of these three methods is illustrated in an analysis of a mass of evidence in a celebrated American law case.

We introduce a new class of graphical representations, expected utility networks (EUNs), and discuss some of its properties and potential applications to artificial intelligence and economic theory. In EUNs not only probabilities, but also utilities enjoy a modular representation. EUNs are undirected graphs with two types of arc, representing probability and utility dependencies respectively. The representation of utilities is based on a novel notion of conditional utility independence, which we introduce and discuss in the context of other existing proposals. Just as probabilistic inference involves the computation of conditional probabilities, strategic inference involves the computation of conditional expected utilities for alternative plans of action. We define a new notion of conditional expected utility (EU) independence, and show that in EUNs node separation with respect to the probability and utility subgraphs implies conditional EU independence.