Robust Bayes classifiers

AbstractNaive Bayes classifiers provide an efficient and scalable approach to supervised classification problems. When some entries in the training set are missing, methods exist to learn these classifiers under some assumptions about the pattern of missing data. Unfortunately, reliable information about the pattern of missing data may be not readily available and recent experimental results show that the enforcement of an incorrect assumption about the pattern of missing data produces a dramatic decrease in accuracy of the classifier. This paper introduces a Robust Bayes Classifier (rbc) able to handle incomplete databases with no assumption about the pattern of missing data. In order to avoid assumptions, the rbc bounds all the possible probability estimates within intervals using a specialized estimation method. These intervals are then used to classify new cases by computing intervals on the posterior probability distributions over the classes given a new case and by ranking the intervals according to some criteria. We provide two scoring methods to rank intervals and a decision theoretic approach to trade off the risk of an erroneous classification and the choice of not classifying unequivocally a case. This decision theoretic approach can also be used to assess the opportunity of adopting assumptions about the pattern of missing data. The proposed approach is evaluated on twenty publicly available databases

Bayesian Clustering by Dynamics

This paper introduces a Bayesian method for clustering dynamic processes. The method models dynamics as Markov chains and then applies an agglomerative clustering procedure to discover the most probable set of clusters capturing different dynamics. To increase ef£ciency, the method uses an entropy-based heuristic search strategy. A controlled experiment suggests that the method is very accurate when applied to artificial time series in a broad range of conditions and, when applied to clustering sensor data from mobile robots, it produces clusters that are meaningful in the domain of application

Probabilistic Reasoning under Ignorance

The Representation of ignorance is a long standing challenge for researchers in probability and decision theory. During the past decade, Artificial Intelligence researchers have developed a class of reasoning systems, called Truth Maintenance Systems, which are able to reason on the basis of incomplete information. In this paper we will describe a new method for dealing with partially specified probabilistic models, by extending a logic-based truth maintenance method from Boolean truth-values to probability intervals. Then we will illustrate how this method can be used to represent Bayesi&n Belief Networks — one of the best known formalisms to reason under uncertainty — thus producing a new class of Bayesian Belief Networks, caUed Ignorant Belief Networks, able to reason on the basis of partially specified prior and conditional probabilities. Finally, we will discuss how this new method relates to some theoretical intuitions and empirical findings in decision theory and cognitive science

Chronic Nodular Dermatosis: A Quiz

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Robust outcome prediction for intensive care patients

Missing data are a major plague of medical databases in general, and of Intensive Care Units databases in particular. The time pressure of work in an Intensive Care Unit pushes the physicians to omit randomly or selectively record data. These different omission strategies give rise to different patterns of missing data and the recommended approach of completing the database using median imputation and fitting a logistic regression model can lead to significant biases. This paper applies a new classification method, called robust Bayes classifier, that does not rely on any particular assumption about the pattern of missing data and compares it to the traditional median imputation approach using a database of 324 Intensive Care Unit patients

Penile intraepithelial carcinoma treated with imiquimod 1% in an HIV-positive patient

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