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Distribution of Mutual Information from Complete And Incomplete Data
 Computational Statistics and Data Analysis
, 2004
"... Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider sampletopopulation inferential approaches. This paper deals with the post ..."
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Cited by 14 (2 self)
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Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider sampletopopulation inferential approaches. This paper deals with the posterior distribution of mutual information, as obtained in a Bayesian framework by a secondorder Dirichlet prior distribution. The exact analytical expression for the mean, and analytical approximations for the variance, skewness and kurtosis are derived. These approximations have a guaranteed accuracy level of the order O(n 3 ), where n is the sample size. Leading order approximations for the mean and the variance are derived in the case of incomplete samples. The derived analytical expressions allow the distribution of mutual information to be approximated reliably and quickly. In fact, the derived expressions can be computed with the same order of complexity needed for descriptive mutual information. This makes the distribution of mutual information become a concrete alternative to descriptive mutual information in many applications which would benefit from moving to the inductive side. Some of these prospective applications are discussed, and one of them, namely feature selection,isshowntoperform significantly better when inductive mutual information is used.
Robust estimators under the Imprecise Dirichlet Model (extended version
, 2003
"... Walley’s Imprecise Dirichlet Model (IDM) for categorical data overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practice, one needs efficient ways for computing the imprecise=robust sets or intervals. The main objective of this work is to ..."
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Cited by 7 (1 self)
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Walley’s Imprecise Dirichlet Model (IDM) for categorical data overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practice, one needs efficient ways for computing the imprecise=robust sets or intervals. The main objective of this work is to derive exact, conservative, and approximate, robust and credible interval estimates under the IDM for a large class of statistical estimators, including the entropy and mutual information.
Bayesian Networks with Imprecise Probabilities: Theory and Application to Classification
, 2010
"... Bayesian network are powerful probabilistic graphical models for modelling uncertainty. Among others, classification represents an important application: some of the most used classifiers are based on Bayesian networks. Bayesian networks are precise models: exact numeric values should be provided fo ..."
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Cited by 5 (2 self)
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Bayesian network are powerful probabilistic graphical models for modelling uncertainty. Among others, classification represents an important application: some of the most used classifiers are based on Bayesian networks. Bayesian networks are precise models: exact numeric values should be provided for quantification. This requirement is sometimes too narrow. Sets instead of single distributions can provide a more realistic description in these cases. Bayesian networks can be generalized to cope with sets of distributions. This leads to a novel class of imprecise probabilistic graphical models, called credal networks. In particular, classifiers based on Bayesian networks are generalized to socalled credal classifiers. Unlike Bayesian classifiers, which always detect a single class as the one maximizing the posterior class probability, a credal classifier may eventually be unable to discriminate a single class. In other words, if the available information is not sufficient, credal classifiers allow for indecision between two or more classes, this providing a less informative but more robust conclusion than Bayesian classifiers.
TreeBased Credal Networks for Classification
 Reliable Computing
"... Bayesian networks are models for uncertain reasoning which are achieving a growing importance also for the data mining task of classification. Credal networks extend Bayesian nets to sets of distributions, or credal sets. This paper extends a stateoftheart Bayesian net for classification, called ..."
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Cited by 4 (0 self)
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Bayesian networks are models for uncertain reasoning which are achieving a growing importance also for the data mining task of classification. Credal networks extend Bayesian nets to sets of distributions, or credal sets. This paper extends a stateoftheart Bayesian net for classification, called treeaugmented naive Bayes classifier, to credal sets originated from probability intervals. This extension is a basis to address the fundamental problem of prior ignorance about the distribution that generates the data, which is a commonplace in data mining applications. This issue is often neglected, but addressing it properly is a key to ultimately draw reliable conclusions from the inferred models. In this paper we formalize the new model, develop an exact lineartime classification algorithm, and evaluate the credal netbased classifier on a number of real data sets. The empirical analysis shows that the new classifier is good and reliable, and raises a problem of excessive caution that is discussed in the paper. Overall, given the favorable tradeo# between expressiveness and e#cient computation, the newly proposed classifier appears to be a good candidate for the widescale application of reliable classifiers based on credal networks, to real and complex tasks.