Inference in possibilistic network classifiers under uncertain observations

Abstract

Possibilistic networks, which are compact representations of possibility distributions, are powerful tools for representing and reasoning with uncertain and incomplete information in the framework of possibility theory. They are like Bayesian networks but lie on possibility theory to deal with uncertainty, imprecision and incompleteness. While classification is a very useful task in many real world applications, possibilistic network-based classification issues are not well investigated in general and possibilistic-based classification inference with uncertain observations in particular. In this paper, we address on one hand the theoretical foundations of inference in possibilistic classifiers under uncertain inputs and propose on the other hand a novel efficient algorithm for the inference in possibilistic networkbased classification under uncertain observations. We start by studying and analyzing the counterpart of Jeffrey's rule in the framework of possibility theory. After that, we address the validity of Markov-blanket criterion in the context of possibilistic networks used for classification with uncertain inputs purposes. Finally, we propose a novel algorithm suitable for possibilistic classifiers with uncertain observations without assuming any independence relations between observations. This algorithm guarantees the same results as if classification were performed using the possibilistic counterpart of Jeffrey's rule. Classification is achieved in polynomial time if the target variable is binary. The basic idea of our algorithm is to only search for 270 S. Benferhat, K. Tabia totally plausible class instances through a series of equivalent and polynomial transformations applied on the possibilistic classifier taking into account the uncertain observations.

Possibilistic Networks: MAP Query and Computational Analysis

“…Most of the works are more or less direct adaptations of probabilistic networks inference algorithms. For examples, a possibilistic elimination variable algorithm can be found in [5] in the context of possibilistic network classifiers. In [7], a possibilistic counterpart of teh wel-known Message passing algorithm is proposed.…”

From Information to Evidence in a Bayesian Network

“…Fixed probabilistic evidence corresponds to the concept described as soft evidence in [4], [33], [42], [44], [48].…”

“…Apart from two exceptions [4], [26] the concepts of fixed and not-fixed probabilistic evidence are never distinguished. Specifically, several published articles clearly distinguish between likelihood evidence and probabilistic evidence -regrouped under the term uncertain evidence-without identifying the distinction between fixed and not-fixed probabilistic evidence [12], [15], [42], [44], [49].…”

Synthesis of the secondary structure of algebraic Bayesian networks: an incremental algorithm and statistical estimation of its complexity

“…Зачастую разме-ры полученных данных, присутствующая в них неопределенность, связанная с нехваткой данных или их неточностью [2], а также общая связность системы в совокупности порождают проблему, для решения которой в информатике и искусственном интеллекте используется декомпозиция исходной системы на совокупность подсистем с целью локализовать вычисления, тем самым экспоненциально сократив затра-ты на решение поставленной задачи. Такие представители класса вероятностных графических моделей, как байесовские сети доверия, а также родственные им алгебраические байесовские сети (АБС), допус-кающие разбиение исходных данных на совокупности локально тесно связанных между собой объек-тов [3], позволяют существенно ускорить процедуру обработки новых поступающих данных (так назы-ваемых свидетельств), а также являются гибкой структурой, способной перестраиваться с учетом новых условий.…”