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Bayesian network classifiers (BNCs) provide a sound formalism for representing probabilistic knowledge and reasoning with uncertainty. Explicit independence assumptions can effectively and efficiently reduce the size of the search space for solving the NP-complete problem of structure learning. Strong conditional dependencies, when added to the network topology of BNC, can relax the independence assumptions, whereas the weak ones may result in biased estimates of conditional probability and degradation in generalization performance. In this paper, we propose an extension to the k -dependence Bayesian classifier (KDB) that achieves the bias/variance trade-off by verifying the rationality of implicit independence assumptions implicated. The informational and probabilistic dependency relationships represented in the learned robust topologies will be more appropriate for fitting labeled and unlabeled data, respectively. The comprehensive experimental results on 40 UCI datasets show that our proposed algorithm achieves competitive classification performance when compared to state-of-the-art BNC learners and their efficient variants in terms of zero-one loss, root mean square error (RMSE), bias and variance. [ABSTRACT FROM AUTHOR]

This paper obtains a measure-theoretic restriction that must be satisfied by a prior probability measure for posteriors to be computed in limited time. Specifically, it is shown that the prior must be factorizable. Factorizability is a set of independence conditions for events in the sample space that allows agents to calculate posteriors using only a subset of the dataset. The result has important implications for models in mathematical economics and finance that rely on a common prior. If one introduces the limited time restriction to Aumann’s famous Agreeing to Disagree setup, one sees that checking for factorizability requires agents to have access to every event in the measure space, thus severely limiting the scope of the agreement result.

This paper obtains a measure-theoretic restriction that must be satisfied by a prior probability measure for posteriors to be computed in limited time. Specifically, it is shown that the prior must be factorizable. Factorizability is a set of independence conditions for events in the sample space that allows agents to calculate posteriors using only a subset of the dataset. The result has important implications for models in mathematical economics and finance that rely on a common prior. If one introduces the limited time restriction to Aumann's famous Agreeing to Disagree setup, one sees that checking for factorizability requires agents to have access to every event in the measure space, thus severely limiting the scope of the agreement result. [ABSTRACT FROM AUTHOR]

The independence assumptions help Bayesian network classifier (BNC), e.g., Naive Bayes (NB), reduce structure complexity and perform surprisingly well in many real-world applications. Semi-naive Bayesian techniques seek to improve the classification performance by relaxing the attribute independence assumption. However, the study of dependence rather than independence has received more attention during the past decade and the validity of independence assumptions needs to be further explored. In this paper, a novel learning technique, called Adaptive Independence Thresholding (AIT), is proposed to automatically identify the informational independence and probabilistic independence. AIT can respectively tune the network topologies of BNC learned from training data and testing instance under the framework of target learning. Zero-one loss, bias, variance and conditional log likelihood are introduced to compare the classification performance in the experimental study. The extensive experimental results on a collection of 36 benchmark datasets from the UCI machine learning repository show that AIT is more effective than other learning techniques (such as structure extension, attribute weighting) and helps make the final BNCs achieve remarkable classification improvements. [ABSTRACT FROM AUTHOR]

Branden Fitelson and Alan Hájek have suggested that it is finally time for a "revolution" in which we jettison Kolmogorov's axiomatization of probability, and move to an alternative like Popper's. According to these authors, not only did Kolmogorov fail to give an adequate analysis of conditional probability, he also failed to give an adequate account of another central notion in probability theory: probabilistic independence. This paper defends Kolmogorov, with a focus on this independence charge. I show that Kolmogorov's sophisticated theory of conditional distributions, advocated by authors such as Kenny Easwaran but often overlooked by philosophers, has the resources to define the notion of independence Fitelson and Hájek seek. I then argue that Kolmogorov's original definition of independence, once suitably reinterpreted as capturing a slight logical weakening of this notion, is not so problematic after all. Indeed, rather than discarding Kolmogorov's definition, we should make room for two distinct notions of probabilistic independence, one stronger and one weaker, which play different theoretical roles. [ABSTRACT FROM AUTHOR]

This paper discusses a simple problem in detection theory using a model with a simple discretized space. This allows the probability problem to be analyzed algebraically to demonstrate that separate targets, independent before entering the detection space, do not have probabilistically independent detection probability distributions. Several variants of the basic case are discussed. [ABSTRACT FROM PUBLISHER]

The image of an opaque object is created by observing the reflection of the light incident on its surface. The dichromatic reflection model describes the surface reflection as the sum of two components, diffuse and specular terms. The specular reflection component is usually strong in its intensity and polarized significantly compared to the diffuse components. On the other hand, the intensity of the diffuse component is weak and it tends to be unpolarized except near occluding contours. Thus, the observation of an object through a rotating polarizer approximately yields images containing constant diffuse component and specular component of different intensity. In this paper, we show that diffuse and specular components of surface reflection can be separated as two independent components when we apply Independent Component Analysis to the images observed through a polarizer of different orientations. We give a separation simulation of artificial data and also give some separation results of real scenes. [ABSTRACT FROM AUTHOR]

We introduce an axiomatic definition of a mathematical structure that we term a separoid. We develop some general mathematical properties of separoids and related axiom systems, as well as connections with other mathematical structures, such as distributive lattices, Hilbert spaces, and graphs. And we show, by means of a detailed account of a number of models of the separoid axioms, how the concept of separoid unifies a variety of notions of ‘irrelevance’ arising out of different formalisms for representing uncertainty in Probability, Statistics, Artificial Intelligence, and other fields. [ABSTRACT FROM AUTHOR]

Bayesian networks are powerful tools for knowledge representation and inference under conditions of uncertainty. However, learning an optimal Bayesian network classifier (BNC) is an NP-hard problem since its topology complexity increases exponentially with the number of attributes. Researchers proposed to apply information-theoretic criteria to measure conditional dependence, and independence assumptions are introduced implicitly or explicitly to simplify the network topology of BNC. In this paper, we clarify the mapping relationship between conditional mutual information and local topology, and then illustrate that informational independence does not correspond to probabilistic independence, the criterion of probabilistic independence does not necessarily hold for the independence topology. A novel framework of semi-naive Bayesian operation, called Hierarchical Independence Thresholding (HIT), is presented to efficiently identify informational conditional independence and probabilistic conditional independence by applying an adaptive thresholding method, redundant edges will be filtered out and the learned topology will fit the data better. Extensive experimental evaluation on 58 publicly available datasets reveals that when HIT is applied to BNCs (such as tree augmented Naive Bayes or k -dependence Bayesian classifier), the final BNCs achieve competitive classification performance compared to state-of-the-art learners such as Random Forest and Logistic regression. [ABSTRACT FROM AUTHOR]