An Information Theoretic Approach to Modeling Neural Network Expert Systems

In this paper we propose several novel techniques for mapping rule bases, such as are used in rule based expert systems, onto neural network architectures. Our objective in doing this is to achieve a system capable of incremental learning, and distributed probabilistic inference. Such a system would be capable of performing inference many orders of magnitude faster than current serial rule based expert systems, and hence be capable of true real time operation. In addition, the rule based formalism gives the system an explicit knowledge representation, unlike current neural models. We propose an information-theoretic approach to this problem, which really has two aspects: firstly learning the model and, secondly, performing inference using this model. We will show a clear pathway to implementing an expert system starting from raw data, via a learned rule-based model, to a neural network that performs distributed inference

Nonmonotonic Probabilistic Logics between Model-Theoretic Probabilistic Logic and Probabilistic Logic under Coherence

Recently, it has been shown that probabilistic entailment under coherence is weaker than model-theoretic probabilistic entailment. Moreover, probabilistic entailment under coherence is a generalization of default entailment in System P. In this paper, we continue this line of research by presenting probabilistic generalizations of more sophisticated notions of classical default entailment that lie between model-theoretic probabilistic entailment and probabilistic entailment under coherence. That is, the new formalisms properly generalize their counterparts in classical default reasoning, they are weaker than model-theoretic probabilistic entailment, and they are stronger than probabilistic entailment under coherence. The new formalisms are useful especially for handling probabilistic inconsistencies related to conditioning on zero events. They can also be applied for probabilistic belief revision. More generally, in the same spirit as a similar previous paper, this paper sheds light on exciting new formalisms for probabilistic reasoning beyond the well-known standard ones.Comment: 10 pages; in Proceedings of the 9th International Workshop on Non-Monotonic Reasoning (NMR-2002), Special Session on Uncertainty Frameworks in Nonmonotonic Reasoning, pages 265-274, Toulouse, France, April 200

Identifying statistical dependence in genomic sequences via mutual information estimates

Questions of understanding and quantifying the representation and amount of information in organisms have become a central part of biological research, as they potentially hold the key to fundamental advances. In this paper, we demonstrate the use of information-theoretic tools for the task of identifying segments of biomolecules (DNA or RNA) that are statistically correlated. We develop a precise and reliable methodology, based on the notion of mutual information, for finding and extracting statistical as well as structural dependencies. A simple threshold function is defined, and its use in quantifying the level of significance of dependencies between biological segments is explored. These tools are used in two specific applications. First, for the identification of correlations between different parts of the maize zmSRp32 gene. There, we find significant dependencies between the 5' untranslated region in zmSRp32 and its alternatively spliced exons. This observation may indicate the presence of as-yet unknown alternative splicing mechanisms or structural scaffolds. Second, using data from the FBI's Combined DNA Index System (CODIS), we demonstrate that our approach is particularly well suited for the problem of discovering short tandem repeats, an application of importance in genetic profiling.Comment: Preliminary version. Final version in EURASIP Journal on Bioinformatics and Systems Biology. See http://www.hindawi.com/journals/bsb

Distributional Sentence Entailment Using Density Matrices

Categorical compositional distributional model of Coecke et al. (2010) suggests a way to combine grammatical composition of the formal, type logical models with the corpus based, empirical word representations of distributional semantics. This paper contributes to the project by expanding the model to also capture entailment relations. This is achieved by extending the representations of words from points in meaning space to density operators, which are probability distributions on the subspaces of the space. A symmetric measure of similarity and an asymmetric measure of entailment is defined, where lexical entailment is measured using von Neumann entropy, the quantum variant of Kullback-Leibler divergence. Lexical entailment, combined with the composition map on word representations, provides a method to obtain entailment relations on the level of sentences. Truth theoretic and corpus-based examples are provided.Comment: 11 page

Complexity, BioComplexity, the Connectionist Conjecture and Ontology of Complexity\ud

This paper develops and integrates major ideas and concepts on complexity and biocomplexity - the connectionist conjecture, universal ontology of complexity, irreducible complexity of totality & inherent randomness, perpetual evolution of information, emergence of criticality and equivalence of symmetry & complexity. This paper introduces the Connectionist Conjecture which states that the one and only representation of Totality is the connectionist one i.e. in terms of nodes and edges. This paper also introduces an idea of Universal Ontology of Complexity and develops concepts in that direction. The paper also develops ideas and concepts on the perpetual evolution of information, irreducibility and computability of totality, all in the context of the Connectionist Conjecture. The paper indicates that the control and communication are the prime functionals that are responsible for the symmetry and complexity of complex phenomenon. The paper takes the stand that the phenomenon of life (including its evolution) is probably the nearest to what we can describe with the term “complexity”. The paper also assumes that signaling and communication within the living world and of the living world with the environment creates the connectionist structure of the biocomplexity. With life and its evolution as the substrate, the paper develops ideas towards the ontology of complexity. The paper introduces new complexity theoretic interpretations of fundamental biomolecular parameters. The paper also develops ideas on the methodology to determine the complexity of “true” complex phenomena.\u

Multiscale Granger causality analysis by \`a trous wavelet transform

Since interactions in neural systems occur across multiple temporal scales, it is likely that information flow will exhibit a multiscale structure, thus requiring a multiscale generalization of classical temporal precedence causality analysis like Granger's approach. However, the computation of multiscale measures of information dynamics is complicated by theoretical and practical issues such as filtering and undersampling: to overcome these problems, we propose a wavelet-based approach for multiscale Granger causality (GC) analysis, which is characterized by the following properties: (i) only the candidate driver variable is wavelet transformed (ii) the decomposition is performed using the \`a trous wavelet transform with cubic B-spline filter. We measure GC, at a given scale, by including the wavelet coefficients of the driver times series, at that scale, in the regression model of the target. To validate our method, we apply it to publicly available scalp EEG signals, and we find that the condition of closed eyes, at rest, is characterized by an enhanced GC among channels at slow scales w.r.t. eye open condition, whilst the standard Granger causality is not significantly different in the two conditions.Comment: 4 pages, 3 figure