Ahmed Y. Tawfik

Temporal Reasoning and Bayesian Networks

This work examines important issues in probabilistic temporal representation and reasoning using Bayesian networks (also known as belief networks). The representation proposed here utilizes temporal (or dynamic) probabilities to represent facts, events, and the effects of events. The architecture of a belief network may change with time to indicate a different causal context. Probability variations with time capture temporal properties such as persistence and causation. They also capture event interaction, and when the interaction between events follows known models such as the competing risks model, the additive model, or the dominating event model, the net effect of many interacting events on the temporal probabilities can be calculated efficiently. This representation of reasoning also exploits the notion of temporal degeneration of relevance due to information obsolescence to improve the efficiency.

Towards a Temporal Extension of Formal Concept Analysis

This article presents a method for analyzing the evolution of concepts represented by concept lattices in a time stamped database, showing how the concepts that evolve with time induce a change in the concept lattice. The purpose of this work is to extend formal concept analysis to handle temporal properties and represent temporally evolving attributes.

Using Qualitative Probability in Reverse-Engineering Gene Regulatory Networks

This paper demonstrates the use of qualitative probabilistic networks (QPNs) to aid Dynamic Bayesian Networks (DBNs) in the process of learning the structure of gene regulatory networks from microarray gene expression data. We present a study which shows that QPNs define monotonic relations that are capable of identifying regulatory interactions in a manner that is less susceptible to the many sources of uncertainty that surround gene expression data. Moreover, we construct a model that maps the regulatory interactions of genetic networks to QPN constructs and show its capability in providing a set of candidate regulators for target genes, which is subsequently used to establish a prior structure that the DBN learning algorithm can use and which 1) distinguishes spurious correlations from true regulations, 2) enables the discovery of sets of coregulators of target genes, and 3) results in a more efficient construction of gene regulatory networks. The model is compared to the existing literature using the known gene regulatory interactions of Drosophila Melanogaster.

An abstract theory and ontology of motion based on the regions connection calculus

In this paper, we present a framework abstracting motion by creating a qualitative representation of classes describing motion, and use the continuity constraints implicitly embedded in the semantics of these classes to create a framework that enables plausible reasoning about them. In particular, we propose a topology-based calculus of motion whose primitive is a motion class. We subsequently construct a set of primitive motion classes that exhaustively describes the change in topology between two moving objects, and show how compound motion classes are formed from these primitive motion classes using continuity constraints we make explicit. We use composition tables to define queries in the spatio-temporal domain and enable the extension of the classes to reason about the change in topology among three objects as they move.

Irrelevance in uncertain temporal reasoning

In the presence of uncertainty, relevance of information degenerates as time evolves. The work shows that this degeneration occurs in probabilistic temporal reasoning. A mechanism for analyzing this phenomenon uses a Markov chain representation and a degree of relevance measure called temporal extraneousness. Efficiency of probabilistic temporal reasoning can be improved by ignoring irrelevant and weakly relevant information. The analysis allows one to identify the portion of event history affecting the time instant of interest. The duration of relevant history depends on the dynamic nature of the system and the chosen relevance threshold. These notions are used to prune time-sliced Bayesian networks which constitute a popular probabilistic temporal reasoning knowledge representation.

Spatio-temporal Reasoning for Vague Regions

This paper extends a mereotopological theory of spatiotemporal reasoning to vague ”egg-yolk” regions. In this extension, the egg and its yolk are allowed to move and change over time. We present a classification of motion classes for vague regions as well as composition tables for reasoning about moving vague regions. We also discuss the formation of scrambled eggs when it becomes impossible to distinguish the yolk from the white and examine how to incorporate temporally and spatially dispersed observations to recover the yolk and white from a scrambled egg. Egg splitting may occur as a result of the recovery process when available information supports multiple egg recovery alternatives. Egg splitting adds another dimension of uncertainty to reasoning with vague regions.

Qualitative Motif Detection in Gene Regulatory Networks

This paper motivates the use of Qualitative Probabilistic Networks (QPNs) in conjunction with or in lieu of Bayesian Networks (BNs) for reconstructing gene regulatory networks from microarray expression data. QPNs are qualitative abstractions of Bayesian Networks that replace the conditional probability tables associated with BNs by qualitative influences, which use signs to encode how the values of variables change. We demonstrate that the qualitative influences defined by QPNs exhibit a natural mapping to naturally-occurring patterns of connections, termed network motifs, embedded in Gene Regulatory Networks and present a model that maps QPN constructs to such motifs.The contribution of this paper is that of discovering motifs by mapping their time-series experimental data to QPN influences and using the discovered motifs to aid the process of reconstructing the corresponding gene regulatory network via Dynamic Bayesian Networks (DBNs). The general aim is to compile a model that uses qualitative equivalents of Dynamic Bayesian Networks to explore gene expression networks and their regulatory mechanisms. Although this aim remains under development, the results we have obtained shows success for the discovery of regulatory motifs in Saccharomyces Cerevisiae and their effectiveness in improving the results obtained in terms of reconstruction using DBNs.

Temporal Relevance in Dynamic Decision Networks with Sparse Evidence

Dynamic decision networks have been used in many applications and they are particularly suited for monitoring applications. However, the networks tend to grow very large resulting in significant performance degradation. In this paper, we study the degeneration of relevance of uncertain temporal information and propose an analytical upper bound for the relevance time of information in a restricted class of dynamic decision networks with sparse evidence. An empirical generalization of this analytical result is presented along with a series of experimental results to verify the performance of the empirical upper bound. By discarding irrelevant and weakly relevant evidence, the performance of the network is significantly improved.

The Degeneration of Relevance in Uncertain Temporal Domains: An Empirical Study

This work examines the relevance of uncertain temporal information. A key observation that motivates the analysis presented here is that in the presence of uncertainty, relevance of information degenerates as time evolves. This paper presents an empirical quantitative study of the degeneration of relevance in time-sliced Belief Networks that aims at extending known results. A simple technique for estimating an upper bound on the relevance time is presented. To validate the proposed technique, results of experiments using realistic and synthetic time-sliced belief networks are presented. The results show that the proposed upper bound holds in more than 98% of the experiments. These results have been obtained using a modified version of the dynamic belief networks roll-up algorithm.

Model-based Diagnosis: A Probabilistic Extension

The present study treats model-based diagnosis as an uncertain reasoning problem. To handle the uncertainty in model-based diagnosis effectively, a probabilistic approach serves as a point of departure. The use of probabilities in diagnosis has proved beneficial to the performance of diagnostic engines.