A linear constraint satisfaction approach to cost-based abduction

Abstract Santos Jr, E., A linear constraint satisfaction approach to cost-based abduction, Artificial Intelligence 65 (1994) 1-27. Abduction is the problem of finding the best explanation for a given set of observations. Within AI, this has been modeled as proving the observation by assuming some set of hypotheses. Cost-based abduction associates a cost with each hypothesis. The best proof is the one which assumes the least costly set. Previous approaches to finding the least cost set have formalized cost-based abduction as a heuristic graph search problem. However, efficient admissible heuristics have proven difficult to find. In this paper, we present a new technique for finding least cost sets by using linear constraints to represent causal relationships. In particular, we are able to recast the problem as a 0-1 integer linear programming problem. We can then use the highly efficient optimization tools of operations research yielding a computationally efficient method for solving cost-based abduction problems. Experiments comparing our linear constraint satisfaction approach to standard graph searching methodologies suggest that our approach is superior to existing search techniques in that our approach exhibits an expected-case polynomial run-time growth rate

Polynomial solvability of cost-based abduction

AbstractIn recent empirical studies we have shown that many interesting cost-based abduction problems can be solved efficiently by considering the linear program relaxation of their integer program formulation. We tie this to the concept of total unimodularity from network flow analysis, a fundamental result in polynomial solvability. From this, we can determine the polynomial solvability of abduction problems and, in addition, present a new heuristic for branch and bound in the non-polynomial cases

Negative Reinforcement and Backtrack-Points for Recurrent Neural Networks for Cost-Based Abduction

Abduction is the process of proceeding from data describing a set of observations or events, to a set of hypotheses which best explains or accounts for the data. Cost-based abduction (CKA) is an AI formalism in which evidence to be explained is treated as a goal to be proven, proofs have costs based on how much needs to be assumed to complete the proof, and the set of assumptions needed to complete the least-cost proof are taken as the best explanation for the given evidence. In this paper, we introduce two techniques for improving the performance of high order recurrent networks (HORN) applied to cost-based abduction. In the backtrack-points technique, we use heuristics to recognize early that the network trajectory is moving in the wrong direction; we then restore the network state to a previously-stored point, and apply heuristic perturbations to nudge the network trajectory in a different direction. In the negative reinforcement technique, we add hyperedges to the network to reduce the attractiveness of local-minima. We apply these techniques on a 300-hypothesis, 900-rule particularly-difficult instance of CBA

Parallel versus iterated: comparing population oriented and chained sequential simulated annealing approaches to cost-based abduction

Stochastic search techniques are used to solve NP-hard combinatorial optimization problems. Simulated annealing, genetic algorithms and hybridization of both, all attempt to find the best solution with minimal cost and time. Guided Evolutionary Simulated Annealing is one technique of such hybridization. It is based on evolutionary programming where a number of simulated annealing chains are working in a generation to find the optimum solution for a problem. Abduction is the problem of finding the best explanation to a given set of observations. In AI, this has been modeled by a set of hypotheses that need to be assumed to prove the observation or goal. Cost-Based Abduction (CBA) associates a cost to each hypothesis. It is an example of an NP-hard problem, where the objective is to minimize the cost of the assumed hypotheses to prove the goal. Analyzing the search space of a problem is one way of understanding its nature and categorizing it into straightforward, misleading or difficult for genetic algorithms. Fitness-Distance Correlation and Fitness-Distance plots are helpful tools in such analysis. This thesis examines solving the CBA problem using Simulated Annealing and Guided Evolutionary Simulated Annealing and analyses the Fitness-Distance landscape of some Cost-Based abduction problem instances

Exploiting World Knowledge inDiscourse Processing – A Comparison of Feature -Based and Inference-Based Approaches–

Tohoku University乾健太郎課

Abduction and Anonymity in Data Mining

This thesis investigates two new research problems that arise in modern data mining: reasoning on data mining results, and privacy implication of data mining results. Most of the data mining algorithms rely on inductive techniques, trying to infer information that is generalized from the input data. But very often this inductive step on raw data is not enough to answer the user questions, and there is the need to process data again using other inference methods. In order to answer high level user needs such as explanation of results, we describe an environment able to perform abductive (hypothetical) reasoning, since often the solutions of such queries can be seen as the set of hypothesis that satisfy some requirements. By using cost-based abduction, we show how classification algorithms can be boosted by performing abductive reasoning over the data mining results, improving the quality of the output. Another growing research area in data mining is the one of privacy-preserving data mining. Due to the availability of large amounts of data, easily collected and stored via computer systems, new applications are emerging, but unfortunately privacy concerns make data mining unsuitable. We study the privacy implications of data mining in a mathematical and logical context, focusing on the anonymity of people whose data are analyzed. A formal theory on anonymity preserving data mining is given, together with a number of anonymity-preserving algorithms for pattern mining. The post-processing improvement on data mining results (w.r.t. utility and privacy) is the central focus of the problems we investigated in this thesis

A Linear Constraint Satisfaction Approach to Cost-Based Abduction

Abduction is the problem of finding the best explanation for a given set of observations. Within AI, this has been modeled as proving the observation by assuming some set of hypotheses. Cost-based abduction associates a cost with each hypothesis. The best proof is the one which assumes the least costly set. Previous approaches to finding the least cost set have formalized cost-based abduction as a heuristic graph search problem. However, efficient admissible heuristics have proven difficult to find. In this paper, we present a new technique for finding least cost sets by using linear constraints to represent causal relationships. In particular, we are able to recast the problem as a 0-1 integer linear programming problem. We can then use the highly efficient optimization tools of operations research yielding a computationally efficient method for solving cost-based abduction problems. Experiments comparing our linear constraint satisfaction approach to standard graph searching methodol..