Cause-effect relationships and partially defined Boolean functions
Annals of Operations Research
The Minimum Satisfiability Problem
SIAM Journal on Discrete Mathematics
Predicting Cause-Effect Relationships from Incomplete Discrete Observations
SIAM Journal on Discrete Mathematics
Randomized algorithms
Logical analysis of numerical data
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Convexity and logical analysis of data
Theoretical Computer Science
Approximation algorithms
An Implementation of Logical Analysis of Data
IEEE Transactions on Knowledge and Data Engineering
Discrete Applied Mathematics
Review: Knowledge discovery in medicine: Current issue and future trend
Expert Systems with Applications: An International Journal
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The objective of this study was to distinguish within a population of patients with and without breast cancer. The study was based on the University of Wisconsin's dataset of 569 patients, of whom 212 were subsequently found to have breast cancer. A subset-conjunctive model, which is related to Logical Analysis of Data, is described to distinguish between the two groups of patients based on the results of a non-invasive procedure called Fine Needle Aspiration, which is often used by physicians before deciding on the need for a biopsy. We formulate the problem of inferring subset-conjunctive rules as a 0-1 integer program, show that it is NP-Hard, and prove that it admits no polynomial-time constant-ratio approximation algorithm. We examine the performance of a randomized algorithm, and of randomization using LP rounding. In both cases, the expected performance ratio is arbitrarily bad. We use a deterministic greedy algorithm to identify a Pareto-efficient set of subset-conjunctive rules; describe how the rules change with a re-weighting of the type-I and type-II errors; how the best rule changes with the subset size; and how much of a tradeoff is required between the two types of error as one selects a more stringent or more lax classification rule. An important aspect of the analysis is that we find a sequence of closely related efficient rules, which can be readily used in a clinical setting because they are simple and have the same structure as the rules currently used in clinical diagnosis.