Average Case Analysis of k-CNF and k-DNF learning algorithms
نویسندگان
چکیده
We present average case models of algorithms for learning Conjunctive Normal Form (CNF, i.e., conjunctions of disjunctions) and Disjunctive Normal Form (DNF, i.e., disjunctions of conjunctions). Our goal is to predict the expected error of the learning algorithm as a function of the number n of training examples, averaging over all sequences of n training examples. We show that our average case models accurately predict the expected error and demonstrate that the analysis can lead to insight into the behavior of the algorithm and the factors that a ect the error.
منابع مشابه
Eecient Read-restricted Monotone Cnf/dnf Dualization by Learning with Membership Queries Produced as Part of the Esprit Working Group in Neural and Computational Learning Ii, Neurocolt2 27150
We consider exact learning monotone CNF formulas in which each variable appears at most some constant k times (\read-k" monotone CNF). Let f : f0;1g n ! f0;1g be expressible as a read-k monotone CNF formula for some natural number k. We give an incremental output polynomial time algorithm for exact learning both the read-k CNF and (not necessarily read restricted) DNF descriptions of f. The alg...
متن کاملEecient Read-restricted Monotone Cnf/dnf Dualization by Learning with Membership Queries
We consider exact learning monotone CNF formulas in which each variable appears at most some constant k times (\read-k" monotone CNF). Let f : f0;1g n ! f0;1g be expressible as a read-k monotone CNF formula for some natural number k. We give an incremental output polynomial time algorithm for exact learning both the read-k CNF and (not necessarily read restricted) DNF descriptions of f. The alg...
متن کاملRead - Restricted Monotone CNF / DNFDualization by Learning with Membership
We consider exact learning monotone CNF formulas in which each variable appears at most some constant k times (\read-k" monotone CNF). Let f : f0;1g n ! f0;1g be expressible as a read-k monotone CNF formula for some natural number k. We give an incremental output polynomial time algorithm for exact learning both the read-k CNF and (not necessarily read restricted) DNF descriptions of f. The alg...
متن کاملAnalysis of Case-Based Representability of Boolean Functions by Monotone Theory
Classi cation is one of major tasks in case-based reasoning(CBR) and many studies have been done for analyzing properties of case-based classi cation [1, 14, 10, 15, 12, 9, 13, 7]. However, these studies only consider numerical similarity measures whereas there are other kinds of similarity measure for di erent tasks. Among these measures, HYPO system [2, 3] in a legal domain uses a similarity ...
متن کاملQuantifying Inductive Bias: AI Learning Algorithms and Valiant's Learning Framework
We show that the notion of inductive bias in concept learning can be quantified in a way that directl_v relates to learning performance in the framework recently introduced by Valiant. Our measure of bias is based on the growth function introduced by Vapnik and Chervonenkis, and on the Vapnik-Chervonenkis dimension. We measure some common language biases, including restriction to conjunctive co...
متن کامل