Learning Fallible Deterministic Finite Automata

We consider the problem of learning from a fallible expert that answers all queries about a concept, but often gives incorrect answers. The expert can also be thought of as a truth table describing the concept which has been partially corrupted. In order to learn the underlying concept with arbitrarily high precision, we would like to use its structure in order to correct most of the incorrect answers. We assume that the expert's errors are uniformly and independently distributed, occur with any fixed probability strictly smaller than 1/2, and are persistent. In particular, we present a polynomial time algorithm using membership queries for correcting and learning fallible Deterministic Finite Automata under the uniform distribution.

[1]  H. Chernoff.  A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[2]  Edward F. Moore,et al.  Gedanken-Experiments on Sequential Machines , 1956 .

[3]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[4]  John E. Hopcroft,et al.  An n log n algorithm for minimizing states in a finite automaton , 1971 .

[5]  Temple F. Smith.  Occam's razor , 1980, Nature.

[6]  Dana Angluin,et al.  A Note on the Number of Queries Needed to Identify Regular Languages , 1981, Inf. Control..

[7]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, STOC '84.

[8]  Leslie Pack Kaelbling,et al.  Inferring finite automata with stochastic output functions and an application to map learning , 1992, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[9]  Ronald L. Rivest,et al.  Diversity-based inference of finite automata , 1994, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[10]  Dana Angluin,et al.  Learning Regular Sets from Queries and Counterexamples , 1987, Inf. Comput..

[11]  Philip D. Laird,et al.  Learning from good data and bad , 1987 .

[12]  Ming Li,et al.  Learning in the presence of malicious errors , 1993, STOC '88.

[13]  Ronald L. Rivest,et al.  Inference of finite automata using homing sequences , 1989, STOC '89.

[14]  Robert E. Schapire,et al.  Inference of Finite Automata Using Homing Sequences (Extended Abstract) , 1989, STOC 1989.

[15]  Robert H. Sloan,et al.  Computational learning theory: new models and algorithms , 1989 .

[16]  Richard J. Lipton,et al.  New Directions In Testing , 1989, Distributed Computing And Cryptography.

[17]  Manfred K. Warmuth,et al.  Learning integer lattices , 1990, COLT '90.

[18]  Manuel Blum,et al.  Self-testing/correcting with applications to numerical problems , 1990, STOC '90.

[19]  Michael Kearns,et al.  Computational complexity of machine learning , 1990, ACM distinguished dissertations.

[20]  Robert E. Schapire,et al.  Efficient distribution-free learning of probabilistic concepts , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[21]  Leonard Pitt,et al.  Prediction-Preserving Reducibility , 1990, J. Comput. Syst. Sci..

[22]  Hans Ulrich Simon,et al.  On learning ring-sum-expansions , 1990, COLT '90.

[23]  Yasubumi Sakakibara,et al.  On Learning from Queries and Counterexamples in the Presence of Noise , 1991, Inf. Process. Lett..

[24]  D. Angluin,et al.  Randomly fallible teachers: Learning monotone DNF with an incomplete membership oracle , 1991, Machine Learning.

[25]  Sally A. Goldman,et al.  Learning k-term DNF formulas with an incomplete membership oracle , 1992, COLT '92.

[26]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[27]  Robert H. Sloan,et al.  Corrigendum to types of noise in data for concept learning , 1988, COLT '92.

[28]  Robert E. Schapire,et al.  Design and analysis of efficient learning algorithms , 1992, ACM Doctoral dissertation award ; 1991.

[29]  Rani Siromoney,et al.  A noise model on learning sets of strings , 1992, COLT '92.

[30]  Michael Kearns,et al.  Efficient noise-tolerant learning from statistical queries , 1993, STOC.

[31]  Ronitt Rubinfeld,et al.  Learning fallible finite state automata , 1993, COLT '93.

[32]  Ronitt Rubinfeld,et al.  Efficient learning of typical finite automata from random walks , 1993, STOC.

[33]  Robert E. Schapire,et al.  Exact Identification of Read-Once Formulas Using Fixed Points of Amplification Functions , 1993, SIAM J. Comput..

[34]  Marek Karpinski,et al.  Learning read-once formulas with queries , 1993, JACM.

[35]  Leslie G. Valiant,et al.  Cryptographic Limitations on Learning Boolean Formulae and Finite Automata , 1993, Machine Learning: From Theory to Applications.

[36]  Michael Frazier,et al.  Learning conjunctions of Horn clauses , 2004, Machine Learning.

[37]  D. Angluin,et al.  Learning From Noisy Examples , 1988, Machine Learning.

[38]  Theodore M. Booth.  Demonstrating hazards in sequential relay circuits , 1963, SWCT.