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

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

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

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

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

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

[8]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, CACM.

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

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

[11]  Leslie G. Valiant,et al.  Cryptographic limitations on learning Boolean formulae and finite automata , 1994, JACM.

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

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

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

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

[16]  Leslie G. Valiant,et al.  Learning Disjunction of Conjunctions , 1985, IJCAI.

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

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

[19]  Kenneth Basye,et al.  Inferring Finite Automata with Stochastic Output Functions and an Application to Map Learning , 2004, Machine Learning.

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

[21]  David Haussler,et al.  Occam's Razor , 1987, Inf. Process. Lett..

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

[23]  Robert E. Schapire,et al.  Efficient Distribution-Free Learning of Probabilistic , 1994 .

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

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

[26]  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).

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

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

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

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

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

[32]  George Shackelford,et al.  Learning k-DNF with noise in the attributes , 1988, Annual Conference Computational Learning Theory.

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

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

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

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

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

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

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

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

[41]  A. Church.  Edward F. Moore. Gedanken-experiments on sequential machines. Automata studies , edited by C. E. Shannon and J. McCarthy, Annals of Mathematics studies no. 34, litho-printed, Princeton University Press, Princeton1956, pp. 129–153. , 1958, Journal of Symbolic Logic.

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

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