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Automatic Learning with Feedback Queries Automatic Refers to Accepted by Finite Automata John Case 1 Sanjay Jain 2 Yuh Shin Ong 2 Pavel Semukhin 3 Frank Stephan 2 1 University of Delaware 2 National University of Singapore 3 University of Regina

  1. Automatic Learning with Feedback Queries Automatic Refers to Accepted by Finite Automata John Case 1 Sanjay Jain 2 Yuh Shin Ong 2 Pavel Semukhin 3 Frank Stephan 2 1 University of Delaware 2 National University of Singapore 3 University of Regina Computability in Europe 2011 Sofia, Bulgaria

  2. For Your Speed Reading Pleasure & Quick Impression ( .. ⌣ ) 1 Background Motivation & Numerical Example Semi Computability-Theoretic Setting Learnable Classes of Regular Languages 2 Automatic Structures & Learning Automatic Structures Automatic Classes Learning Automatic Classes & Further Motivation Memory Restrictions Formulate Automatic Feedback Learning 3 Examples & Results Examples Results CJOSS (UD, NUS, UR) Auto Learn w/ Feedback Queries CiE’11, Sofia, Bulgaria 2 / 13

  3. Background Motivation & Example Motivation & Numerical Example A motivation: Program of Khoussainov & Nerode 1995 re ≈ effect of replacing TMs by finite automata in computable model theory. Present paper: One in a series (Jain, Luo and Stephan 2010; Jain, Ong, Pu, Stephan 2010; Case, Jain, Le, Ong, Semukhin, Stephan LATA-2011) devoted to effect on computability-theoretic learning theory under above replacement. Example unrestricted learning from positive data: Data Hypotheses 2 Set of all even numbers; 2,3 Set of all numbers; 2,3,5 Set of all prime numbers; 2,3,5,13 Set of all prime numbers; 2,3,5,13,1 Set of all Fibonacci numbers; 2,3,5,13,1,8 Set of all Fibonacci numbers. . . . . . . Success: Algorithmic learner outputs a sequence of hypotheses which eventually stabilizes on a correct hypothesis. CJOSS (UD, NUS, UR) Auto Learn w/ Feedback Queries CiE’11, Sofia, Bulgaria 3 / 13

  4. Background Motivation & Example Motivation & Numerical Example A motivation: Program of Khoussainov & Nerode 1995 re ≈ effect of replacing TMs by finite automata in computable model theory. Present paper: One in a series (Jain, Luo and Stephan 2010; Jain, Ong, Pu, Stephan 2010; Case, Jain, Le, Ong, Semukhin, Stephan LATA-2011) devoted to effect on computability-theoretic learning theory under above replacement. Example unrestricted learning from positive data: Data Hypotheses 2 Set of all even numbers; 2,3 Set of all numbers; 2,3,5 Set of all prime numbers; 2,3,5,13 Set of all prime numbers; 2,3,5,13,1 Set of all Fibonacci numbers; 2,3,5,13,1,8 Set of all Fibonacci numbers. . . . . . . Success: Algorithmic learner outputs a sequence of hypotheses which eventually stabilizes on a correct hypothesis. CJOSS (UD, NUS, UR) Auto Learn w/ Feedback Queries CiE’11, Sofia, Bulgaria 3 / 13

  5. Background Motivation & Example Motivation & Numerical Example A motivation: Program of Khoussainov & Nerode 1995 re ≈ effect of replacing TMs by finite automata in computable model theory. Present paper: One in a series (Jain, Luo and Stephan 2010; Jain, Ong, Pu, Stephan 2010; Case, Jain, Le, Ong, Semukhin, Stephan LATA-2011) devoted to effect on computability-theoretic learning theory under above replacement. Example unrestricted learning from positive data: Data Hypotheses 2 Set of all even numbers; 2,3 Set of all numbers; 2,3,5 Set of all prime numbers; 2,3,5,13 Set of all prime numbers; 2,3,5,13,1 Set of all Fibonacci numbers; 2,3,5,13,1,8 Set of all Fibonacci numbers. . . . . . . Success: Algorithmic learner outputs a sequence of hypotheses which eventually stabilizes on a correct hypothesis. CJOSS (UD, NUS, UR) Auto Learn w/ Feedback Queries CiE’11, Sofia, Bulgaria 3 / 13

  6. Background Motivation & Example Motivation & Numerical Example A motivation: Program of Khoussainov & Nerode 1995 re ≈ effect of replacing TMs by finite automata in computable model theory. Present paper: One in a series (Jain, Luo and Stephan 2010; Jain, Ong, Pu, Stephan 2010; Case, Jain, Le, Ong, Semukhin, Stephan LATA-2011) devoted to effect on computability-theoretic learning theory under above replacement. Example unrestricted learning from positive data: Data Hypotheses 2 Set of all even numbers; 2,3 Set of all numbers; 2,3,5 Set of all prime numbers; 2,3,5,13 Set of all prime numbers; 2,3,5,13,1 Set of all Fibonacci numbers; 2,3,5,13,1,8 Set of all Fibonacci numbers. . . . . . . Success: Algorithmic learner outputs a sequence of hypotheses which eventually stabilizes on a correct hypothesis. CJOSS (UD, NUS, UR) Auto Learn w/ Feedback Queries CiE’11, Sofia, Bulgaria 3 / 13

  7. Background Motivation & Example Motivation & Numerical Example A motivation: Program of Khoussainov & Nerode 1995 re ≈ effect of replacing TMs by finite automata in computable model theory. Present paper: One in a series (Jain, Luo and Stephan 2010; Jain, Ong, Pu, Stephan 2010; Case, Jain, Le, Ong, Semukhin, Stephan LATA-2011) devoted to effect on computability-theoretic learning theory under above replacement. Example unrestricted learning from positive data: Data Hypotheses 2 Set of all even numbers; 2,3 Set of all numbers; 2,3,5 Set of all prime numbers; 2,3,5,13 Set of all prime numbers; 2,3,5,13,1 Set of all Fibonacci numbers; 2,3,5,13,1,8 Set of all Fibonacci numbers. . . . . . . Success: Algorithmic learner outputs a sequence of hypotheses which eventually stabilizes on a correct hypothesis. CJOSS (UD, NUS, UR) Auto Learn w/ Feedback Queries CiE’11, Sofia, Bulgaria 3 / 13

  8. Background Motivation & Example Motivation & Numerical Example A motivation: Program of Khoussainov & Nerode 1995 re ≈ effect of replacing TMs by finite automata in computable model theory. Present paper: One in a series (Jain, Luo and Stephan 2010; Jain, Ong, Pu, Stephan 2010; Case, Jain, Le, Ong, Semukhin, Stephan LATA-2011) devoted to effect on computability-theoretic learning theory under above replacement. Example unrestricted learning from positive data: Data Hypotheses 2 Set of all even numbers; 2,3 Set of all numbers; 2,3,5 Set of all prime numbers; 2,3,5,13 Set of all prime numbers; 2,3,5,13,1 Set of all Fibonacci numbers; 2,3,5,13,1,8 Set of all Fibonacci numbers. . . . . . . Success: Algorithmic learner outputs a sequence of hypotheses which eventually stabilizes on a correct hypothesis. CJOSS (UD, NUS, UR) Auto Learn w/ Feedback Queries CiE’11, Sofia, Bulgaria 3 / 13

  9. Background Motivation & Example Motivation & Numerical Example A motivation: Program of Khoussainov & Nerode 1995 re ≈ effect of replacing TMs by finite automata in computable model theory. Present paper: One in a series (Jain, Luo and Stephan 2010; Jain, Ong, Pu, Stephan 2010; Case, Jain, Le, Ong, Semukhin, Stephan LATA-2011) devoted to effect on computability-theoretic learning theory under above replacement. Example unrestricted learning from positive data: Data Hypotheses 2 Set of all even numbers; 2,3 Set of all numbers; 2,3,5 Set of all prime numbers; 2,3,5,13 Set of all prime numbers; 2,3,5,13,1 Set of all Fibonacci numbers; 2,3,5,13,1,8 Set of all Fibonacci numbers. . . . . . . Success: Algorithmic learner outputs a sequence of hypotheses which eventually stabilizes on a correct hypothesis. CJOSS (UD, NUS, UR) Auto Learn w/ Feedback Queries CiE’11, Sofia, Bulgaria 3 / 13

  10. Background Motivation & Example Motivation & Numerical Example A motivation: Program of Khoussainov & Nerode 1995 re ≈ effect of replacing TMs by finite automata in computable model theory. Present paper: One in a series (Jain, Luo and Stephan 2010; Jain, Ong, Pu, Stephan 2010; Case, Jain, Le, Ong, Semukhin, Stephan LATA-2011) devoted to effect on computability-theoretic learning theory under above replacement. Example unrestricted learning from positive data: Data Hypotheses 2 Set of all even numbers; 2,3 Set of all numbers; 2,3,5 Set of all prime numbers; 2,3,5,13 Set of all prime numbers; 2,3,5,13,1 Set of all Fibonacci numbers; 2,3,5,13,1,8 Set of all Fibonacci numbers. . . . . . . Success: Algorithmic learner outputs a sequence of hypotheses which eventually stabilizes on a correct hypothesis. CJOSS (UD, NUS, UR) Auto Learn w/ Feedback Queries CiE’11, Sofia, Bulgaria 3 / 13

  11. Background Motivation & Example Motivation & Numerical Example A motivation: Program of Khoussainov & Nerode 1995 re ≈ effect of replacing TMs by finite automata in computable model theory. Present paper: One in a series (Jain, Luo and Stephan 2010; Jain, Ong, Pu, Stephan 2010; Case, Jain, Le, Ong, Semukhin, Stephan LATA-2011) devoted to effect on computability-theoretic learning theory under above replacement. Example unrestricted learning from positive data: Data Hypotheses 2 Set of all even numbers; 2,3 Set of all numbers; 2,3,5 Set of all prime numbers; 2,3,5,13 Set of all prime numbers; 2,3,5,13,1 Set of all Fibonacci numbers; 2,3,5,13,1,8 Set of all Fibonacci numbers. . . . . . . Success: Algorithmic learner outputs a sequence of hypotheses which eventually stabilizes on a correct hypothesis. CJOSS (UD, NUS, UR) Auto Learn w/ Feedback Queries CiE’11, Sofia, Bulgaria 3 / 13

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