Active sampling for multiple output identification

Abstract We study functions with multiple output values, and use active sampling to identify an example for each of the possible output values. Our results for this setting include: (1) Efficient active sampling algorithms for simple geometric concepts, such as intervals on a line and axis parallel boxes. (2) A characterization for the case of binary output value in a transductive setting. (3) An analysis of active sampling with uniform distribution in the plane. (4) An efficient algorithm for the Boolean hypercube when each output value is a monomial.

[1]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[2]  A. Rényi,et al.  über die konvexe Hülle von n zufällig gewählten Punkten , 1963 .

[3]  B. Efron.  The convex hull of a random set of points , 1965 .

[4]  Vladimir Vapnik,et al.  Chervonenkis: On the uniform convergence of relative frequencies of events to their probabilities , 1971 .

[5]  Norbert Sauer,et al.  On the Density of Families of Sets , 1972, J. Comb. Theory, Ser. A.

[6]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[7]  H. Sebastian Seung,et al.  Query by committee , 1992, COLT '92.

[8]  Michael E. Saks,et al.  Efficient construction of a small hitting set for combinatorial rectangles in high dimension , 1993, Comb..

[9]  Prasad Tadepalli,et al.  Active Learning with Committees for Text Categorization , 1997, AAAI/IAAI.

[10]  Eli Shamir,et al.  Query by Committee, Linear Separation and Random Walks , 1999, EuroCOLT.

[11]  S. Ur,et al.  Micro architecture coverage directed generation of test programs , 1999, Proceedings 1999 Design Automation Conference (Cat. No. 99CH36361).

[12]  Eitan Farchi,et al.  Multithreaded Java program test generation , 2002, IBM Syst. J..

[13]  Avi Ziv,et al.  Coverage directed test generation for functional verification using Bayesian networks , 2003, Proceedings 2003. Design Automation Conference (IEEE Cat. No.03CH37451).

[14]  H. Sebastian Seung,et al.  Selective Sampling Using the Query by Committee Algorithm , 1997, Machine Learning.

[15]  John N. Tsitsiklis,et al.  Active Learning Using Arbitrary Binary Valued Queries , 1993, Machine Learning.

[16]  Sanjoy Dasgupta,et al.  Analysis of a greedy active learning strategy , 2004, NIPS.

[17]  Andrew Piziali,et al.  Functional verification coverage measurement and analysis , 2004 .

[18]  Wolfgang Roesner,et al.  Comprehensive Functional Verification: The Complete Industry Cycle (Systems on Silicon) , 2005 .

[19]  Wolfgang Roesner,et al.  Comprehensive Functional Verification: The Complete Industry Cycle , 2005 .

[20]  Adam Tauman Kalai,et al.  Analysis of Perceptron-Based Active Learning , 2009, COLT.

[21]  Sanjoy Dasgupta,et al.  Coarse sample complexity bounds for active learning , 2005, NIPS.