A New Family of Weak Estimators for Training in Non-stationary Distributions

In this paper, we formally present a novel estimation method, referred to as the Stochastic Learning Weak Estimator (SLWE), which is used to estimate the parameters of a binomial distribution, where the convergence of the estimate is weak, i.e. in law. The estimation is based on the principles of stochastic learning. Even though our new method includes a learning coefficient, λ , it turns out that the mean of the final estimate is independent of λ , the variance of the final distribution decreases with λ , and the speed decreases with λ . Similar results are true for the multinomial case. An empirical analysis on synthetic data shows the advantages of the scheme for non-stationary distributions. Conclusive results demonstrate the advantage of SLWE for a pattern-recognition problem which has direct implications in data compression. In this case, the underlying distribution in the data file to be compressed is non-stationary, and it is estimated and learnt using the principles highlighted here. By classifying its variation and using it in the compression, the superiority of the scheme is documented.

[1]  M. A. L. THATHACHAR,et al.  A new approach to the design of reinforcement schemes for learning automata , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  S. Lakshmivarahan,et al.  Learning Algorithms Theory and Applications , 1981 .

[3]  Kanagasabai Rajaraman,et al.  Finite time analysis of the pursuit algorithm for learning automata , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[4]  Georgios I. Papadimitriou.  A New Approach to the Design of Reinforcement Schemes for Learning Automata: Stochastic Estimator Learning Algorithms , 1994, IEEE Trans. Knowl. Data Eng..

[5]  A Gordon,et al.  Classification, 2nd Edition , 1999 .

[6]  B. John Oommen,et al.  Continuous and discretized pursuit learning schemes: various algorithms and their comparison , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[7]  P. S. Sastry,et al.  A Class of Rapidly Converging Algorithms for Learning Automata , 1984 .

[8]  Sheldon M. Ross,et al.  Introduction to probability models , 1975 .

[9]  D. Vere-Jones.  Markov Chains , 1972, Nature.

[10]  David G. Stork,et al.  Pattern Classification , 1973 .

[11]  B.J. Oommen,et al.  Ε-optimal Discretized Linear Reward-penalty Learning Automata , 1988, IEEE Trans. Syst. Man Cybern..

[12]  Kumpati S. Narendra,et al.  Learning automata - an introduction , 1989 .

[13]  B. John Oommen,et al.  Absorbing and Ergodic Discretized Two-Action Learning Automata , 1986, IEEE Trans. Syst. Man Cybern..

[14]  Andrew R. Webb,et al.  Statistical Pattern Recognition , 1999 .

[15]  B. John Oommen,et al.  Discretized pursuit learning automata , 1990, IEEE Trans. Syst. Man Cybern..

[16]  David G. Stork,et al.  Pattern Classification (2nd ed.) , 1999 .

[17]  B. John Oommen,et al.  Discretized estimator learning automata , 1992, IEEE Trans. Syst. Man Cybern..

[18]  David G. Stork,et al.  Pattern classification, 2nd Edition , 2000 .

[19]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.