In this paper, we formally present a novel estimation method, referred to as the Stochastic Learning Weak Estimator (SLWE), which yields the estimate of the parameters of a binomial distribution, where the convergence of the estimate is weak, i.e. with regard to the first and second moments. The estimation is based on the principles of stochastic learning. The mean of the final estimate is independent of the scheme's learning coefficient, λ, and both the variance of the final distribution and the speed decrease with λ. Similar results are true for the multinomial case, except that the equations transform from being of a scalar type to be of a vector type. Amazingly enough, the speed of the latter only depends on the same parameter, λ, which turns out to be the only non-unity eigenvalue of the underlying stochastic matrix that determines the time-dependence of the estimates. An empirical analysis on synthetic data shows the advantages of the scheme for non-stationary distributions. The paper also briefly reports (without detailed explanation) conclusive results that demonstrate the superiority of SLWE in pattern-recognition-based data compression, where the underlying data distribution is non-stationary. Finally, and more importantly, the paper includes the results of two pattern recognition exercises, the first of which involves artificial data, and the second which involves the recognition of the types of data that are present in news reports of the Canadian Broadcasting Corporation (CBC). The superiority of the SLWE in both these cases is demonstrated.

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Pattern Recognition
School of Computer Science

Oommen, J, & Rueda, L. (Luis). (2006). Stochastic learning-based weak estimation of multinomial random variables and its applications to pattern recognition in non-stationary environments. Pattern Recognition, 39(3), 328–341. doi:10.1016/j.patcog.2005.09.007