A Stochastic Search on the Line-Based Solution to Discretized Estimation

Recently, Oommen and Rueda [11] presented a strategy by which the parameters of a binomial/multinomial distribution can be estimated when the underlying distribution is nonstationary. The method has been referred to as the Stochastic Learning Weak Estimator (SLWE), and is based on the principles of continuous stochastic Learning Automata (LA). In this paper, we consider a new family of stochastic discretized weak estimators pertinent to tracking time-varying binomial distributions. As opposed to the SLWE, our proposed estimator is discretized , i.e., the estimate can assume only a finite number of values. It is well known in the field of LA that discretized schemes achieve faster convergence speed than their corresponding continuous counterparts. By virtue of discretization, our estimator realizes extremely fast adjustments of the running estimates by jumps, and it is thus able to robustly, and very quickly, track changes in the parameters of the distribution after a switch has occurred in the environment. The design principle of our strategy is based on a solution, pioneered by Oommen [7], for the Stochastic Search on the Line (SSL) problem. The SSL solution proposed in [7], assumes the existence of an Oracle which informs the LA whether to go “right” or “left”. In our application domain, in order to achieve efficient estimation, we have to first infer (or rather simulate ) such an Oracle. In order to overcome this difficulty, we rather intelligently construct an “Artificial Oracle” that suggests whether we are to increase the current estimate or to decrease it. The paper briefly reports conclusive experimental results that demonstrate the ability of the proposed estimator to cope with non-stationary environments with a high adaptation rate, and with an accuracy that depends on its resolution. The results which we present are, to the best of our knowledge, the first reported results that resolve the problem of discretized weak estimation using a SSL-based solution

Discretized Pursuit Learning Automata

The problem of a stochastic learning automation interacting with an unknown random environment is considered. The fundamental problem is that of learning, through interaction, the best action allowed by the environment O.e., the action that is rewarded optimally). By using running estimates of reward probabilities to learn the optimal action, an extremely efficient pursuit algorithm (PA) was reported in earlier works, which is presently among the fastest algorithms known. The improvements gained by rendering the PA discrete is investigated. This is done by restricting the probability of selecting an action to a finite, and hence, discrete subset of [0,1]. This improved scheme is proven to be ∈ -optimal in all stationary environments. Furthermore, the experimental results seem to indicate that the algorithm presented in the paper is faster than the fastest “nonestimator” learning automata reported to date and also faster than the continuous pursuit automaton pursuit algorithm is also presented

On utilizing stochastic learning weak estimators for training and classification of patterns with non-stationary distributions

Pattern recognition essentially deals with the training and classification of patterns, where the distribution of the features is assumed unknown. However, in almost all the reported results, a fundamental assumption made is that this distribution, although unknown, is stationary. In this paper, we shall relax this assumption and assume that the class-conditional distribution is non-stationary. To now render the training and classification feasible, we present a novel estimation strategy, involving the so-called Stochastic Learning Weak Estimator (SLWE). The latter, whose convergence is weak, is used to estimate the parameters of a binomial distribution using the principles of stochastic learning. Even though our 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. To demonstrate the power of these estimates in data which is truly "nonstationary", we have used them in 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