A novel Stochastic Discretized Weak Estimator operating in non-stationary environments

The task of designing estimators that are able to track time-varying distributions has found promising applications in many real-life problems. A particularly interesting family of distributions are the binomial/multinomial distributions. Existing approaches resort to sliding windows that track changes by discarding old observations. In this paper, we report a novel estimator referred to as the Stochastic Discretized Weak Estimator (SDWE), that is based on the principles of Learning Automata (LA). In brief, the estimator is able to estimate the parameters of a time varying binomial distribution using finite memory. The estimator tracks changes in the distribution by operating on a controlled random walk in a discretized probability space. The steps of the estimator are discretized so that the updates are done in jumps, and thus the convergence speed is increased. The analogous results for binomial distribution have also been extended for the multinomial case. Interestingly, the estimator possesses a low computational complexity that is independent of the number of parameters of the multinomial distribution. The paper briefly reports conclusive experimental results that demonstrate the ability of the SDWE to cope with non-stationary environments with high adaptation rate and accuracy.