Stochastic Learning-based Weak Estimation and Its Applications

Stochastic Learning-based Weak Estimation and Its Applications

B. John Oommen (Carleton University, Canada and University of Agder, Norway) and Luis Rueda (University of Windsor, Canada)
DOI: 10.4018/978-1-61692-811-7.ch001
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Although the field of Artificial Intelligence (AI) has been researched for more than five decades, researchers, scientists and practitioners are constantly seeking superior methods that are applicable for increasingly difficult problems. In this chapter, our aim is to consider knowledge-based novel and intelligent cybernetic approaches for problems in which the environment (or medium) is time-varying. While problems of this sort can be approached from various perspectives, including those that appropriately model the time-varying nature of the environment, in this chapter, we shall concentrate on using new estimation or “training” methods. The new methods that we propose are based on the principles of stochastic learning, and are referred to as the Stochastic Learning Weak Estimators (SLWE). An empirical analysis on synthetic data shows the advantages of the scheme for non-stationary distributions, which is where we claim to advance the state-of-the-art. We also examine how these new methods can be applicable to learning and intelligent systems, and to Pattern Recognition (PR). The chapter briefly reports conclusive results that demonstrate the superiority of the SLWE in two applications, namely in PR and data compression. The application in PR involves artificial data and real-life news reports from the Canadian Broadcasting Corporation (CBC). We also demonstrate its applicabilty in data compression, where the underlying distribution of the files being compressed is, again, modeled as being non-stationary. The superiority of the SLWE in both these cases is demonstrated.
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The theory of estimation has been studied for hundreds of years (Bickel & Doksum, 2000 ; Casella & Berger, 2001 ; Jones, Garthwaite, & Jolliffe, 2002). Besides, the learning (training) phase of a statistical PR system is, indeed, based on estimation theory (Duda, Hart, & Stork, 2000, Ch.3; Theodoridis & Koutroumbas, 2006, pp. 28-34; Herbrich, 2001, pp.107; Webb, 2002, pp. 40-76). Estimation methods generally fall into various categories, including the Maximum Likelihood Estimates (MLE) and the Bayesian family of estimates (Bickel & Doksum, 2000, Ch.2; Casella & Berger, 2001, pp. 315-325; Duda, Hart & Stork, 2000, Ch.3; Theodoridis & Koutroumbas, 2006, pp. 28-34).

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