Model Selection and Automatic Model Selection for Statistical Learning: A Comparative Study on Local Factor Analysis
نویسندگان
چکیده
Given a paremetric model, the task of statistical learning consists of a parameter learning part for determining unknown parameters and a model selection part for selecting an appropriate scale for a model that accommodates these parameters. Typically, the two tasks are implemented in a twophase procedure. First, a number of models of a same architecture but in different scales are enumerated, with the unknown parameters estimated via the maximum likelihood (ML). Second, one of typical learning theories, being different from a ML principle, is applied to select the best model. There are four major types of theories are available in the literatures, including (a) AIC and extensions (Akaike,1974; Bozdogan&Ramirez,1988; Cavanaugh, 1997), (b) Bayesian approach related criteria, i.e., BIC (Schwarz, 1978), or equivalently MML (Wallace, 1966, 1999) and MDL (Rissanen, 1986, 1989), (c) the cross validation based criteria (Stone, 1978; Rivals & Personnaz, 1999), and (d) Vapnik SRM based error bound (Vapnik, 1977, 1995).
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