PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Model selection by sequentially normalized least squares
Jorma Rissanen, Teemu Roos and Petri Myllymäki
Journal of Multivariate Analysis 2009.


Model selection by means of the predictive least squares (PLS) principle has been thoroughly studied in the context of regression model selection and autoregressive (AR) model order estimation. We introduce a new criterion based on sequentially minimized squared deviations, which are smaller than both the usual least squares and the squared prediction errors used in PLS. We also prove that our criterion has a probabilistic interpretation as a model which is asymptotically optimal within the given class of distributions by reaching the lower bound on the logarithmic prediction errors, given by the so called stochastic complexity, and approximated by BIC. This holds when the regressor (design) matrix is non-random or determined by the observed data as in AR models. The advantages of the criterion include the fact that it can be evaluated efficiently and exactly, without asymptotic approximations, and importantly, there are no adjustable hyper-parameters, which makes it applicable to both small and large amounts of data.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
ID Code:5527
Deposited By:Teemu Roos
Deposited On:15 February 2010