Takeuchi's Information Criteria as a Form of Regularization
26 Pages Posted: 16 Mar 2018 Last revised: 18 Apr 2018
Date Written: April 5, 2018
Takeuchi's Information Criteria (TIC) is a linearization of maximum likelihood estimator bias which shrinks the model parameters towards the maximum entropy distribution, even when the model is mis-specified. In statistical machine learning, $L_2$ regularization (a.k.a. ridge regression) also introduces a parameterized bias term with the goal of minimizing out-of-sample entropy, but generally requires a numerical solver to find the regularization parameter. This paper presents a novel regularization approach based on TIC; the approach does not assume a data generation process and results in a higher entropy distribution through more efficient sample noise suppression. The resulting objective function can be directly minimized to estimate and select the best model, without the need to select a regularization parameter, as in ridge regression. Numerical results applied to a synthetic high dimensional dataset generated from a logistic regression model demonstrate superior model performance when using the TIC based regularization over a $L_1$ and a $L_2$ penalty term.
Keywords: regularization, information criterion, statistical inference
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