A1982
Title: Information criterion for Bayesian trend filtering in generalized linear models
Authors: Yuko Kakikawa - Institute of Science Tokyo (Japan) [presenting]
Yoshiyuki Ninomiya - The Institute of Statistical Mathematics (Japan)
Abstract: Data observed across adjacent locations or time points often exhibit smooth structures with some abrupt changes. To analyze such data, Bayesian sparse regularization based on differences of regression coefficients has been studied. In particular, methods based on first-order differences such as fused lasso have received attention. However, it is often insufficient for representing complex variation in data, for which regularization based on higher-order differences such as trend filtering is regarded as more suitable. To select models based on such regularization, the widely applicable information criterion (WAIC) can be a useful approach. However, two points require careful consideration. First, WAIC is derived under asymptotic settings in which the influence of priors becomes negligible. Thus, WAIC might not appropriately reflect the properties of estimators. Second, since WAIC does not include a penalty term reflecting the complexity of the prior, it inevitably selects the prior class with the highest complexity when comparing models that have different classes of priors. To address this, the prior intensified information criterion (PIIC) was proposed and subsequently extended to Bayesian sparse regularization frameworks. However, existing methods are not directly applicable to Bayesian trend filtering, a typical regularization based on higher-order differences. To overcome this limitation, PIIC for Bayesian trend filtering under generalized linear models is proposed.
