Detecting Change Points in High Dimensional Data

• In Event: Causal Inference

Abstract

As the number of available explanatory variables grows, regularization using sparsity-inducing priors or penalized likelihood functions (best known as least absolute shrinkage and selection operator, LASSO) has received increasing attention in political methodology. However, existing regularization methods have two important limitations in applications to political science data, the points of which we address in this paper. First, existing regularization methods do not consider the possibility that effects of covariates (i.e. size of regression coefficients) may change over time. When some covariates have time-dependent effects, existing regularization methods either zero them out or report time-averaged coefficients, both of which are invalid. Second, although Bayesian regularization methods are known to outperform classical regularization methods (Park and Casella 2008, Efron 2009, Hans 2009), existing Bayesian regularization estimators suffer from a slow mixing especially when a design matrix is highly correlated. This limitation is particularly worrisome because most observational data in political science tend to have highly correlated input variables. In this paper, we present a suite of statistical models that combine Bayesian change-point models with Bayesian regularized estimators for high dimensional data in the univariate setting, the time-series cross-sectional setting, and the temporal network setting. For parameter regularization, we use Polson, Scott, and Windle’s (2014) Bayesian bridge estimator that allows fast mixing and robust performance in prediction and estimation under correlated design matrices. For change-point models, we use Chib’s (1998) non-ergodic hidden Markov approach. We implement the resulting hidden Markov Bayesian bridge model in the univariate setting, the time-series cross-sectional setting, and the temporal network setting in a publicly available software and discuss issues related with model-building, estimation, and model diagnostics. We test our model using simulated data and observed data in political science.

Authors

• Jong Hee Park, Seoul National University

• Yunkyu Sohn, Waseda University

• Soichiro Yamauchi, Princeton University