Time varying regression with hidden linear dynamics

The distribution of labels given the covariates changes over time in a variety of applications of regression. Some example domains where such problems arise include economics, marketing, fashion, and supply chain optimization, where market properties evolve over time. Motivated by such problems, we revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. One way to account for distribution change in linear regression is to assume that the unknown model parameters change slowly with time [2, 15, 37]. While this assumption simplifies the problem and makes it tractable, it misses on exploiting additional structure available and it also fails to model periodicity (e.g., due to seasonality) present in some problems. As an alternative, we are interested in a dynamic model previously studied by Chow [7], Carraro [5], and Shumway et al. [26].