Time-Varying Regression Coefficients via Hilbert Space Gaussian Process Approximation

In this notebook we present an example of a regression model with time varying coefficients using Gaussian processes. In particular, we use a Hilbert space Gaussian process approximation in pymc to speed up the computations (see HSGP). We continue using the bikes dataset from the previous posts (Exploring Tools for Interpretable Machine Learning and Time-Varying Regression Coefficients via Gaussian Random Walk in PyMC). Please refer to those posts for more details on the dataset, EDA and base models. In essence, we are trying to model bike count rentals as a function of meteorological variables and seasonality. We are particularly interested in the marginal effect of temperature on bike rentals, which we expect to be non-linear.