Dirichlet Process Mixtures of Generalized Linear Models

We propose Dirichlet Process-Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and any response that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean function estimate and give a practical example for when those conditions hold. Additionally, we provide Bayesian bounds on the distance of the estimate from the true mean function based on the number of observations and posterior samples. We evaluate DP-GLM on several data sets, comparing it to modern methods of nonparametric regression like CART and Gaussian processes. We show that the DP-GLM is competitive with the other methods, while accommodating various inputs and outputs and being robust when confronted with heteroscedasticity.