A Non-parametric Conditional Factor Regression Model for Multi-Dimensional Input and Response

In this paper, we propose a non-parametric conditional factor regression (NCFR) model for domains with multi-dimensional input and response. NCFR enhances linear regression in two ways: a) introducing lowdimensional latent factors leading to dimensionality reduction and b) integrating the Indian Buet Process as prior for the latent layer to dynamically derive an optimal number of sparse factors. Thanks to IBP’s enhancements to the latent factors, NCFR can signicantly avoid over-tting even in the case of a very small sample size compared to the dimensionality. Experimental results on three diverse datasets comparing NCRF to a few baseline alternatives give evidence of its robust learning, remarkable predictive performance, good mixing and computational efciency.