Multi-kernel probability distribution regressions

This paper presents a multi-layer reproducing kernel Hilbert space (RKHS) approach for probability distribution to real and probability distribution to function regressions. The approach maps the distributions into RKHS by distribution embeddings and, then, constructs a multi-layer RKHS within which the multi-kernel distribution regression can be implemented using an existing kernel regression algorithm, such as kernel recursive least squares (KRLS). The numerical simulations on synthetic data obtained via Gaussian mixtures show that the proposed approach outperforms existing probability distribution (DR) regression algorithms by achieving smaller mean squared errors (MSEs) and requiring less training samples.