Mixture of Probabilistic Linear Regressions: A unified view of GMM-based mapping techiques

This paper introduces a model of mixture of probabilistic linear regressions (MPLR) to learn a mapping function between two feature spaces. The MPLR consists of weighted combination of several probabilistic linear regressions, whose parameters are estimated by using matrix calculation. The mixture nature of MPLR allows it to model nonlinear transformation. The formulation of MPLR is general and independent of the types of the density models used. Two well-known GMM-based mapping methods for voice conversion [1, 2] can be regarded as special cases of MPLR. This unified view not only provides insights to the GMM-based mapping techniques, but also indicates methods to improve them. Compared to [1], our formulation of MPLR avoids solving complex linear equations and yields a faster estimation of the transform parameters. As for [2], the MPLR estimation provides a modified mapping function which overcomes an implicit problem in [2]-s mapping function. We carried out experiments to compare the MPLR-based methods with the traditional GMM-based methods [1, 2] on a voice conversion task. The experimental results show that the MPLR-based methods always have better performance in various parameter setups.