Copula-based Kernel Dependency Measures

The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous properties. Similarly to Shannon mutual information, the proposed dependence measure is invariant to any strictly increasing transformation of the marginal variables. This is important in many applications, for example in feature selection. The estimator is consistent, robust to outliers, and uses rank statistics only. We derive upper bounds on the convergence rate and propose independence tests too. We illustrate the theoretical contributions through a series of experiments in feature selection and low-dimensional embedding of distributions.

Joint modelling of voicing label and continuous F0 for HMM based speech synthesis

Fundamental frequency, or F0 is critical for high quality speech synthesis in HMM based speech synthesis. Traditionally, F0 values are considered to depend on a binary voicing decision such that they are continuous in voiced regions and undefined in unvoiced regions. Multi-space distribution HMM (MSDHMM) has been used for modelling the discontinuous F0. Recently, a continuous F0 modelling framework has been proposed and shown to be effective, where continuous F0 observations are assumed to always exist and voicing labels are explicitly modelled by an independent stream. In this paper, a refined continuous F0 modelling approach is proposed. Here, F0 values are assumed to be dependent on voicing labels and both are jointly modelled in a single stream. Due to the enforced dependency, the new method can effectively reduce the voicing classification error. Subjective listening tests also demonstrate that the new approach can yield significant improvements on the naturalness of the synthesised speech. A dynamic random unvoiced F0 generation method is also investigated. Experiments show that it has significant effect on the quality of synthesised speech. © 2011 IEEE.