A Distribution Free Formulation Of The Total Variability Model

The Total Variability Model (TVM) [1] has been widely used in audio signal processing as a framework for capturing differences in feature space distributions across variable length sequences by mapping them into a fixed-dimensional representation. Its formulation requires making an assumption about the source data distribution being a Gaussian Mixture Model (GMM). In this paper, we show that it is possible to arrive at the same model formulation without requiring such an assumption about distribution of the data, by showing asymptotic normality of the statistics used to estimate the model. We highlight some connections between TVM and heteroscedastic Principal Component Analysis (PCA), as well as the matrix completion problem, which lead to a computationally efficient formulation of the Maximum Likelihood estimation problem for the model.