A Distribution Free Formulation of the Total Variability Model

Total Variability Model Conventionally formulated as generative model over features Assumes that feature vector distribution is a GMM Distribution Free Formulation Follows from asymptotic normality of Baum-Welch statistics Connections to probabilistic PCA, matrix completion Leads to a stochastic subgradient descent based estimation algorithm Conventional Formulation Collection of feature vectors : X = {Xu}Uu=1 , Xu = {xut} Tu t=1 Model Assumption wu ∼ N (0, I), xut|wu ∼ GMM {pc,μuc = μc + Tcwu,Σc} C c=1 Mu = M0 + Twu M0 = μ1 .. μC  Mu = μu1 .. μuC  T = T1 .. TC  Distribution Free Formulation Baum-Welch Statistics Γc : R 7→ [0,∞) , γutc = Γc(xut)