Google Research

A Gaussian Mixture Model Layer Jointly Optimized with Discriminative Features within A Deep Neural Network Architecture



This article proposes and evaluates a Gaussian Mixture Model (GMM) represented as the last layer of a Deep Neural Network (DNN) architecture and jointly optimized with all previous layers using Asynchronous Stochastic Gradient Descent (ASGD). The resulting “Deep GMM” architecture was investigated with special attention to the following issues: (1) The extent to which joint optimization improves over separate optimization of the DNN-based feature extraction layers and the GMM layer; (2) The extent to which depth (measured in number of layers, for a matched total number of parameters) helps a deep generative model based on the GMM layer, compared to a vanilla DNN model; (3) Head-to-head performance of Deep GMM architectures vs. equivalent DNN architectures of comparable depth, using the same optimization criterion (frame-level Cross Entropy (CE)) and optimization method (ASGD); (4) Expanded possibilities for modeling offered by the Deep GMM generative model. The proposed Deep GMMs were found to yield Word Error Rates (WERs) competitive with state-of-the-art DNN systems, at the cost of pre-training using standard DNNs to initialize the Deep GMM feature extraction layers. An extension to Deep Subspace GMMs is described, resulting in additional gains.

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