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We present a generative model and inference algorithm for 3D nonrigid object tracking. The model, which we call G-flow, enables the joint inference of 3D position, orientation, and nonrigid deformations, as well as object texture and background texture. Optimal inference under G-flow reduces to a conditionally Gaussian stochastic filtering problem. The optimal solution to this problem reveals a new...
We present a new method for multi-talker speech recognition using a single-channel that combines loopy belief propagation and variational inference methods to control the complexity of inference. The method models each source using an HMM with a hierarchical set of acoustic states, and uses the max model to approximate how the sources interact to generate mixed data. Inference involves inferring a...
In model-based pattern recognition it is often useful to change the structure, or refactor, a model. For example, we may wish to find a Gaussian mixture model (GMM) with fewer components that best approximates a reference model. One application for this arises in speech recognition, where a variety of model size requirements exists for different platforms. Since the target size may not be known a...
We address the problem of single-channel speech separation and recognition using loopy belief propagation in a way that enables efficient inference for an arbitrary number of speech sources. The graphical model consists of a set of N Markov chains, each of which represents a language model or grammar for a given speaker. A Gaussian mixture model with shared states is used to model the hidden acoustic...
It has been a common practice in speech recognition and elsewhere to approximate the log likelihood of a Gaussian mixture model (GMM) with the maximum component log likelihood. While often a computational necessity, the max approximation comes at a price of inferior modeling when the Gaussian components significantly overlap. This paper shows how the approximation error can be reduced by changing...
We present a new probabilistic architecture for analyzing composite non-negative data, called Non-negative Subspace Analysis (NSA). The NSA model provides a framework for understanding the relationships between sparse subspace and mixture model based approaches, and encompasses a range of models, including Sparse Non-negative Matrix Factorization (SNMF) [1] and mixture-model based analysis as special...
Kullback Leibler (KL) divergence is widely used as a measure of dissimilarity between two probability distributions; however, the required integral is not tractable for gaussian mixture models (GMMs), and naive Monte-Carlo sampling methods can be expensive. Our work aims to improve the estimation of KL divergence for QMMs by sampling methods. We show how to accelerate Monte-Carlo sampling using variational...
Many applications require the use of divergence measures between probability distributions. Several of these, such as the Kullback-Leibler (KL) divergence and the Bhattacharyya divergence, are tractable for simple distributions such as Gaussians, but are intractable for more complex distributions such as hidden Markov models (HMMs) used in speech recognizers. For tasks related to classification error,...
The Kullback Leibler (KL) divergence is a widely used tool in statistics and pattern recognition. The KL divergence between two Gaussian mixture models (GMMs) is frequently needed in the fields of speech and image recognition. Unfortunately the KL divergence between two GMMs is not analytically tractable, nor does any efficient computational algorithm exist. Some techniques cope with this problem...
In speech recognition it is often useful to determine how confusable two words are. For speech models this comes down to computing the Bayes error between two HMMs. This problem is analytically and numerically intractable. A common alternative, that is numerically approachable, uses the KL divergence in place of the Bayes error. We present new approaches to approximating the KL divergence, that combine...
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