2,263 research outputs found
Sliced Wasserstein Distance for Learning Gaussian Mixture Models
Gaussian mixture models (GMM) are powerful parametric tools with many
applications in machine learning and computer vision. Expectation maximization
(EM) is the most popular algorithm for estimating the GMM parameters. However,
EM guarantees only convergence to a stationary point of the log-likelihood
function, which could be arbitrarily worse than the optimal solution. Inspired
by the relationship between the negative log-likelihood function and the
Kullback-Leibler (KL) divergence, we propose an alternative formulation for
estimating the GMM parameters using the sliced Wasserstein distance, which
gives rise to a new algorithm. Specifically, we propose minimizing the
sliced-Wasserstein distance between the mixture model and the data distribution
with respect to the GMM parameters. In contrast to the KL-divergence, the
energy landscape for the sliced-Wasserstein distance is more well-behaved and
therefore more suitable for a stochastic gradient descent scheme to obtain the
optimal GMM parameters. We show that our formulation results in parameter
estimates that are more robust to random initializations and demonstrate that
it can estimate high-dimensional data distributions more faithfully than the EM
algorithm
Porting concepts from DNNs back to GMMs
Deep neural networks (DNNs) have been shown to outperform Gaussian Mixture Models (GMM) on a variety of speech recognition benchmarks. In this paper we analyze the differences between the DNN and GMM modeling techniques and port the best ideas from the DNN-based modeling to a GMM-based system. By going both deep (multiple layers) and wide (multiple parallel sub-models) and by sharing model parameters, we are able to close the gap between the two modeling techniques on the TIMIT database. Since the 'deep' GMMs retain the maximum-likelihood trained Gaussians as first layer, advanced techniques such as speaker adaptation and model-based noise robustness can be readily incorporated. Regardless of their similarities, the DNNs and the deep GMMs still show a sufficient amount of complementarity to allow effective system combination
Bio-Inspired Multi-Layer Spiking Neural Network Extracts Discriminative Features from Speech Signals
Spiking neural networks (SNNs) enable power-efficient implementations due to
their sparse, spike-based coding scheme. This paper develops a bio-inspired SNN
that uses unsupervised learning to extract discriminative features from speech
signals, which can subsequently be used in a classifier. The architecture
consists of a spiking convolutional/pooling layer followed by a fully connected
spiking layer for feature discovery. The convolutional layer of leaky,
integrate-and-fire (LIF) neurons represents primary acoustic features. The
fully connected layer is equipped with a probabilistic spike-timing-dependent
plasticity learning rule. This layer represents the discriminative features
through probabilistic, LIF neurons. To assess the discriminative power of the
learned features, they are used in a hidden Markov model (HMM) for spoken digit
recognition. The experimental results show performance above 96% that compares
favorably with popular statistical feature extraction methods. Our results
provide a novel demonstration of unsupervised feature acquisition in an SNN
An Open Source C++ Implementation of Multi-Threaded Gaussian Mixture Models, k-Means and Expectation Maximisation
Modelling of multivariate densities is a core component in many signal
processing, pattern recognition and machine learning applications. The
modelling is often done via Gaussian mixture models (GMMs), which use
computationally expensive and potentially unstable training algorithms. We
provide an overview of a fast and robust implementation of GMMs in the C++
language, employing multi-threaded versions of the Expectation Maximisation
(EM) and k-means training algorithms. Multi-threading is achieved through
reformulation of the EM and k-means algorithms into a MapReduce-like framework.
Furthermore, the implementation uses several techniques to improve numerical
stability and modelling accuracy. We demonstrate that the multi-threaded
implementation achieves a speedup of an order of magnitude on a recent 16 core
machine, and that it can achieve higher modelling accuracy than a previously
well-established publically accessible implementation. The multi-threaded
implementation is included as a user-friendly class in recent releases of the
open source Armadillo C++ linear algebra library. The library is provided under
the permissive Apache~2.0 license, allowing unencumbered use in commercial
products
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