Heteroscedastic Gaussian Research Articles

Nonparametric signal detection with small type I and type II error probabilities

In the problem of signal detection in the heteroscedastic Gaussian white noise we show asymptotic minimaxity of kernel-based tests. The test statistics equal L 2- norms of kernel estimators. The sets of alternatives are defined by the sets of all signals such that L 2- norms of signals smoothed by the kernel exceed some constants $${\rho_\epsilon}$$ . The constants $${\rho_\epsilon}$$ depend on the power $${\epsilon}$$ of noise and $${\rho_\epsilon \to 0}$$ as $${\epsilon \to 0}$$ . The setup is considered in the zone of moderate deviation probabilities. We suppose that type I or type II error probabilities of tests tend to zero as $${\epsilon \to 0}$$ .

How to compare interpretatively different models for the conditional variance function

This study considers regression-type models with heteroscedastic Gaussian errors. The conditional variance is assumed to depend on the explanatory variables via a parametric or non-parametric variance function. The variance function has usually been selected on the basis of the log-likelihoods of fitted models. However, log-likelihood is a difficult quantity to interpret – the practical importance of differences in log-likelihoods has been difficult to assess. This study overcomes these difficulties by transforming the difference in log-likelihood to easily interpretative difference in the error of predicted deviation. In addition, methods for testing the statistical significance of the observed difference in test data log-likelihood are proposed.

Minimax detection of a signal in the heteroscedastic Gaussian white noise

We consider the problem of signal detection in the heteroscedastic Gaussian white noise when the set of alternatives is essentially nonparametric. In this setting, we find a family of asymptotically minimax tests. The results are extended to the case of testing a parametric hypothesis against nonparametric sets of alternatives. Bibliography: 8 titles.

Maximum Likelihood Topographic Map Formation

We introduce a new unsupervised learning algorithm for kernel-based topographic map formation of heteroscedastic gaussian mixtures that allows for a unified account of distortion error (vector quantization), log-likelihood, and Kullback-Leibler divergence.

Heteroscedastic discriminant analysis and reduced rank HMMs for improved speech recognition

We present the theory for heteroscedastic discriminant analysis (HDA), a model-based generalization of linear discriminant analysis (LDA) derived in the maximum-likelihood framework to handle heteroscedastic-unequal variance-classifier models. We show how to estimate the heteroscedastic Gaussian model parameters jointly with the dimensionality reducing transform, using the EM algorithm. In doing so, we alleviate the need for an a priori ad hoc class assignment. We apply the theoretical results to the problem of speech recognition and observe word-error reduction in systems that employed both diagonal and full covariance heteroscedastic Gaussian models tested on the TI-DIGITS database.