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34
Maximum A Posteriori Estimation for Multivariate Gaussian Mixture Observations of Markov Chains
 IEEE Transactions on Speech and Audio Processing
, 1994
"... In this paper a framework for maximum a posteriori (MAP) estimation of hidden Markov models (HMM) is presented. Three key issues of MAP estimation, namely the choice of prior distribution family, the specification of the parameters of prior densities and the evaluation of the MAP estimates, are addr ..."
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Cited by 491 (39 self)
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In this paper a framework for maximum a posteriori (MAP) estimation of hidden Markov models (HMM) is presented. Three key issues of MAP estimation, namely the choice of prior distribution family, the specification of the parameters of prior densities and the evaluation of the MAP estimates, are addressed. Using HMMs with Gaussian mixture state observation densities as an example, it is assumed that the prior densities for the HMM parameters can be adequately represented as a product of Dirichlet and normalWishart densities. The classical maximum likelihood estimation algorithms, namely the forwardbackward algorithm and the segmental kmeans algorithm, are expanded and MAP estimation formulas are developed. Prior density estimation issues are discussed for two classes of applications: parameter smoothing and model adaptation, and some experimental results are given illustrating the practical interest of this approach. Because of its adaptive nature, Bayesian learning is shown to serve as a unified approach for a wide range of speech recognition applications
Image denoising using a scale mixture of Gaussians in the wavelet domain
 IEEE Trans Image Processing
, 2003
"... Abstract—We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussi ..."
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Cited by 350 (18 self)
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Abstract—We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error.
Image Denoising using Gaussian Scale Mixtures in the Wavelet Domain
 IEEE Transactions on Image Processing
, 2002
"... We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vecto ..."
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Cited by 40 (3 self)
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We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier.
On adaptive decision rules and decision parameter adaptation for automatic speech recognition
 Proc. IEEE
, 2000
"... Recent advances in automatic speech recognition are accomplished by designing a plugin maximum a posteriori decision rule such that the forms of the acoustic and language model distributions are specified and the parameters of the assumed distributions are estimated from a collection of speech and ..."
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Cited by 27 (4 self)
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Recent advances in automatic speech recognition are accomplished by designing a plugin maximum a posteriori decision rule such that the forms of the acoustic and language model distributions are specified and the parameters of the assumed distributions are estimated from a collection of speech and language training corpora. Maximumlikelihood point estimation is by far the most prevailing training method. However, due to the problems of unknown speech distributions, sparse training data, high spectral and temporal variabilities in speech, and possible mismatch between training and testing conditions, a dynamic training strategy is needed. To cope with the changing speakers and speaking conditions in real operational conditions for highperformance speech recognition, such paradigms incorporate a small amount of speaker and environment specific adaptation data into the training process. Bayesian adaptive learning is an optimal way to combine
Bayesian Adaptive Learning of the Parameters of Hidden Markov Model for Speech Recognition
"... In this paper a theoretical framework for Bayesian adaptive learning of discrete HMM and semicontinuous one with Gaussian mixture state observation densities is presented. Corresponding to the wellknown BaumWelch and segmental kmeans algorithms respectively for HMM training, formulations of MAP ..."
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Cited by 26 (4 self)
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In this paper a theoretical framework for Bayesian adaptive learning of discrete HMM and semicontinuous one with Gaussian mixture state observation densities is presented. Corresponding to the wellknown BaumWelch and segmental kmeans algorithms respectively for HMM training, formulations of MAP (maximum aposteriori) and segmental MAP estimation of HMM parameters are developed. Furthermore, a computationally efficient method of the segmental quasiBayes estimation for semicontinuous HMM is also presented. The important issue of prior density estimation is discussed and a simplified method of moment estimate is given. The method proposed in this paper will be applicable to some problems in HMM training for speech recognition such as sequential or batch training, model adaptation, and parameter smoothing, etc.
MAP Estimation of Continuous Density HMM: Theory and Applications
 In: Proceedings of DARPA Speech and Natural Language Workshop
, 1992
"... We discuss maximum a posteriori estimation of continuous density hidden Markovmodels(CDHMM).The classical MLE reestimation algorithms, namely the forwardbackward algorithm and the segmental kmeans algorithm, are expanded and reestimation formulas are given for HMM with Gaussian mixture observation ..."
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Cited by 25 (6 self)
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We discuss maximum a posteriori estimation of continuous density hidden Markovmodels(CDHMM).The classical MLE reestimation algorithms, namely the forwardbackward algorithm and the segmental kmeans algorithm, are expanded and reestimation formulas are given for HMM with Gaussian mixture observation densities. Because of its adaptive nature, Bayesian learning serves as a unified approach for the following four speech recognition applications, namely parameter smoothing, speaker adaptation, speaker group modeling and corrective training. New experimental results on all four applications are provided to show the effectiveness of the MAP estimation approach. INTRODUCTION Estimation of hidden Markov model (HMM) is usually obtained by the method of maximum likelihood (ML) [1, 10, 6] assuming that the size of the training data is large enough to provide robust estimates. This paper investigates maximum a posteriori (MAP) estimate of continuous density hidden Markov models (CDHMM). The MAP ...
Predictable returns and asset allocation: Should a skeptical investor time the market
 Journal of Econometrics
, 2009
"... are grateful for financial support from the Aronson+Johnson+Ortiz fellowship through the Rodney L. White Center for Financial Research. This manuscript does not reflect the views of the Board of Governors of the Federal Reserve System. Predictable returns and asset allocation: Should a skeptical inv ..."
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Cited by 16 (0 self)
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are grateful for financial support from the Aronson+Johnson+Ortiz fellowship through the Rodney L. White Center for Financial Research. This manuscript does not reflect the views of the Board of Governors of the Federal Reserve System. Predictable returns and asset allocation: Should a skeptical investor time the market? We investigate optimal portfolio choice for an investor who is skeptical about the degree to which excess returns are predictable. Skepticism is modeled as an informative prior over the R 2 of the predictive regression. We find that the evidence is sufficient to convince even an investor with a highly skeptical prior to vary his portfolio on the basis of the dividendprice ratio and the yield spread. The resulting weights are less volatile and deliver superior outofsample performance as compared to the weights implied by an entirely modelbased Are excess returns predictable, and if so, what does this mean for investors? In classic studies of rational valuation (e.g. Samuelson (1965, 1973), Shiller (1981)), risk premia are constant over time and thus excess returns are unpredictable. 1
Blind minimax estimation
 2005, EE Dept., Technion–Israel Institute of Technology; submitted to IEEE Trans. Signal Processing
"... Abstract—We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded parameter set minimax estimator, whose parameter s ..."
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Cited by 15 (14 self)
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Abstract—We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded parameter set minimax estimator, whose parameter set is itself estimated from measurements. Thus, our approach does not require any prior assumption or knowledge, and the proposed estimator can be applied to any linear regression problem. We demonstrate analytically that the BMEs strictly dominate the leastsquares (LS) estimator, i.e., they achieve lower meansquared error (MSE) for any value of the parameter vector. Both Stein’s estimator and its positivepart correction can be derived within the blind minimax framework. Furthermore, our approach can be readily extended to a wider class of estimation problems than Stein’s estimator, which is defined only for white noise and nontransformed measurements. We show through simulations that the BMEs generally outperform previous extensions of Stein’s technique. Index Terms—Biased estimation, James–Stein estimation, minimax estimation, linear regression model. I.
When did Bayesian inference become “Bayesian"?
 BAYESIAN ANALYSIS
, 2006
"... While Bayes’ theorem has a 250year history, and the method of inverse probability that flowed from it dominated statistical thinking into the twentieth century, the adjective “Bayesian” was not part of the statistical lexicon until relatively recently. This paper provides an overview of key Bayesi ..."
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Cited by 10 (1 self)
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While Bayes’ theorem has a 250year history, and the method of inverse probability that flowed from it dominated statistical thinking into the twentieth century, the adjective “Bayesian” was not part of the statistical lexicon until relatively recently. This paper provides an overview of key Bayesian developments, beginning with Bayes’ posthumously published 1763 paper and continuing up through approximately 1970, including the period of time when “Bayesian” emerged as the label of choice for those who advocated Bayesian methods.