The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Michael S. Lewicki - One of the best experts on this subject based on the ideXlab platform.
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A hierarchical Bayesian model for learning nonlinear statistical regularities in nonstationary natural signals
Neural Computation, 2005Co-Authors: Yan Karklin, Michael S. LewickiAbstract:Capturing statistical regularities in complex, high-dimensional data is an important problem in machine learning and signal processing. Models such as principal component analysis (PCA) and independent component analysis (ICA) make few assumptions about the structure in the data and have good scaling properties, but they are limited to representing linear statistical regularities and assume that the distribution of the data is stationary. For many natural, complex signals, the latent variables often exhibit residual dependencies as well as nonstationary statistics. Here we present a hierarchical Bayesian model that is able to capture higher-order nonlinear structure and represent nonstationary data distributions. The model is a generalization of ICA in which the basis function coefficients are no longer assumed to be independent; instead, the dependencies in their magnitudes are captured by a set of Density components. Each Density component describes a common pattern of deviation from the Marginal Density of the pattern ensemble; in different combinations, they can describe nonstationary distributions. Adapting the model to image or audio data yields a nonlinear, distributed code for higher-order statistical regularities that reflect more abstract, invariant properties of the signal. View full abstract
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A Hierarchical Bayesian Model for Learning Nonlinear Statistical Regularities in Nonstationary Natural Signals
Neural Computation, 2005Co-Authors: Yan Karklin, Michael S. LewickiAbstract:Capturing statistical regularities in complex, high-dimensional data is an important problem in machine learning and signal processing. Models such as principal component analysis (PCA) and independent component analysis (ICA) make few assumptions about the structure in the data and have good scaling properties, but they are limited to representing linear statistical regularities and assume that the distribution of the data is stationary. For many natural, complex signals, the latent variables often exhibit residual dependencies as well as nonstationary statistics. Here we present a hierarchical Bayesian model that is able to capture higher-order nonlinear structure and represent nonstationary data distributions. The model is a generalization of ICA in which the basis function coefficients are no longer assumed to be independent; instead, the dependencies in their magnitudes are captured by a set of Density components. Each Density component describes a common pattern of deviation from the Marginal Density of the pattern ensemble; in different combinations, they can describe nonstationary distributions. Adapting the model to image or audio data yields a nonlinear, distributed code for higher-order statistical regularities that reflect more abstract, invariant properties of the signal.
Minghui Chen - One of the best experts on this subject based on the ideXlab platform.
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partition weighted approach for estimating the Marginal posterior Density with applications
Journal of Computational and Graphical Statistics, 2019Co-Authors: Yubo Wang, Minghui Chen, Paul O LewisAbstract:The computation of Marginal posterior Density in Bayesian analysis is essential in that it can provide complete information about parameters of interest. Furthermore, the Marginal posterior Density can be used for computing Bayes factors, posterior model probabilities, and diagnostic measures. The conditional Marginal Density estimator (CMDE) is theoretically the best for Marginal Density estimation but requires the closed-form expression of the conditional posterior Density, which is often not available in many applications. We develop the partition weighted Marginal Density estimator (PWMDE) to realize the CMDE. This unbiased estimator requires only a single MCMC output from the joint posterior distribution and the known unnormalized posterior Density. The theoretical properties and various applications of the We carry out simulation studies to investigate the empirical performance of the PWMDE and further demonstrate the desirable features of the proposed method with two real data sets from a study of dissociative identity disorder patients and a prostate cancer study, respectively.
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performance study of Marginal posterior Density estimation via kullback leibler divergence
Test, 1997Co-Authors: Minghui Chen, Qiman ShaoAbstract:In this article, we introduce Kullback-Leibler (K-L) divergence as a performance measure of Marginal posterior Density estimation. We show that the K-L divergence can be used to compare two Density estimators as well as to assess convergence of a Marginal Density estimator. We also examine performance of the importance-weighted Marginal Density estimation (IWMDE) proposed by Chen (1994) under the K-L divergence and we further extend the IWMDE to some more complex Bayesian models where the kernel method, which is widely used for estimating Marginal densities using Markov chain Monte Carlo (MCMC) sampling outputs is not applicable. Finally, we use a constrained linear multiple regression model as an example to illustrate our methodology.
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importance weighted Marginal bayesian posterior Density estimation
Journal of the American Statistical Association, 1994Co-Authors: Minghui ChenAbstract:Abstract Markov chain sampling schemes generate dependent observations {Θi, 0 ≤ i ≤ n} from a full joint posterior distribution π(θdata). Frequently, only certain Marginals of this full posterior Density are of interest; thus an interesting problem is how to estimate the Marginal posterior densities based on the dependent observations {Θi, 0 ≤ i ≤ n} from π(θ data). We propose a new importance-weighted Marginal Density estimation (IWMDE) method. An IWMDE is obtained by averaging many dependent observations of the ratio of the full joint posterior densities multiplied by a weighting conditional Density w. The asymptotic properties for the IWMDE and the guidelines for choosing a weighting conditional Density w are also considered. A bivariate normal model and a constrained linear multiple regression model are used to illustrate how to derive the IWMDE's for the Marginal posterior densities.
S Violante - One of the best experts on this subject based on the ideXlab platform.
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Marginal Density expansions for diffusions and stochastic volatility ii applications
Communications on Pure and Applied Mathematics, 2014Co-Authors: Jeandominique Deuschel, Peter K Friz, Antoine Jacquier, S ViolanteAbstract:In [17] we discussed Density expansions for multidimensional diffusions X 1 ,...,X d � , at fixed time T and projected to their first l coordinates, in the small noise regime. Global conditions were found which replace the well-known ”not-in-cutlocus” condition known from heat-kernel asymptotics. In the present paper we discuss financial applications; these include tail and implied volatility asymptotics in some correlated stochastic volatility models. In particular, we solve a problem left open by A. Gulisashvili and E.M. Stein (2009).
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Marginal Density expansions for diffusions and stochastic volatility i theoretical foundations
Communications on Pure and Applied Mathematics, 2014Co-Authors: Jeandominique Deuschel, Peter K Friz, Antoine Jacquier, S ViolanteAbstract:Density expansions for hypoelliptic diffusions $(X^1,...,X^d)$ are revisited. In particular, we are interested in Density expansions of the projection $(X_T^1,...,X_T^l)$, at time $T>0$, with $l \leq d$. Global conditions are found which replace the well-known "not-in-cutlocus" condition known from heat-kernel asymptotics. Our small noise expansion allows for a "second order" exponential factor. As application, new light is shed on the Takanobu--Watanabe expansion of Brownian motion and Levy's stochastic area. Further applications include tail and implied volatility asymptotics in some stochastic volatility models, discussed in a compagnion paper.
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Marginal Density expansions for diffusions and stochastic volatility part ii applications to the stein stein model
arXiv: Probability, 2013Co-Authors: Jeandominique Deuschel, Peter K Friz, Antoine Jacquier, S ViolanteAbstract:In the compagnion paper [Marginal Density expansions for diffusions and stochastic volatility, part I] we discussed Density expansions for multidimensional diffusions $(X^1,...,X^d)$, at fixed time $T$ and projected to their first $l$ coordinates, in the small noise regime. Global conditions were found which replace the well-known "not-in-cutlocus" condition known from heat-kernel asymptotics. In the present paper we discuss financial applications; these include tail and implied volatility asymptotics in some correlated stochastic volatility models. In particular, we solve a problem left open by A. Gulisashvili and E.M. Stein (2009).
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Marginal Density expansions for diffusions and stochastic volatility
2012Co-Authors: Jeandominique Deuschel, Peter K Friz, Antoine Jacquier, S ViolanteAbstract:Density expansions for hypoelliptic diffusions (X1^,...,X^d) are revisited. In particular, we are interested in Density expansions of the projection (X^1_T,...,X^l_T) at time $T>0$, with $l \le d$. Global conditions are found which replace the well-known ”not-in-cutlocus” condition known from heat-kernel asymptotics; cf. G. Ben Arous (88). Our small noise expansion allows for a ”second order” exponential factor. Applications include tail and implied volatility asymptotics in some correlated stochastic volatility models; in particular, we solve a problem left open by A. Gulisashvili and E.M. Stein (2009).
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Marginal Density expansions for diffusions and stochastic volatility part i theoretical foundations
arXiv: Probability, 2011Co-Authors: Jeandominique Deuschel, Peter K Friz, Antoine Jacquier, S ViolanteAbstract:Density expansions for hypoelliptic diffusions $(X^1,...,X^d)$ are revisited. In particular, we are interested in Density expansions of the projection $(X_T^1,...,X_T^l)$, at time $T>0$, with $l \leq d$. Global conditions are found which replace the well-known "not-in-cutlocus" condition known from heat-kernel asymptotics. Our small noise expansion allows for a "second order" exponential factor. As application, new light is shed on the Takanobu--Watanabe expansion of Brownian motion and Levy's stochastic area. Further applications include tail and implied volatility asymptotics in some stochastic volatility models, discussed in a compagnion paper.
Angeles Saavedra - One of the best experts on this subject based on the ideXlab platform.
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on the estimation of the Marginal Density of a moving average process
Canadian Journal of Statistics-revue Canadienne De Statistique, 2000Co-Authors: Angeles SaavedraAbstract:The authors present a new convolution-type kernel estimator of the Marginal Density of an MA(1) process with general error distribution. They prove the √n; -consistency of the nonparametric estimator and give asymptotic expressions for the mean square and the integrated mean square error of some unobservable version of the estimator. An extension to MA(q) processes is presented in the case of the mean integrated square error. Finally, a simulation study shows the good practical behaviour of the estimator and the strong connection between the estimator and its unobservable version in terms of the choice of the bandwidth. RESUME Les auteurs montrent comment estimer par la methode du noyau la densite Marginale d'un processus de moyenne mobile MA(1) dont la loi des erreurs est quelconque. Ils demontrent la convergence d'ordre √n; de cet estimateur non parametrique de type convolution et donnent, pour une version non-observable dudit estimateur, des expressions asymptotiques pour les erreurs quadratiques moyennes classique et integreAe. Dans ce dernier cas, ils indiquent en outre comment leur resultat limite s'etend au modele MA(q). Une etude de simulation vient confirmerle bon comportement du nouvel estimateur, qui s'avere fortement lie a sa version non-observable en ce qui touche le choix de la fenětre
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a comparative study of two convolution type estimators of the Marginal Density of moving average processes
Computational Statistics, 1999Co-Authors: Angeles SaavedraAbstract:In this paper, the mean integrated squared error of two convolution-type kernel estimators of the Marginal Density function of a moving average process is studied. Direct calculations lead to an exact expression for the MISE when the process is assumed to be Gaussian. Theses results, together with a simulation study carried out for some normal mixture distributions, are useful to compare the relative performance of these estimators with respect to the classical Parzen-Rosenblatt kernel Density estimator.
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rate of convergence of a convolution type estimator of the Marginal Density of a ma 1 process
Stochastic Processes and their Applications, 1999Co-Authors: Angeles SaavedraAbstract:In this paper moving-average processes with no parametric assumption on the error distribution are considered. A new convolution-type estimator of the Marginal Density of a MA(1) is presented. This estimator is closely related to some previous ones used to estimate the integrated squared Density and has a structure similar to the ordinary kernel Density estimator. For second-order kernels, the rate of convergence of this new estimator is investigated and the rate of the optimal bandwidth obtained. Under limit conditions on the smoothing parameter the convolution-type estimator is proved to be -consistent, which contrasts with the asymptotic behavior of the ordinary kernel Density estimator, that is only -consistent.
Yan Karklin - One of the best experts on this subject based on the ideXlab platform.
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A hierarchical Bayesian model for learning nonlinear statistical regularities in nonstationary natural signals
Neural Computation, 2005Co-Authors: Yan Karklin, Michael S. LewickiAbstract:Capturing statistical regularities in complex, high-dimensional data is an important problem in machine learning and signal processing. Models such as principal component analysis (PCA) and independent component analysis (ICA) make few assumptions about the structure in the data and have good scaling properties, but they are limited to representing linear statistical regularities and assume that the distribution of the data is stationary. For many natural, complex signals, the latent variables often exhibit residual dependencies as well as nonstationary statistics. Here we present a hierarchical Bayesian model that is able to capture higher-order nonlinear structure and represent nonstationary data distributions. The model is a generalization of ICA in which the basis function coefficients are no longer assumed to be independent; instead, the dependencies in their magnitudes are captured by a set of Density components. Each Density component describes a common pattern of deviation from the Marginal Density of the pattern ensemble; in different combinations, they can describe nonstationary distributions. Adapting the model to image or audio data yields a nonlinear, distributed code for higher-order statistical regularities that reflect more abstract, invariant properties of the signal. View full abstract
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A Hierarchical Bayesian Model for Learning Nonlinear Statistical Regularities in Nonstationary Natural Signals
Neural Computation, 2005Co-Authors: Yan Karklin, Michael S. LewickiAbstract:Capturing statistical regularities in complex, high-dimensional data is an important problem in machine learning and signal processing. Models such as principal component analysis (PCA) and independent component analysis (ICA) make few assumptions about the structure in the data and have good scaling properties, but they are limited to representing linear statistical regularities and assume that the distribution of the data is stationary. For many natural, complex signals, the latent variables often exhibit residual dependencies as well as nonstationary statistics. Here we present a hierarchical Bayesian model that is able to capture higher-order nonlinear structure and represent nonstationary data distributions. The model is a generalization of ICA in which the basis function coefficients are no longer assumed to be independent; instead, the dependencies in their magnitudes are captured by a set of Density components. Each Density component describes a common pattern of deviation from the Marginal Density of the pattern ensemble; in different combinations, they can describe nonstationary distributions. Adapting the model to image or audio data yields a nonlinear, distributed code for higher-order statistical regularities that reflect more abstract, invariant properties of the signal.