49,762 research outputs found
Bayesian Repulsive Gaussian Mixture Model
We develop a general class of Bayesian repulsive Gaussian mixture models that
encourage well-separated clusters, aiming at reducing potentially redundant
components produced by independent priors for locations (such as the Dirichlet
process). The asymptotic results for the posterior distribution of the proposed
models are derived, including posterior consistency and posterior contraction
rate in the context of nonparametric density estimation. More importantly, we
show that compared to the independent prior on the component centers, the
repulsive prior introduces additional shrinkage effect on the tail probability
of the posterior number of components, which serves as a measurement of the
model complexity. In addition, an efficient and easy-to-implement
blocked-collapsed Gibbs sampler is developed based on the exchangeable
partition distribution and the corresponding urn model. We evaluate the
performance and demonstrate the advantages of the proposed model through
extensive simulation studies and real data analysis. The R code is available at
https://drive.google.com/open?id=0B_zFse0eqxBHZnF5cEhsUFk0cVE
PCA-Kernel Estimation
International audienceMany statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample \bX_1, \hdots, \bX_n onto the first eigenvectors of the Principal Component Analysis (PCA) associated with the empirical projector . Classical nonparametric inference methods such as kernel density estimation or kernel regression analysis are then performed in the (usually small) -di\-men\-sio\-nal space. However, the mathematical analysis of this data-driven dimension reduction scheme raises technical problems, due to the fact that the random variables of the projected sample ( \hat \Pi_D\bX_1,\hdots, \hat \Pi_D\bX_n ) are no more independent. As a reference for further studies, we offer in this paper several results showing the asymptotic equivalencies between important kernel-related quantities based on the empirical projector and its theoretical counterpart. As an illustration, we provide an in-depth analysis of the nonparametric kernel regression cas
Particle Learning for General Mixtures
This paper develops particle learning (PL) methods for the estimation of general mixture models. The approach is distinguished from alternative particle filtering methods in two major ways. First, each iteration begins by resampling particles according to posterior predictive probability, leading to a more efficient set for propagation. Second, each particle tracks only the "essential state vector" thus leading to reduced dimensional inference. In addition, we describe how the approach will apply to more general mixture models of current interest in the literature; it is hoped that this will inspire a greater number of researchers to adopt sequential Monte Carlo methods for fitting their sophisticated mixture based models. Finally, we show that PL leads to straight forward tools for marginal likelihood calculation and posterior cluster allocation.Business Administratio
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