arXiv subjects

Fangzheng Xie

Publications and source records attributed to Fangzheng Xie.

21 records · Page 2Linked to original sources

arXiv2018

Adaptive Bayesian nonparametric regression using kernel mixture of polynomials with application to partial linear model

We propose a kernel mixture of polynomials prior for Bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weights. We obtain the minimax-optimal rate of contraction of the full posterior distribution up to a logarithmic factor that adapts to the smoothness level of the true function by estimating metric entropies of certain function classes. We also provide a frequentist sieve maximum likelihood estimator with a near-optimal convergence rate. We further investigate the application of the kernel mixture of polynomials to the partial linear model and obtain both the near-optimal rate of contraction for the nonparametric component and the Bernstein-von Mises limit (i.e., asymptotic normality) of the parametric component. The proposed method is illustrated with numerical examples and shows superior performance in terms of computational efficiency, accuracy, and uncertainty quantification compared to the local polynomial regression, DiceKriging, and the robust Gaussian stochastic process.

math.ST↗

arXiv2017

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.

stat.ME↗

arXiv2017

BayCount: A Bayesian Decomposition Method for Inferring Tumor Heterogeneity using RNA-Seq Counts

Tumor is heterogeneous - a tumor sample usually consists of a set of subclones with distinct transcriptional profiles and potentially different degrees of aggressiveness and responses to drugs. Understanding tumor heterogeneity is therefore critical to precise cancer prognosis and treatment. In this paper, we introduce BayCount, a Bayesian decomposition method to infer tumor heterogeneity with highly over-dispersed RNA sequencing count data. Using negative binomial factor analysis, BayCount takes into account both the between-sample and gene-specific random effects on raw counts of sequencing reads mapped to each gene. For posterior inference, we develop an efficient compound Poisson based blocked Gibbs sampler. Through extensive simulation studies and analysis of The Cancer Genome Atlas lung cancer and kidney cancer RNA sequencing count data, we show that BayCount is able to accurately estimate the number of subclones, the proportions of these subclones in each tumor sample, and the gene expression profiles in each subclone. Our method represents the first effort in characterizing tumor heterogeneity using RNA sequencing count data that simultaneously removes the need of normalizing the counts, achieves statistical robustness, and obtains biologically and clinically meaningful insights.

stat.AP↗