Gaussian Graphical Model Estimation with False Discovery Rate Control

This paper studies the estimation of high dimensional Gaussian graphical model (GGM). Typically, the existing methods depend on regularization techniques. As a result, it is necessary to choose the regularized parameter. However, the precise relationship between the regularized parameter and the number of false edges in GGM estimation is unclear. Hence, it is impossible to evaluate their performance rigorously. In this paper, we propose an alternative method by a multiple testing procedure. Based on our new test statistics for conditional dependence, we propose a simultaneous testing procedure for conditional dependence in GGM. Our method can control the false discovery rate (FDR) asymptotically. The numerical performance of the proposed method shows that our method works quite well

A Direct Estimation Approach to Sparse Linear Discriminant Analysis

This paper considers sparse linear discriminant analysis of high-dimensional data. In contrast to the existing methods which are based on separate estimation of the precision matrix \O and the difference \de of the mean vectors, we introduce a simple and effective classifier by estimating the product \O\de directly through constrained $\ell_1$ minimization. The estimator can be implemented efficiently using linear programming and the resulting classifier is called the linear programming discriminant (LPD) rule. The LPD rule is shown to have desirable theoretical and numerical properties. It exploits the approximate sparsity of \O\de and as a consequence allows cases where it can still perform well even when \O and/or \de cannot be estimated consistently. Asymptotic properties of the LPD rule are investigated and consistency and rate of convergence results are given. The LPD classifier has superior finite sample performance and significant computational advantages over the existing methods that require separate estimation of \O and \de. The LPD rule is also applied to analyze real datasets from lung cancer and leukemia studies. The classifier performs favorably in comparison to existing methods.Comment: 39 pages.To appear in Journal of the American Statistical Associatio

Simultaneous nonparametric inference of time series

We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and regression estimates are asymptotically Gumbel. Our results substantially generalize earlier ones which were obtained under independence or beta mixing assumptions. The asymptotic results can be applied to assess patterns of marginal densities or regression functions via the construction of simultaneous confidence bands for which one can perform goodness-of-fit tests. As an application, we construct simultaneous confidence bands for drift and volatility functions in a dynamic short-term rate model for the U.S. Treasury yield curve rates data.Comment: Published in at http://dx.doi.org/10.1214/09-AOS789 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Adaptive Thresholding for Sparse Covariance Matrix Estimation

In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covariance matrices under the spectral norm. In contrast, the commonly used universal thresholding estimators are shown to be sub-optimal over the same parameter spaces. Support recovery is also discussed. The adaptive thresholding estimators are easy to implement. Numerical performance of the estimators is studied using both simulated and real data. Simulation results show that the adaptive thresholding estimators uniformly outperform the universal thresholding estimators. The method is also illustrated in an analysis on a dataset from a small round blue-cell tumors microarray experiment. A supplement to this paper which contains additional technical proofs is available online.Comment: To appear in Journal of the American Statistical Associatio

Instance-level Facial Attributes Transfer with Geometry-Aware Flow

We address the problem of instance-level facial attribute transfer without paired training data, e.g. faithfully transferring the exact mustache from a source face to a target face. This is a more challenging task than the conventional semantic-level attribute transfer, which only preserves the generic attribute style instead of instance-level traits. We propose the use of geometry-aware flow, which serves as a well-suited representation for modeling the transformation between instance-level facial attributes. Specifically, we leverage the facial landmarks as the geometric guidance to learn the differentiable flows automatically, despite of the large pose gap existed. Geometry-aware flow is able to warp the source face attribute into the target face context and generate a warp-and-blend result. To compensate for the potential appearance gap between source and target faces, we propose a hallucination sub-network that produces an appearance residual to further refine the warp-and-blend result. Finally, a cycle-consistency framework consisting of both attribute transfer module and attribute removal module is designed, so that abundant unpaired face images can be used as training data. Extensive evaluations validate the capability of our approach in transferring instance-level facial attributes faithfully across large pose and appearance gaps. Thanks to the flow representation, our approach can readily be applied to generate realistic details on high-resolution images.Comment: To appear in AAAI 2019. Code and models are available at: https://github.com/wdyin/GeoGA

On non-stationary threshold autoregressive models

In this paper we study the limiting distributions of the least-squares estimators for the non-stationary first-order threshold autoregressive (TAR(1)) model. It is proved that the limiting behaviors of the TAR(1) process are very different from those of the classical unit root model and the explosive AR(1).Comment: Published in at http://dx.doi.org/10.3150/10-BEJ306 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm