Lingzhou Xue

Lingzhou Xue
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Lingzhou Xue

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Statistics - Theory (6)
Mathematics - Statistics (6)
Statistics - Machine Learning (6)
Statistics - Methodology (5)
Mathematics - Optimization and Control (2)
Statistics - Applications (1)
Statistics - Computation (1)

Publications Authored By Lingzhou Xue

We consider forecasting a single time series using high-dimensional predictors in the presence of a possible nonlinear forecast function. The sufficient forecasting (Fan et al., 2016) used sliced inverse regression to estimate lower-dimensional sufficient indices for nonparametric forecasting using factor models. Read More

Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from different resources and have heterogeneous hidden commonality in real-world applications. Thus, it is of great importance to estimate heterogeneous dependencies and discover subpopulation with certain commonality across the whole population. Read More

Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives are two important testing procedures for high-dimensional independence. However, quadratic form statistics suffer from low power against sparse alternatives, and extreme-value form statistics suffer from low power against dense alternatives with small disturbances and may have size distortions due to its slow convergence. Read More

We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional (approximate) factor model implemented by the principal component analysis. Using the extracted factors, we develop a novel forecasting method called the sufficient forecasting, which provides a set of sufficient predictive indices, inferred from high-dimensional predictors, to deliver additional predictive power. Read More

A sparse precision matrix can be directly translated into a sparse Gaussian graphical model under the assumption that the data follow a joint normal distribution. This neat property makes high-dimensional precision matrix estimation very appealing in many applications. However, in practice we often face nonnormal data, and variable transformation is often used to achieve normality. Read More

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. Read More

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To simultaneously achieve sparsity and positive definiteness, we develop a positive definite $\ell_1$-penalized covariance estimator for estimating sparse large covariance matrices. An efficient alternating direction method is derived to solve the challenging optimization problem and its convergence properties are established. Read More

The Ising model is a useful tool for studying complex interactions within a system. The estimation of such a model, however, is rather challenging, especially in the presence of high-dimensional parameters. In this work, we propose efficient procedures for learning a sparse Ising model based on a penalized composite conditional likelihood with nonconcave penalties. Read More

Chandrasekaran, Parrilo and Willsky (2010) proposed a convex optimization problem to characterize graphical model selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance matrix that can be decomposed into a sparse matrix minus a low-rank matrix from sample data. Solving this convex optimization problem is very challenging, especially for large problems. Read More