The estimation of large covariance and precision matrices is fundamental in modern multivariate analysis. However, problems arise from the statistical analysis of large panel economic and financial data. The covariance matrix reveals marginal correlations between variables, while the precision matrix encodes conditional correlations between pairs of variables given the remaining variables. In this paper, we provide a selective review of several recent developments on the estimation of large covariance and precision matrices. We focus on two general approaches: a rankbased method and a factormodelbased method. Theories and applications of both approaches are presented. These methods are expected to be widely applicable to the analysis of economic and financial data.

This paper presents a method for generative design of decorative architectural parts such as corbel,moulding and panel, which usually have clear structure and aesthetic details. The method is composed of two components: offline learning and online generation. The offline learning trains a 2D CurveInfoGAN and a 3D VoxelVAE that learn the feature representations of the parts in a dataset. The online generation proceeds with an evolution procedure that evolves to product new generation of part components by selecting, crossing over and mutating features, followed by a feature-driven deformation that synthesizes the 3D mesh representation of new models. Built upon these technical components, a generative design tool is developed, which allows the user to input a decorative architectural model as a reference and then generates a set of new models that are “more of the same” as the reference and meanwhile exhibit some “surprising” elements. The experiments demonstrate the effectiveness of the method and also showcase the use of classic geometric modelling and advanced machine learning techniques in modelling of architectural parts.

Double-blind randomized controlled trials are traditionally seen as the gold standard for causal inferences as the difference-in-means estimator is an unbiased estimator of the average treatment effect in the experiment. The fact that this estimator is unbiased over all possible randomizations does not, however, mean that any given estimate is close to the true treatment effect. Similarly, while predetermined covariates will be balanced between treatment and control groups on average, large imbalances may be observed in a given experiment and the researcher may therefore want to condition on such covariates using linear regression. This article studies the theoretical properties of both the difference-in-means and OLS estimators conditional on observed differences in covariates. By deriving the statistical properties of the conditional estimators, we can establish guidance for how to deal with covariate imbalances.

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In this paper, we generalize the point integral method to solve the general elliptic PDEs with variable coefficients and corresponding eigenvalue problems with Neumann, Robin and Dirichlet boundary conditions on point cloud. The main idea is using integral equations to approximate the original PDEs. The integral equations are easy to discretize on the point cloud. The truncation error of the integral approximation is analyzed. Numerical examples are presented to demonstrate that PIM is an effective method to solve the elliptic PDEs with smooth coefficients on point cloud.