A novel robust estimation for high-dimensional precision matrices.

In this paper we propose a new robust estimation of precision matrices for high-dimensional data when the number of variables is larger than the sample size. Different from the existing methods in literature, the proposed model combines the technique of modified Cholesky decomposition (MCD) with the robust generalized M-estimators. The MCD reparameterizes a precision matrix and transforms its estimation into solving a series of linear regressions, in which the commonly used robust techniques can be conveniently incorporated. Additionally, the proposed method adopts the model averaging idea to address the ordering issue in the MCD approach, resulting in an accurate estimation for precision matrices. Simulations and real data analysis are conducted to illustrate the merits of the proposed estimator.

UPST-NeRF: Universal Photorealistic Style Transfer of Neural Radiance Fields for 3D Scene.

Photorealistic stylization of 3D scenes aims to generate photorealistic images from arbitrary novel views according to a given style image, while ensuring consistency when rendering video from different viewpoints. Some existing stylization methods using neural radiance fields can effectively predict stylized scenes by combining the features of the style image with multi-view images to train 3D scenes. However, these methods generate novel view images that contain undesirable artifacts. In addition, they cannot achieve universal photorealistic stylization for a 3D scene. Therefore, a stylization image needs to retrain a 3D scene representation network based on a neural radiation field. We propose a novel photorealistic 3D scene stylization transfer framework to address these issues. It can realize photorealistic 3D scene style transfer with a 2D style image for novel view video rendering. We first pre-trained a 2D photorealistic style transfer network, which can satisfy the photorealistic style transfer between any content image and style image. Then, we use voxel features to optimize a 3D scene and obtain the geometric representation of the scene. Finally, we jointly optimize a hypernetwork to realize the photorealistic style transfer of arbitrary style images. In the transfer stage, we use a pre-trained 2D photorealistic network to constrain the photorealistic style of different views and different style images in the 3D scene. The experimental results show that our method not only realizes the 3D photorealistic style transfer of arbitrary style images, but also outperforms the existing methods in terms of visual quality and consistency. Project page:https://semchan.github.io/UPST_NeRF/.

A Cholesky-based estimation for large-dimensional covariance matrices.

This paper develops a new method to estimate a large-dimensional covariance matrix when the variables have no natural ordering among themselves. The modified Cholesky decomposition technique is used to provide a set of estimates of the covariance matrix under multiple orderings of variables. The proposed estimator is in the form of a linear combination of these available estimates and the identity matrix. It is positive definite and applicable in large dimensions. The merits of the proposed estimator are demonstrated through the numerical study and a real data example by comparison with several existing methods.