CoNES: Convex Natural Evolutionary Strategies

Inference Under Convex Cone Alternatives for Correlated Data

In this research, inferential theory for hypothesis testing under general convex cone alternatives for correlated data is developed. While there exists extensive theory for hypothesis testing under smooth cone alternatives with independent observations, extension to correlated data under general convex cone alternatives remains an open problem. This long-pending problem is addressed by (1) establishing that a "generalized quasi-score" statistic is asymptotically equivalent to the squared length of the projection of the standard Gaussian vector onto the convex cone and (2) showing that the asym…

The geometry of hypothesis testing over convex cones: Generalized likelihood tests and minimax radii

We consider a compound testing problem within the Gaussian sequence model in which the null and alternative are specified by a pair of closed, convex cones. Such cone testing problem arise in various applications, including detection of treatment effects, trend detection in econometrics, signal detection in radar processing, and shape-constrained inference in non-parametric statistics. We provide a sharp characterization of the GLRT testing radius up to a universal multiplicative constant in terms of the geometric structure of the underlying convex cones. When applied to concrete examples, thi…

高斯随机投影的凸锥：近似运动公式及其应用

Gaussian random projections of convex cones: approximate kinematic formulae and applications

本文研究高斯随机投影的凸锥的运动行为，推导近似运动公式，并应用于统计学习、数学规划和几何分析等领域。

Exact Partitioning of High-order Models with a Novel Convex Tensor Cone Relaxation

In this paper we propose an algorithm for exact partitioning of high-order models. We define a general class of $m$-degree Homogeneous Polynomial Models, which subsumes several examples motivated from prior literature. Exact partitioning can be formulated as a tensor optimization problem. We relax this high-order combinatorial problem to a convex conic form problem. To this end, we carefully define the Carathéodory symmetric tensor cone, and show its convexity, and the convexity of its dual cone. This allows us to construct a primal-dual certificate to show that the solution of the convex rela…

对称锥上在线凸优化的乘法更新

Multiplicative Updates for Online Convex Optimization over Symmetric Cones

本文提出对称锥乘法权重更新算法SCMWU，将乘法权重更新方法推广到任意对称锥的迹一元素集合上，并证明其无遗憾性质。

Constrained Mutual Convex Cone Method for Image Set Based Recognition

In this paper, we propose a method for image-set classification based on convex cone models. Image set classification aims to classify a set of images, which were usually obtained from video frames or multi-view cameras, into a target object. To accurately and stably classify a set, it is essential to represent structural information of the set accurately. There are various representative image features, such as histogram based features, HLAC, and Convolutional Neural Network (CNN) features. We should note that most of them have non-negativity and thus can be effectively represented by a conve…