research
∙
08/30/2023
Computational Lower Bounds for Graphon Estimation via Low-degree Polynomials
Graphon estimation has been one of the most fundamental problems in netw...
share
research
∙
03/05/2023
Iterative Approximate Cross-Validation
Cross-validation (CV) is one of the most popular tools for assessing and...
research
∙
09/29/2022
Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspective
We study a general matrix optimization problem with a fixed-rank positiv...
research
∙
06/17/2022
Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplay
We study the tensor-on-tensor regression, where the goal is to connect t...
research
∙
10/23/2021
On Geometric Connections of Embedded and Quotient Geometries in Riemannian Fixed-rank Matrix Optimization
In this paper, we propose a general procedure for establishing the lands...
research
∙
08/03/2021
Nonconvex Factorization and Manifold Formulations are Almost Equivalent in Low-rank Matrix Optimization
In this paper, we consider the geometric landscape connection of the wid...
research
∙
04/24/2021
Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergence
In this paper, we consider the estimation of a low Tucker rank tensor fr...
research
∙
12/18/2020
Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit
High-order clustering aims to identify heterogeneous substructure in mul...
research
∙
11/17/2020
Recursive Importance Sketching for Rank Constrained Least Squares: Algorithms and High-order Convergence
In this paper, we propose a new ecursive mportance ketching algorithm fo...
research
∙
09/12/2020
Open Problem: Average-Case Hardness of Hypergraphic Planted Clique Detection
We note the significance of hypergraphic planted clique (HPC) detection ...
research
∙
08/06/2020
A Sharp Blockwise Tensor Perturbation Bound for Orthogonal Iteration
In this paper, we develop novel perturbation bounds for the high-order o...
research
∙
08/04/2020
A Schatten-q Matrix Perturbation Theory via Perturbation Projection Error Bound
This paper studies the Schatten-q error of low-rank matrix estimation by...
research
∙
05/21/2020
Tensor Clustering with Planted Structures: Statistical Optimality and Computational Limits
This paper studies the statistical and computational limits of high-orde...
research
∙
11/09/2019