Search Results for author: Yuetian Luo

Found 14 papers, 3 papers with code

The Limits of Assumption-free Tests for Algorithm Performance

no code implementations12 Feb 2024 Yuetian Luo, Rina Foygel Barber

In particular, we make a distinction between two questions: how good is an algorithm $A$ at the problem of learning from a training set of size $n$, versus, how good is a particular fitted model produced by running $A$ on a particular training data set of size $n$?

Computational Lower Bounds for Graphon Estimation via Low-degree Polynomials

no code implementations30 Aug 2023 Yuetian Luo, Chao GAO

From the statistical perspective, the minimax error rate of graphon estimation has been established by Gao et al (2015) for both stochastic block model (SBM) and nonparametric graphon estimation.

Community Detection Graphon Estimation +1

Iterative Approximate Cross-Validation

1 code implementation5 Mar 2023 Yuetian Luo, Zhimei Ren, Rina Foygel Barber

Cross-validation (CV) is one of the most popular tools for assessing and selecting predictive models.

Computational Efficiency

Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspective

no code implementations29 Sep 2022 Yuetian Luo, Nicolas Garcia Trillos

To prove our results we provide a comprehensive landscape analysis of a matrix factorization problem with a least squares objective, which serves as a critical bridge.

Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplay

no code implementations17 Jun 2022 Yuetian Luo, Anru R. Zhang

We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without the prior knowledge of its intrinsic rank.

regression Riemannian optimization

On Geometric Connections of Embedded and Quotient Geometries in Riemannian Fixed-rank Matrix Optimization

no code implementations23 Oct 2021 Yuetian Luo, Xudong Li, Anru R. Zhang

By applying the general procedure to the fixed-rank positive semidefinite (PSD) and general matrix optimization, we establish an exact Riemannian gradient connection under two geometries at every point on the manifold and sandwich inequalities between the spectra of Riemannian Hessians at Riemannian first-order stationary points (FOSPs).

Riemannian optimization

Nonconvex Factorization and Manifold Formulations are Almost Equivalent in Low-rank Matrix Optimization

no code implementations3 Aug 2021 Yuetian Luo, Xudong Li, Anru R. Zhang

In this paper, we consider the geometric landscape connection of the widely studied manifold and factorization formulations in low-rank positive semidefinite (PSD) and general matrix optimization.

Relation Retrieval

Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergence

1 code implementation24 Apr 2021 Yuetian Luo, Anru R. Zhang

In this paper, we consider the estimation of a low Tucker rank tensor from a number of noisy linear measurements.

regression

Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit

1 code implementation18 Dec 2020 Rungang Han, Yuetian Luo, Miaoyan Wang, Anru R. Zhang

High-order clustering aims to identify heterogeneous substructures in multiway datasets that arise commonly in neuroimaging, genomics, social network studies, etc.

Clustering

Recursive Importance Sketching for Rank Constrained Least Squares: Algorithms and High-order Convergence

no code implementations17 Nov 2020 Yuetian Luo, Wen Huang, Xudong Li, Anru R. Zhang

In this paper, we propose {\it \underline{R}ecursive} {\it \underline{I}mportance} {\it \underline{S}ketching} algorithm for {\it \underline{R}ank} constrained least squares {\it \underline{O}ptimization} (RISRO).

Retrieval

Open Problem: Average-Case Hardness of Hypergraphic Planted Clique Detection

no code implementations12 Sep 2020 Yuetian Luo, Anru R. Zhang

We note the significance of hypergraphic planted clique (HPC) detection in the investigation of computational hardness for a range of tensor problems.

A Sharp Blockwise Tensor Perturbation Bound for Orthogonal Iteration

no code implementations6 Aug 2020 Yuetian Luo, Garvesh Raskutti, Ming Yuan, Anru R. Zhang

Rate matching deterministic lower bound for tensor reconstruction, which demonstrates the optimality of HOOI, is also provided.

Clustering Denoising

Tensor Clustering with Planted Structures: Statistical Optimality and Computational Limits

no code implementations21 May 2020 Yuetian Luo, Anru R. Zhang

We also develop the tight computational thresholds: when the signal-to-noise ratio is below these thresholds, we prove that polynomial-time algorithms cannot solve these problems under the computational hardness conjectures of hypergraphic planted clique (HPC) detection and hypergraphic planted dense subgraph (HPDS) recovery.

Clustering

ISLET: Fast and Optimal Low-rank Tensor Regression via Importance Sketching

no code implementations9 Nov 2019 Anru Zhang, Yuetian Luo, Garvesh Raskutti, Ming Yuan

In this paper, we develop a novel procedure for low-rank tensor regression, namely \emph{\underline{I}mportance \underline{S}ketching \underline{L}ow-rank \underline{E}stimation for \underline{T}ensors} (ISLET).

Distributed Computing regression

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