no code implementations • 12 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 $n$?
no code implementations • 30 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.
1 code implementation • 5 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.
no code implementations • 29 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.
no code implementations • 17 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.
no code implementations • 23 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).
no code implementations • 3 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.
1 code implementation • 24 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.
1 code implementation • 18 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.
no code implementations • 17 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).
no code implementations • 12 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.
no code implementations • 6 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.
no code implementations • 21 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.
no code implementations • 9 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).