no code implementations • 11 Sep 2024 • Zehao Dou, Subhodh Kotekal, Zhehao Xu, Harrison H. Zhou

samples from an unknown \(\alpha\)-H\"{o}lder density \(f\) supported on \([-1, 1]\), we prove the minimax rate of estimating the score function of the diffused distribution \(f * \mathcal{N}(0, t)\) with respect to the score matching loss is \(\frac{1}{nt^2} \wedge \frac{1}{nt^{3/2}} \wedge (t^{\alpha-1} + n^{-2(\alpha-1)/(2\alpha+1)})\) for all \(\alpha > 0\) and \(t \ge 0\).

no code implementations • 13 Mar 2024 • Heejune Sheen, Siyu Chen, Tianhao Wang, Harrison H. Zhou

Under a separability assumption on the data, we show that when gradient flow achieves the minimal loss value, it further implicitly minimizes the nuclear norm of the product of the key and query weight matrices.

no code implementations • 30 May 2022 • Anderson Y. Zhang, Harrison H. Zhou

The singular subspaces perturbation theory is of fundamental importance in probability and statistics.

no code implementations • 14 Feb 2020 • Natalie Doss, Yihong Wu, Pengkun Yang, Harrison H. Zhou

This paper studies the optimal rate of estimation in a finite Gaussian location mixture model in high dimensions without separation conditions.

no code implementations • 1 Nov 2019 • Matthias Löffler, Anderson Y. Zhang, Harrison H. Zhou

Spectral clustering is one of the most popular algorithms to group high dimensional data.

no code implementations • 28 Aug 2019 • Yihong Wu, Harrison H. Zhou

We analyze the classical EM algorithm for parameter estimation in the symmetric two-component Gaussian mixtures in $d$ dimensions.

no code implementations • 30 Oct 2017 • Anderson Y. Zhang, Harrison H. Zhou

Its iterative Coordinate Ascent Variational Inference algorithm has been widely applied to large scale Bayesian inference.

no code implementations • 7 Dec 2016 • Yu Lu, Harrison H. Zhou

Lloyd's algorithm, proposed in 1957, is still possibly the most widely used clustering algorithm in practice due to its simplicity and empirical performance.

no code implementations • 24 Jul 2016 • Chao Gao, Zongming Ma, Anderson Y. Zhang, Harrison H. Zhou

Community detection is a central problem of network data analysis.

no code implementations • 1 Dec 2015 • Chao Gao, Yu Lu, Zongming Ma, Harrison H. Zhou

Biclustering structures in data matrices were first formalized in a seminal paper by John Hartigan (1972) where one seeks to cluster cases and variables simultaneously.

no code implementations • 14 May 2015 • Chao Gao, Zongming Ma, Anderson Y. Zhang, Harrison H. Zhou

Community detection is a fundamental statistical problem in network data analysis.

no code implementations • 24 Nov 2013 • Mengjie Chen, Chao GAO, Zhao Ren, Harrison H. Zhou

Sparse Canonical Correlation Analysis (CCA) has received considerable attention in high-dimensional data analysis to study the relationship between two sets of random variables.

no code implementations • 24 Sep 2013 • Zhao Ren, Tingni Sun, Cun-Hui Zhang, Harrison H. Zhou

This paper considers a fundamental question: When is it possible to estimate low-dimensional parameters at parametric square-root rate in a large Gaussian graphical model?

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