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Found 12 papers, 0 papers with code
Implicit Regularization of Gradient Flow on One-Layer Softmax Attention
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.
Leave-one-out Singular Subspace Perturbation Analysis for Spectral Clustering
The singular subspaces perturbation theory is of fundamental importance in probability and statistics.
Optimal estimation of high-dimensional location Gaussian mixtures
This paper studies the optimal rate of estimation in a finite Gaussian location mixture model in high dimensions without separation conditions.
Optimality of Spectral Clustering in the Gaussian Mixture Model
Spectral clustering is one of the most popular algorithms to group high dimensional data.
Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations
We analyze the classical EM algorithm for parameter estimation in the symmetric two-component Gaussian mixtures in $d$ dimensions.
Theoretical and Computational Guarantees of Mean Field Variational Inference for Community Detection
Its iterative Coordinate Ascent Variational Inference algorithm has been widely applied to large scale Bayesian inference.
Statistical and Computational Guarantees of Lloyd's Algorithm and its Variants
Lloyd's algorithm, proposed in 1957, is still possibly the most widely used clustering algorithm in practice due to its simplicity and empirical performance.
Community Detection in Degree-Corrected Block Models
Community detection is a central problem of network data analysis.
Optimal Estimation and Completion of Matrices with Biclustering Structures
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.
Achieving Optimal Misclassification Proportion in Stochastic Block Model
Community detection is a fundamental statistical problem in network data analysis.
Sparse CCA via Precision Adjusted Iterative Thresholding
Sparse Canonical Correlation Analysis (CCA) has received considerable attention in high-dimensional data analysis to study the relationship between two sets of random variables.
Asymptotic normality and optimalities in estimation of large Gaussian graphical models
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?
