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Found 32 papers, 3 papers with code
Optimal Differentially Private PCA and Estimation for Spiked Covariance Matrices
Estimating a covariance matrix and its associated principal components is a fundamental problem in contemporary statistics.
Multiple Testing of Linear Forms for Noisy Matrix Completion
Many important tasks of large-scale recommender systems can be naturally cast as testing multiple linear forms for noisy matrix completion.
Optimal Clustering of Discrete Mixtures: Binomial, Poisson, Block Models, and Multi-layer Networks
Under the mixture multi-layer stochastic block model (MMSBM), we show that the minimax optimal network clustering error rate, which takes an exponential form and is characterized by the Renyi divergence between the edge probability distributions of the component networks.
High-dimensional Linear Bandits with Knapsacks
We study the contextual bandits with knapsack (CBwK) problem under the high-dimensional setting where the dimension of the feature is large.
Online Tensor Learning: Computational and Statistical Trade-offs, Adaptivity and Optimal Regret
Under the fixed step size regime, a fascinating trilemma concerning the convergence rate, statistical error rate, and regret is observed.
Computationally Efficient and Statistically Optimal Robust High-Dimensional Linear Regression
The algorithm is not only computationally efficient with linear convergence but also statistically optimal, be the noise Gaussian or heavy-tailed with a finite 1 + epsilon moment.
rMultiNet: An R Package For Multilayer Networks Analysis
This paper develops an R package rMultiNet to analyze multilayer network data.
Consensus Knowledge Graph Learning via Multi-view Sparse Low Rank Block Model
Network analysis has been a powerful tool to unveil relationships and interactions among a large number of objects.
Optimal Regularized Online Allocation by Adaptive Re-Solving
This paper introduces a dual-based algorithm framework for solving the regularized online resource allocation problems, which have potentially non-concave cumulative rewards, hard resource constraints, and a non-separable regularizer.
Higher-order accurate two-sample network inference and network hashing
Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural assumptions; achieving finite-sample higher-order accuracy; handling different network sizes and sparsity levels; fast computation and memory parsimony; controlling false discovery rate (FDR) in multiple testing; and theoretical understandings, particularly regarding finite-sample accuracy and minimax optimality.
Optimal Clustering by Lloyd Algorithm for Low-Rank Mixture Model
Comparable to GMM, the minimax optimal clustering error rate is decided by the separation strength, i. e., the minimal distance between population center matrices.
Computationally Efficient and Statistically Optimal Robust Low-rank Matrix and Tensor Estimation
Lastly, RsGrad is applicable for low-rank tensor estimation under heavy-tailed noise where a statistically optimal rate is attainable with the same phenomenon of dual-phase convergence, and a novel shrinkage-based second-order moment method is guaranteed to deliver a warm initialization.
Optimal Estimation and Computational Limit of Low-rank Gaussian Mixtures
If the signal is stronger than a certain threshold, called the computational limit, we design a computationally fast estimator based on spectral aggregation and demonstrate its minimax optimality.
Provable Tensor-Train Format Tensor Completion by Riemannian Optimization
In this paper, we provide, to our best knowledge, the first theoretical guarantees of the convergence of RGrad algorithm for TT-format tensor completion, under a nearly optimal sample size condition.
Latent Space Model for Higher-order Networks and Generalized Tensor Decomposition
We formulate the relationship between the latent positions and the observed data via a generalized multilinear kernel as the link function.
Inference for Low-rank Tensors -- No Need to Debias
In all these models, we observe that different from many matrix/vector settings in existing work, debiasing is not required to establish the asymptotic distribution of estimates or to make statistical inference on low-rank tensors.
Edgeworth expansions for network moments
In this paper, we present the first higher-order accurate approximation to the sampling CDF of a studentized network moment by Edgeworth expansion.
Community Detection on Mixture Multi-layer Networks via Regularized Tensor Decomposition
We show that the TWIST procedure can accurately detect the communities with small misclassification error as the number of nodes and/or the number of layers increases.
Statistical Inferences of Linear Forms for Noisy Matrix Completion
We introduce a flexible framework for making inferences about general linear forms of a large matrix based on noisy observations of a subset of its entries.
Non-asymptotic bounds for percentiles of independent non-identical random variables
This note displays an interesting phenomenon for percentiles of independent but non-identical random variables.
Confidence Region of Singular Subspaces for Low-rank Matrix Regression
We investigate the distribution of the joint projection distance between the empirical singular subspace and the unknown true singular subspace.
Statistically Optimal and Computationally Efficient Low Rank Tensor Completion from Noisy Entries
To fill in this void, in this article, we characterize the fundamental statistical limits of noisy tensor completion by establishing minimax optimal rates of convergence for estimating a $k$th order low rank tensor under the general $\ell_p$ ($1\le p\le 2$) norm which suggest significant room for improvement over the existing approaches.
Effective Tensor Sketching via Sparsification
In particular, we show that for a $k$th order $d\times\cdots\times d$ cubic tensor of {\it stable rank} $r_s$, the sample size requirement for achieving a relative error $\varepsilon$ is, up to a logarithmic factor, of the order $r_s^{1/2} d^{k/2} /\varepsilon$ when $\varepsilon$ is relatively large, and $r_s d /\varepsilon^2$ and essentially optimal when $\varepsilon$ is sufficiently small.
The Sup-norm Perturbation of HOSVD and Low Rank Tensor Denoising
In addition, the bounds established for HOSVD also elaborate the one-sided sup-norm perturbation bounds for the singular subspaces of unbalanced (or fat) matrices.
Tensor SVD: Statistical and Computational Limits
In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data.
On Polynomial Time Methods for Exact Low Rank Tensor Completion
In this paper, we investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries.
Estimation of low rank density matrices by Pauli measurements
First, we establish the minimax lower bounds in Schatten $p$-norms with $1\leq p\leq +\infty$ for low rank density matrices estimation by Pauli measurements.
Estimation of low rank density matrices: bounds in Schatten norms and other distances
Let ${\mathcal S}_m$ be the set of all $m\times m$ density matrices (Hermitian positively semi-definite matrices of unit trace).
Optimal Estimation of Low Rank Density Matrices
The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system.
Exploring Sparsity in Multi-class Linear Discriminant Analysis
Recent studies in the literature have paid much attention to the sparsity in linear classification tasks.
Optimal Schatten-q and Ky-Fan-k Norm Rate of Low Rank Matrix Estimation
We also give upper bounds and matching minimax lower bound(except some logarithmic terms) for estimation accuracy under Schatten-q norm for every $1\leq q\leq\infty$.
