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Found 35 papers, 5 papers with code
Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedure
Transfer learning for nonparametric regression is considered.
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.
Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning
The score attack method is based on the tracing attack concept in differential privacy and can be applied to any statistical model with a well-defined score statistic.
Testing High-dimensional Multinomials with Applications to Text Analysis
Motivated by applications in text mining and discrete distribution inference, we investigate the testing for equality of probability mass functions of $K$ groups of high-dimensional multinomial distributions.
Transfer Learning for Contextual Multi-armed Bandits
The results quantify the contribution of the data from the source domains for learning in the target domain in the context of nonparametric contextual multi-armed bandits.
Locally Adaptive Algorithms for Multiple Testing with Network Structure, with Application to Genome-Wide Association Studies
Linkage analysis has provided valuable insights to the GWAS studies, particularly in revealing that SNPs in linkage disequilibrium (LD) can jointly influence disease phenotypes.
Matrix Reordering for Noisy Disordered Matrices: Optimality and Computationally Efficient Algorithms
Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrix reordering based on a noisy disordered monotone Toeplitz matrix model.
Distributed Nonparametric Function Estimation: Optimal Rate of Convergence and Cost of Adaptation
Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied.
Theoretical Foundations of t-SNE for Visualizing High-Dimensional Clustered Data
This paper investigates the theoretical foundations of the t-distributed stochastic neighbor embedding (t-SNE) algorithm, a popular nonlinear dimension reduction and data visualization method.
The Cost of Privacy in Generalized Linear Models: Algorithms and Minimax Lower Bounds
We propose differentially private algorithms for parameter estimation in both low-dimensional and high-dimensional sparse generalized linear models (GLMs) by constructing private versions of projected gradient descent.
Estimation, Confidence Intervals, and Large-Scale Hypotheses Testing for High-Dimensional Mixed Linear Regression
Based on the iterative estimators, we further construct debiased estimators and establish their asymptotic normality.
Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Control
Transfer learning for high-dimensional Gaussian graphical models (GGMs) is studied with the goal of estimating the target GGM by utilizing the data from similar and related auxiliary studies.
Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality
This paper considers the estimation and prediction of a high-dimensional linear regression in the setting of transfer learning, using samples from the target model as well as auxiliary samples from different but possibly related regression models.
Optimal Structured Principal Subspace Estimation: Metric Entropy and Minimax Rates
Driven by a wide range of applications, many principal subspace estimation problems have been studied individually under different structural constraints.
Distributed Gaussian Mean Estimation under Communication Constraints: Optimal Rates and Communication-Efficient Algorithms
Although optimal estimation of a Gaussian mean is relatively simple in the conventional setting, it is quite involved under the communication constraints, both in terms of the optimal procedure design and lower bound argument.
High Dimensional M-Estimation with Missing Outcomes: A Semi-Parametric Framework
Under mild tail assumptions and arbitrarily chosen (working) models for the propensity score (PS) and the outcome regression (OR) estimators, satisfying only some high-level conditions, we establish finite sample performance bounds for the DDR estimator showing its (optimal) $L_2$ error rate to be $\sqrt{s (\log d)/ n}$ when both models are correct, and its consistency and DR properties when only one of them is correct.
Sparse Group Lasso: Optimal Sample Complexity, Convergence Rate, and Statistical Inference
We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse.
Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier
In this paper, we study transfer learning in the context of nonparametric classification based on observations from different distributions under the posterior drift model, which is a general framework and arises in many practical problems.
The Cost of Privacy: Optimal Rates of Convergence for Parameter Estimation with Differential Privacy
By refining the "tracing adversary" technique for lower bounds in the theoretical computer science literature, we formulate a general lower bound argument for minimax risks with differential privacy constraints, and apply this argument to high-dimensional mean estimation and linear regression problems.
Heteroskedastic PCA: Algorithm, Optimality, and Applications
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced.
Weighted Message Passing and Minimum Energy Flow for Heterogeneous Stochastic Block Models with Side Information
We develop an optimally weighted message passing algorithm to reconstruct labels for SBM based on the minimum energy flow and the eigenvectors of a certain Markov transition matrix.
Semi-supervised Inference: General Theory and Estimation of Means
Estimators are proposed along with corresponding confidence intervals for the population mean.
On Detection and Structural Reconstruction of Small-World Random Networks
In this paper, we study detection and fast reconstruction of the celebrated Watts-Strogatz (WS) small-world random graph model \citep{watts1998collective} which aims to describe real-world complex networks that exhibit both high clustering and short average length properties.
Inference via Message Passing on Partially Labeled Stochastic Block Models
We study the community detection and recovery problem in partially-labeled stochastic block models (SBM).
A Sparse PCA Approach to Clustering
We discuss a clustering method for Gaussian mixture model based on the sparse principal component analysis (SPCA) method and compare it with the IF-PCA method.
Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise $\epsilon_j$.
Structured Matrix Completion with Applications to Genomic Data Integration
Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering.
Computational and Statistical Boundaries for Submatrix Localization in a Large Noisy Matrix
The second threshold, $\sf SNR_s$, captures the statistical boundary, below which no method can succeed with probability going to one in the minimax sense.
Rate-Optimal Detection of Very Short Signal Segments
Motivated by a range of applications in engineering and genomics, we consider in this paper detection of very short signal segments in three settings: signals with known shape, arbitrary signals, and smooth signals.
Robust and computationally feasible community detection in the presence of arbitrary outlier nodes
To the best of the authors' knowledge, our result is the first in the literature in terms of clustering communities with fast growing numbers under the GSBM where a portion of arbitrary outlier nodes exist.
Geometric Inference for General High-Dimensional Linear Inverse Problems
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation, and noisy matrix completion.
ROP: Matrix recovery via rank-one projections
In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case.
A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion
The rate of convergence for the estimate is obtained.
Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-rank Matrices
It is shown that for any given constant $t\ge {4/3}$, in compressed sensing $\delta_{tk}^A < \sqrt{(t-1)/t}$ guarantees the exact recovery of all $k$ sparse signals in the noiseless case through the constrained $\ell_1$ minimization, and similarly in affine rank minimization $\delta_{tr}^\mathcal{M}< \sqrt{(t-1)/t}$ ensures the exact reconstruction of all matrices with rank at most $r$ in the noiseless case via the constrained nuclear norm minimization.
Matrix Completion via Max-Norm Constrained Optimization
Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting.
