The paper derives oracle inequalities for estimators with fast and slow rates.
problem Developing fast and slow oracle inequalities for estimators.
method Direct study of analysis estimator and adaptation of Dalalyan, Hebiri and Lederer's arguments.
result Constant-friendly rates for (square root) total variation regularized estimators over graphs.
Paper introduces a new histogram estimator for nonparametric density estimation that improves performance.
problem Smoothness-based nonparametric density estimators are not optimal for all types of data.
method Incorporates a multi-view latent variable model into histogram-style estimators.
result A new histogram estimator converges faster to multi-view models in L1 error. Develops asymptotic analysis for RandNLA sampling estimators in least-squares problems.
problem Lack of distributional information for RandNLA estimators in statistical inference.
method Asymptotic analysis of sampling estimators for least-squares problems in two settings.
result Sampling estimators are asymptotically normally distributed under mild conditions.
Independent component analysis (ICA) has been widely used for blind source separation in many fields such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on M-estimates have been proposed for estimating the mixing matrix. Recently, several nonparametric methods have…
Survey on manifold ends with new heat kernel estimates.
problem Analyzing geometric properties on manifolds with ends.
method Constructing manifolds with ends and analyzing their heat kernel estimates.
result Found manifolds with ends that have different heat kernel estimates.
Study compares estimators for causal mediation analysis with multiple mediators.
problem Estimating causal effects through multiple mediators in observational studies.
method Parametric and non-parametric estimators, including multiply robust and double machine learning approaches.
result Advanced estimators perform well across various settings and real data.
VarFA efficiently estimates student skill levels with uncertainty for adaptive testing.
problem Efficiently estimating student skill levels with uncertainty for adaptive testing.
method VarFA uses variational inference to extend factor analysis models for educational data.
result VarFA efficiently handles large datasets and produces uncertainty estimates.
Study improves model estimation and variable selection using GANs with Lasso penalty.
problem Variable selection in high-dimensional data with deep networks.
method Conditional Wasserstein Generative Adversarial Networks with Group Lasso penalization.
result Established convergence rate for variable selection in censored survival data.
This paper surveys some recent developments in fundamental limits and optimal algorithms for network analysis. We focus on minimax optimal rates in three fundamental problems of network analysis: graphon estimation, community detection, and hypothesis testing. For each problem, we review state-of-the-art results in the…
Proposes MPCA for robust PCA using mode estimation.
problem Outliers sensitivity in PCA.
method Modal Principal Component Analysis (MPCA) based on mode estimation.
result MPCA shows advantages over conventional methods.
The estimation of covariance matrices of gene expressions has many applications in cancer systems biology. Many gene expression studies, however, are hampered by low sample size and it has therefore become popular to increase sample size by collecting gene expression data across studies. Motivated by the traditional me…
We examine the performance of six estimators of the power-law cross-correlations -- the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle e…
Paper analyzes ECE bias and provides bounds for its estimation.
problem Understanding the estimation bias in ECE for machine learning models.
method Information-theoretic approach to analyze bias in uniform mass and uniform width binning strategies.
result Established upper bounds on ECE estimation bias and optimal number of bins.
This paper tackles distributed estimation of the top-L eigenspace in PCA for large data sets.
problem Challenges in estimating the top-L eigenspace in principal component analysis for large data sets.
method Proposes a novel multi-round algorithm using shift-and-invert preconditioning and convex optimization.
result Achieves a fast convergence rate and covers the targeted top-L eigenspace without explicit eigengap assumption.
Efficiently estimates covariance for sparse functional data.
problem Sparse data in functional analysis.
method Random-knots and B-spline estimators for covariance function.
result Asymptotic pointwise covariance estimates for sparsified data.
New approach estimates treatment effects from decentralized data.
problem Estimating treatment effects from multiple studies with limited data.
method Three classes of ATE estimators derived from Plug-in G-Formula.
result Asymptotic variance of estimators for linear models derived.
We provide a conceptual map to navigate causal analysis problems. Focusing on the case of discrete random variables, we consider the case of causal effect estimation from observational data. The presented approaches apply also to continuous variables, but the issue of estimation becomes more complex. We then introduce …
KSG mutual information estimator, which is based on the distances of each sample to its k-th nearest neighbor, is widely used to estimate mutual information between two continuous random variables. Existing work has analyzed the convergence rate of this estimator for random variables whose densities are bounded away fr…
New method stabilizes IF-based estimators for causal mediation analysis with continuous mediators.
problem Stability issues in IF-based estimators for continuous mediators.
method Nonparametric weighted balancing method to estimate nuisance functions.
result Significant reductions in bias and variance compared to existing methods.
The Rasch model is widely used for item response analysis in applications ranging from recommender systems to psychology, education, and finance. While a number of estimators have been proposed for the Rasch model over the last decades, the available analytical performance guarantees are mostly asymptotic. This paper p…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A distribution-free analysis shows that by observing just a single linear measure…
New method improves PCA for high-dimensional data with n < p.
problem PCA struggles in high-dimensional settings with n < p.
method Pairwise differences covariance estimation with four regularized versions.
result Proposed methods outperform existing estimators in high-dimensional data settings.
Consistent estimator for mixtures of nonparametric elliptical distributions helps cluster analysis.
problem Consistency of maximum likelihood estimator for mixtures of nonparametric elliptical distributions.
method Maximum likelihood estimation for mixtures of elliptically-symmetric distributions under nonparametric P. result Components of the estimator correspond to well-separated components of the underlying distribution P. Paper constructs L2 estimates for flat vector bundles and generalizes Prékopa's theorem.
problem Constructing L2 estimates for flat vector bundles. method Using Hörmander's L2-estimate for the operator d on a flat vector bundle over a p-convex Riemannian manifold. result Generalizes Prékopa's theorem in convex analysis.
This work gives a simultaneous analysis of both the ordinary least squares estimator and the ridge regression estimator in the random design setting under mild assumptions on the covariate/response distributions. In particular, the analysis provides sharp results on the ``out-of-sample'' prediction error, as opposed to…
Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain smoothed analysis estimates for elements in this class depending only on geometric inva…
ARA combines aggregated RAPPOR and Tf-Idf estimation for centralized DP analysis.
problem Gap between local and central DP approaches in terms of data storage, analysis speed, and amount of data.
method Collects RAPPOR reports from multiple clients, pushes them to a Tf-Idf estimation model, and analyzes them for centralized DP.
result Successfully and efficiently analyzed major truth values from multiple clients.
ICA accurately estimates treatment effects even with confounders.
problem Estimating treatment effects in the presence of confounding variables.
method Uses Independent Component Analysis (ICA) to identify latent sources and estimate mixing coefficients.
result Linear ICA can consistently estimate multiple treatment effects, even with Gaussian confounders, and is more sample-efficient than Orthogonal Machine Learning (OML).
Analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. This paper presents generalizations of such estimation error analysis on all four aspe…
Method quantifies sensitivity of reliability analysis to uncertainty sources.
problem Computational expense in reliability analysis of complex models.
method Gaussian process surrogate model, active learning, sensitivity analysis.
result Reduces main source of error in estimating rare event probabilities.
The paper introduces a method for interpretable principal component analysis of high-dimensional time series.
problem Inconsistent and difficult-to-interpret principal component estimates in high-dimensional regimes.
method Localized sparse principal component analysis of spectral density matrices in frequency domain.
result Efficient algorithm for sparse-localized estimates of principal subspaces.
The paper provides bounds on estimation error in a distributed online learning setting.
problem Estimating an unknown parameter in a distributed and online manner with finite sample guarantees.
method Proposes a distributed online estimation algorithm that improves accuracy through communication, providing non-asymptotic bounds on estimation error.
result Demonstrates a trade-off between estimation error and communication costs, and determines a stopping time for communication based on desired accuracy.
We prove a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Our probability estimates depend only on geometric invariants of the corresponding sets of ill-posed inputs. Several applications to linear and polynomial equation solving show that the estima…
The study analyzes weighted manifolds with curvature bounds, proving eigenvalue estimates and inequalities.
problem Analyzing geometric properties of weighted manifolds under Ricci curvature bounds.
method Develops geometric analysis techniques on weighted Riemannian manifolds with lower 0-weighted Ricci curvature bounds. result Proves eigenvalue estimates for Steklov and ABP inequalities on weighted manifolds.
Nonasymptotic error bounds and strong consistency rates for survival analysis methods.
problem Establishing reliable error bounds and consistency rates for survival analysis methods.
method Nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators in metric spaces.
result Rates of strong consistency match existing lower bounds for conditional CDF estimation.
Statistical analysis of regularization in continual learning tasks.
problem Understanding how regularization affects model performance in sequential learning.
method Derivation of convergence rates, iterative update formula, and optimal hyperparameters for generalized ℓ2-regularization.
result Optimal hyperparameters balance forward and backward knowledge transfer, improving model performance.
Study on estimating invertible functions with minimax analysis.
problem Minimizing risk of estimating invertible functions on a plane.
method Introduce two types of L2-risks, derive lower and upper rates for minimax values, develop an asymptotically almost everywhere invertible estimator. result Invertibility does not reduce the complexity of the estimation problem in terms of the rate.
A new framework estimates policy value robustly against confounders.
problem Estimating policy value in the presence of unobserved confounders.
method Convex programming for sharp lower bounds.
result Sharp lower bounds on policy value for robust inference.
Principal Component Analysis (PCA) is the most common nonparametric method for estimating the volatility structure of Gaussian interest rate models. One major difficulty in the estimation of these models is the fact that forward rate curves are not directly observable from the market so that non-trivial observational e…
Enhances sensitivity analysis for correlated inputs.
problem Estimating sensitivity indices in models with correlated inputs.
method Proposes an extension of Sobol' estimator using a linear correlation model.
result Improves accuracy in variance-based sensitivity analysis.
Framework for efficient statistical estimation with privacy guarantees.
problem Statistical estimation problems with differential privacy constraints.
method High-dimensional Propose-Test-Release (HPTR) framework combining exponential mechanism, robust statistics, and resilience.
result Near-optimal utility guarantees and tight local sensitivity bounds for various statistical problems.
The paper proves estimates for Hodge Laplacians on Lie groups.
problem Estimating Hodge Laplacians on semisimple Lie groups.
method Proves Schwartz estimates for Hodge Laplacian and Dirac operators.
result Generalizes results on symmetric spaces to Lie groups.
Metaparametric neural networks improve survival analysis without prior knowledge.
problem Current neural networks restrict survival analysis to pre-determined times and fixed function shapes.
method Metaparametric neural network framework that extends existing methods to estimate generic functions.
result Metaparametric neural networks outperform state-of-the-art methods in capturing nonlinearities and identifying temporal patterns.
We propose a communication-efficient distributed estimation method for sparse linear discriminant analysis (LDA) in the high dimensional regime. Our method distributes the data of size N into m machines, and estimates a local sparse LDA estimator on each machine using the data subset of size N/m. After the distri…
In high-dimensional data analysis, penalized likelihood estimators are shown to provide superior results in both variable selection and parameter estimation. A new algorithm, APPLE, is proposed for calculating the Approximate Path for Penalized Likelihood Estimators. Both the convex penalty (such as LASSO) and the nonc…
Cost-benefit analysis often assumes accurate estimates, but this study finds significant inaccuracies.
problem Inaccurate cost and benefit estimates in public investments.
method Largest dataset of public investments, statistical analysis of cost overruns and benefit shortfalls.
result Significant inaccuracies in cost and benefit estimates of public investments.
Develops exact and invariant study-based decompositions for network meta-analysis.
problem Lack of exact contribution decompositions in network meta-analysis.
method Contrast-space projection formulation of NMA, study-based definition of direct and indirect evidence.
result Exact covariance-aware decompositions of NMA estimator into direct and indirect contributions.
Develops non-standard analysis for coherent risk estimation.
problem Estimating coherent risk measures in financial contexts.
method Non-standard analysis, hyperfinite representations, discrete Kusuoka formulae, plug-in asymptotics.
result Uniform almost sure consistency and asymptotic normality of spectral plug-in estimators.