Study GLS estimator properties in multivariate regression with heteroskedastic and autocorrelated errors.
problem Asymptotic properties of GLS estimator in multivariate regression with specific error structures.
method Derive Wald statistics for linear restrictions and assess their performance.
result Wald statistics remain robust to heteroskedasticity and autocorrelation.
We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Thus, it has minimal variance among all unbiased estimators and is asymptotically normally dis…
Paper develops error rates for physics-informed learning, comparing it to data-driven methods.
problem Understanding the trade-off between soft penalties and hard constraints in PISL.
method Develops complexity-dependent error rates using the small-ball method.
result Physics-informed estimators have comparable error rates to hard constrained methods, differing only by constants.
This work analyzes CoT prompting methods from a statistical estimation perspective.
problem Improving the effectiveness of LLMs in solving multi-step reasoning problems.
method Introducing a multi-step latent variable model to characterize CoT prompting from a statistical estimation viewpoint.
result The CoT estimator is equivalent to a Bayesian estimator when the pretraining dataset is large.
Optimal kernel improves estimation accuracy in modal statistical methods.
problem Estimation accuracy of kernel-based modal statistical methods depends on the kernel used.
method The study theoretically shows an optimal kernel that minimizes asymptotic error criterion.
result An optimal kernel minimizes the error criterion when using an optimal bandwidth.
Efficiently estimates private least squares with linear error growth.
problem Private estimation of ordinary least squares with bounded residuals and leverage.
method Scaled noise added to a stable nonprivate estimator of the regression vector.
result Near-optimal accuracy guarantee with linear error growth in dimension.
The paper shows how sketching data can simplify regression inference even when errors are heteroskedastic.
problem Performing robust inference with heteroskedastic errors using sketched data.
method Using random projections to sketch data, the paper shows that sketched estimates behave as if errors are homoskedastic.
result Estimation by random sampling does not have the same property, and sketched estimates are asymptotically normal with homoskedastic variance.
Neural networks estimate statistical divergences with performance guarantees.
problem Estimating statistical divergences with theoretical performance guarantees.
method Parametrizing empirical variational form by a neural network and optimizing over parameter space.
result Established non-asymptotic absolute error bounds for neural estimators of four f-divergences. Study identifies and analyzes three types of errors in learning Fourier operators.
problem Statistical, discretization, and truncation errors in learning Fourier operators.
method Analysis of a Discrete Fourier Transform (DFT) based least squares estimator.
result Established upper and lower bounds on statistical, discretization, and truncation errors.
We propose an optimum mechanism for providing monetary incentives to the data sources of a statistical estimator such as linear regression, so that high quality data is provided at low cost, in the sense that the sum of payments and estimation error is minimized. The mechanism applies to a broad range of estimators, in…
New algorithm estimates transport maps with nearly optimal error.
problem Estimating smooth transport maps efficiently and accurately.
method Solving semi-dual formulation of optimal transport with kernel sums-of-squares.
result Statistical L2 error on maps nearly matches minimax lower-bounds. Study trade-offs between statistical and computational efficiency in variational inference.
problem Optimizing statistical accuracy vs. computational efficiency in Bayesian inference.
method Case study on Gaussian inferential models with diagonal plus low-rank precision matrices, analyzing Bayesian posterior inference and frequentist uncertainty quantification errors.
result Lower-rank models reduce variance and accelerate convergence but increase posterior inference error.
WAEs offer a statistical understanding of density estimation and error bounds.
problem Concurrent density estimation with neural network-induced transformations.
method Statistical analysis of WAEs focusing on upper bounds and error propagation.
result Established deterministic upper bounds on WAE errors and explored their resilience.
New framework assesses extreme errors in machine learning models.
problem Current validation methods fail to quantify extreme errors in high-stakes domains.
method Uses Extreme Value Theory (EVT) to estimate worst-case failures.
result Establishes EVT as a fundamental tool for assessing model reliability.
We present eigenvalue decay estimates of integral operators associated with compositional dot-product kernels. The estimates improve on previous ones established for power series kernels on spheres. This allows us to obtain the volumes of balls in the corresponding reproducing kernel Hilbert spaces. We discuss the cons…
Study on statistical estimation over Gaussian MAC, comparing analog and digital schemes.
problem Distributed minimax statistical estimation over a Gaussian MAC.
method Developed analog joint estimation-communication schemes and derived information-theoretic lower bounds.
result Achieved risk within a logarithmic factor of information-theoretic lower bounds.
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.
New evidence shows computational barriers in graphon estimation using low-degree polynomials.
problem Estimating graphons efficiently and accurately.
method Low-degree polynomials to analyze computational limits.
result Low-degree polynomial estimators cannot significantly outperform USVT in graphon estimation.
We study the tradeoff between the statistical error and communication cost of distributed statistical estimation problems in high dimensions. In the distributed sparse Gaussian mean estimation problem, each of the m machines receives n data points from a d-dimensional Gaussian distribution with unknown mean θ w…
Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators, where performance is evaluated using a matrix-weighted two-norm of the defect of …
TD learning reduces prediction error in Markov chain problems.
problem Estimating value functions in Markov chains with temporal inconsistency.
method Temporal difference learning minimizes temporal inconsistency between successive estimates.
result TD learning can significantly reduce mean-squared error in value estimates.
Develops statistical guarantees for neural networks with regularization.
problem Lack of comprehensive mathematical theories for neural networks.
method General statistical guarantee for least-squares with regularizers.
result Prediction error increases sub-linearly in layers, logarithmically in parameters.
New method for scalable inference in large-scale regression models with complex error structures.
problem Challenges in statistical inference for large-scale regression models with dependent errors.
method Generalized Method of Wavelet Moments with Exogenous variables (GMWMX).
result Statistical validity and scalability of GMWMX for linear models with complex error structures.
DP-PCA improves privacy in PCA computations with optimal statistical error.
problem Differentially private principal component analysis with sub-linear sample complexity.
method Private minibatch gradient ascent with private mean estimation.
result Achieves optimal statistical error rates for sub-Gaussian data with n=ildeO(d) samples. In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution. However, no finite sample statistical guarantees and no computationally efficient o…
Markov chain (MC) algorithms are ubiquitous in machine learning and statistics and many other disciplines. Typically, these algorithms can be formulated as acceptance rejection methods. In this work we present a novel estimator applicable to these methods, dubbed Markov chain importance sampling (MCIS), which efficient…
TCE measures calibration error with a test-based approach.
problem Measuring calibration error of probabilistic binary classifiers.
method TCE uses a novel loss function based on a statistical test.
result TCE offers clear interpretation, consistent scale, and enhanced visual representation.
New methods reduce bias in estimating calibration error.
problem Reducing bias in estimating calibration error.
method Synthesizing model outputs and using equal-mass bins.
result Two reliable calibration-error estimators found: debiased estimator and ECE_sweep.
Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using generalized Gini distance, an energy distance in reproducing kernel Hilbert spaces (RK…
This paper provides performance guarantees for neural estimation of statistical distances.
problem Developing performance guarantees for neural estimation of statistical distances.
method Non-asymptotic error bounds using function approximation theorems and empirical process theory.
result Established a fundamental tradeoff between approximation and estimation errors in neural estimation of statistical distances.
New method resolves density ratio estimation saturation issues.
problem Error saturation in density ratio estimation methods.
method Iterated regularization to improve kernel methods.
result Achieves fast error rates on regular learning problems.
Dual Bayesian Affine Estimators for Wiener-type state-space models
problem Estimating parameters in Wiener-type state-space models
method Fixed-point architecture combining two affine estimators
result Dual basis-parameter estimator achieves comparable parameter MSE to purely affine estimator
Paper analyzes deep neural networks with dependent data, establishing convergence rates and error bounds.
problem Statistical analysis of deep neural networks under dependent data.
method Establishes rates of convergence and L2-error bounds for nonparametric sieve estimators of DNNs. result Non-asymptotic probability bounds on L2-errors for DNN estimators under stationary β-mixing data. MIC consistently estimates dependence in large datasets.
problem Estimating dependence between variable pairs in large datasets.
method Proving consistency of MIC as an estimator.
result MIC is a consistent estimator of population statistic MIC*.
Paper introduces statistical learning for point processes.
problem Statistical learning for point processes in general spaces.
method Combines bivariate innovations and point process cross-validation.
result Statistical learning approach outperforms state of the art.
We derive formulas for F measures' standard error and confidence intervals.
problem Estimating F measures' accuracy with confidence.
method Analytic formulas based on asymptotic normality.
result Valid formulas for sample size planning.
We revisit the problem of linear regression under a differential privacy constraint. By consolidating existing pieces in the literature, we clarify the correct dependence of the feature, label and coefficient domains in the optimization error and estimation error, hence revealing the delicate price of differential priv…
Study shows heavy-tailed distributions affect reliability of machine learning calibration statistics.
problem Reliability of calibration statistics for machine learning regression tasks is affected by heavy-tailed uncertainty and error distributions.
method Examined two calibration error estimation methods (CE and ZMS) and found ZMS to be less sensitive to heavy-tailed distributions.
result Heavy-tailed distributions make MSE and MV unreliable, but ZMS remains a reliable approach.
Improved estimator reduces bias in statistical learning models.
problem Asymptotic bias in classic WDRO estimator.
method Adjusted Wasserstein distributionally robust estimator.
result Asymptotic unbiased estimator with smaller MSE.
Paper develops methods for statistical inference with SGD in nonconvex optimization.
problem Statistical inference for nonconvex optimization problems.
method Proposes two online inferential procedures combining SGD and bootstrap techniques.
result Establishes error convergence rates and asymptotically valid bootstrap confidence intervals.
We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS…
Paper develops RGN method for estimating low-rank tensors from noisy measurements.
problem Estimating low-rank tensors from noisy linear measurements.
method Riemannian Gauss-Newton (RGN) method for efficient low-rank tensor estimation.
result First local quadratic convergence guarantee of RGN for low-rank tensor estimation in noisy settings.
A statistical model predicts generalization in few-shot learning.
problem Lack of validation sets in few-shot learning makes generalization estimation difficult.
method Introduced a Gaussian model of feature distribution and an unbiased estimator for class-conditional density distances.
result Our approach outperforms alternatives like leave-one-out cross-validation.
This study uses neural networks to approximate Bayesian filtering problems.
problem Estimating latent time-series signal statistics from observation sequences.
method Formulated a generic recurrent neural network framework to learn recursive mappings directly.
result Approximation error bounds for filtering in non-compact domains and strong time-uniform bounds.
Improved GANs estimate convergence rate for density estimation.
problem Improving the accuracy of density estimation with GANs.
method Proved an oracle inequality for JS divergence between GAN estimate and true density.
result JS-divergence rate of convergence is (logn/n)2β/(2β+d). Biased mean regression estimates factors exceeding expected loss or radiation release severity.
problem Estimating factors exceeding expected loss or radiation severity levels.
method Biased mean regression using superexpectation error minimization.
result Equivalent to quantile regression and CVaR optimization under specific conditions.
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…
Transforms robust algorithms into private ones with optimal error rates.
problem Balancing privacy and robustness in machine learning.
method Black-box transformation method to convert robust algorithms to private ones with optimal error rates.
result Optimal private estimators for various tasks, including Gaussian and PCA.