arXiv research

Study on Transfer Elastic Net error bounds and grouping effect.

Improved estimator for least squares using random projections achieves smaller error.

The paper provides bounds on estimation error in a distributed online learning setting.

Data-driven method for error estimation without needing class complexity.

In this paper, we obtain generic bounds on the variances of estimation and prediction errors in time series analysis via an information-theoretic approach. It is seen in general that the error bounds are determined by the conditional entropy of the data point to be estimated or predicted given the side information or p…

Study of estimation errors in surrogate loss minimizers, providing stronger guarantees than existing methods.

New bounds quantify estimation error in kernel-based system identification with unknown hyperparameters.

Paper extends Bayesian Cramér-Rao bound with geometric considerations.

We address the problem of learning to benchmark the best achievable classifier performance. In this problem the objective is to establish statistically consistent estimates of the Bayes misclassification error rate without having to learn a Bayes-optimal classifier. Our learning to benchmark framework improves on previ…

New method preserves unitarity for Schrödinger equation learning, reducing errors and improving time generalization.

Unified learning bound for covariate and concept shifts.

Optimal a priori estimates are derived for the population risk, also known as the generalization error, of a regularized residual network model. An important part of the regularized model is the usage of a new path norm, called the weighted path norm, as the regularization term. The weighted path norm treats the skip c…

The paper analyzes kNN density estimation's convergence rates under different conditions.

Confidence measures for the generalization error are crucial when small training samples are used to construct classifiers. A common approach is to estimate the generalization error by resampling and then assume the resampled estimator follows a known distribution to form a confidence set [Kohavi 1995, Martin 1996,Yang…

The study sets lower bounds on MMSE for inferring sensitive features from noisy data.

New risk bound for drift estimator in stochastic models.

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…

In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of $\ell_0$-regularized estimation. In this note, we show that $\ell_1$-regularized estimation in some important cases can achieve the same order of error bounds as those in the aforementioned …

We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these nonparametric estimators and, up to a log factor, match an existing lower bound for c…

The paper develops estimators for variance in graph structures using fused lasso.

Study non-asymptotic bounds for robust estimators under misspecified models.

Sharp bounds found on expert error in binary advice aggregation.

SGD-trained deep nets have bounds on their generalization error.

Paper proposes deep neural networks for nonparametric regression from dependent data.

Estimates convex hulls of smooth function images with error bounds.

New method gives provable error bounds for neural nets under distribution shift.

Consider the task of estimating a 3-order $n \times n \times n$ tensor from noisy observations of randomly chosen entries in the sparse regime. We introduce a similarity based collaborative filtering algorithm for estimating a tensor from sparse observations and argue that it achieves sample complexity that nearly matc…

We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on the rates of convergence of the LSE when the errors have uniformly …

Paper analyzes ECE bias and provides bounds for its estimation.

This work bounds classification error in machine learning for low Bayes error conditions.

The paper analyzes sampling and estimation on manifolds using Langevin diffusion.

The paper develops generalization bounds for deep compound Gaussian neural networks.

We relate two notions of local error for integration schemes on Riemannian homogeneous spaces, and show how to derive global error estimates from such local bounds. In doing so, we prove for the first time that the Lie-Butcher theory of Lie group integrators leads to global error estimates.

Paper bounds subspace estimator error from noisy projections.

Several new estimation methods have been recently proposed for the linear regression model with observation error in the design. Different assumptions on the data generating process have motivated different estimators and analysis. In particular, the literature considered (1) observation errors in the design uniformly …

The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local optimization heuristics without global optimality guarantees or with guarantees valid only…

This paper develops a bootstrap method to estimate errors in Random Fourier Features.

The paper provides PAC bounds for estimating causal effects using covariate adjustment with a valid set.

Unified approach for robust low rank matrix estimation with adversaries.

The paper bounds the mean absolute error in DNN vector-to-vector regression.

We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the Wasserstein metric. We go on to prove an error bound for the value-function estimate arisi…

Optimal Gaussian noise mechanisms achieve nearly optimal error in unbiased mean estimation.

We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising it; and a priori bounds on the error of each entry, individually. In the noiseless…

Estimating average causal effect (ACE) is useful whenever we want to know the effect of an intervention on a given outcome. In the absence of a randomized experiment, many methods such as stratification and inverse propensity weighting have been proposed to estimate ACE. However, it is hard to know which method is opti…

Paper analyzes deep neural networks with dependent data, establishing convergence rates and error bounds.

The study analyzes prediction errors in systems with memory kernels, providing bounds and stability results.

Paper improves uncertainty quantification in PINNs using error bounds and solution bundles.

HAVER improves error bounds for estimating the largest mean in machine learning tasks.