arXiv research

New estimator adapts to various error distributions.

Study analyzes error in ReLU networks with local connections.

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.

Active learning method improves local model validity estimation.

New framework reduces private mean estimation error with optimal efficiency.

We show that if $F$ is a convex class of functions that is $L$-subgaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by `local' covering estimates of the class, rather than by the gaussian averages. To that end, we establish new sharp upper and lower e…

Corrects local error estimates for UBU integrator in SDEs, improving complexity guarantees.

Improved locally private sparse estimation with multiple samples per user.

This letter presents an improved version of diffusion least mean ppower (LMP) algorithm for distributed estimation. Instead of sum of mean square errors, a weighted sum of mean square error is defined as the cost function for global and local cost functions of a network of sensors. The weight coefficients are updated b…

We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and covariates. We first establish a form of local statistical consistency for the penalize…

The paper develops a neural network method for estimating drift functions of diffusion processes from discrete observations.

RQMC improves QMC by providing practical error bounds for financial applications.

New algorithm optimizes robust estimation under mixed local and global corruptions.

Analyzes error sources in global feature effect estimation methods.

Normalizing Flows improve prediction interval efficiency in CP.

We study the problem of estimating a set of $d$ linear queries with respect to some unknown distribution $\mathbf{p}$ over a domain $\mathcal{J}=[J]$ based on a sensitive data set of $n$ individuals under the constraint of local differential privacy. This problem subsumes a wide range of estimation tasks, e.g., distrib…

How to self-localize large teams of underwater nodes using only noisy range measurements? How to do it in a distributed way, and incorporating dynamics into the problem? How to reject outliers and produce trustworthy position estimates? The stringent acoustic communication channel and the accuracy needs of our geophysi…

Private KL distribution estimation improved with instance-optimality.

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 …

Localized diffusion models reduce training complexity by exploiting low-dimensional structure.

In many signal detection and classification problems, we have knowledge of the distribution under each hypothesis, but not the prior probabilities. This paper is aimed at providing theory to quantify the performance of detection via estimating prior probabilities from either labeled or unlabeled training data. The erro…

Bayesian method improves EEG source localization and estimates skull conductivity.

A reliable, accurate, and affordable positioning service is highly required in wireless networks. In this paper, the novel Message Passing Hybrid Localization (MPHL) algorithm is proposed to solve the problem of cooperative distributed localization using distance and direction estimates. This hybrid approach combines t…

The paper develops a minimax optimal method for high-dimensional regression using auxiliary data.

Active local learning uses fewer labels to predict near-optimal functions.

New schemes improve error estimates for sampling from non-log-concave distributions.

A framework assesses the trustworthiness of probabilistic classifiers using local calibration error.

Adaptive method improves prediction intervals with global coverage guarantees and local error distribution.

The report studies ranking from pairwise comparisons in graphs, achieving optimal error bounds and proposing efficient algorithms.

Neural networks can approximate complex stochastic equations well.

Data processing inequalities link Fisher information to local differential privacy constraints.

For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of restrictive conditions on the design matrix, popular polynomial-time methods only guarante…

TransNet improves community detection on target networks using privacy-preserved source networks.

We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar Lévy-type stochastic processes. We derive rigorous error bounds for the approximate solutions. We also provide numerical examples illustrating the usefulness a…

We consider a distributed learning setup where a sparse signal is estimated over a network. Our main interest is to save communication resource for information exchange over the network and reduce processing time. Each node of the network uses a convex optimization based algorithm that provides a locally optimum soluti…

We consider a model-based approach to perform batch off-policy evaluation in reinforcement learning. Our method takes a mixture-of-experts approach to combine parametric and non-parametric models of the environment such that the final value estimate has the least expected error. We do so by first estimating the local a…

We propose the orthogonal random forest, an algorithm that combines Neyman-orthogonality to reduce sensitivity with respect to estimation error of nuisance parameters with generalized random forests (Athey et al., 2017)--a flexible non-parametric method for statistical estimation of conditional moment models using rand…

Study problem-dependent rates in statistical learning theory, achieving optimal generalization error bounds.

Paper improves spectral learning of HMMs to avoid local optima and improve robustness.

Improved manifold-adaptive dimension estimator for better data complexity assessment.

We provide a formulation for Local Support Vector Machines (LSVMs) that generalizes previous formulations, and brings out the explicit connections to local polynomial learning used in nonparametric estimation literature. We investigate the simplest type of LSVMs called Local Linear Support Vector Machines (LLSVMs). For…

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

This paper introduces an elasticity reconstruction method based on local displacement observations of elastic bodies. Sparse reconstruction theory is applied to formulate the underdetermined inverse problems of elasticity reconstruction including unobserved areas. An online local clustering scheme called a superelement…

We consider the question of efficient estimation in the tails of Gaussian copulas. Our special focus is estimating expectations over multi-dimensional constrained sets that have a small implied measure under the Gaussian copula. We propose three estimators, all of which rely on a simple idea: identify certain \emph{dom…

Study finds simple model-agreement scores perform well in various error estimation scenarios.

The electroencephalography (EEG) source imaging problem is very sensitive to the electrical modelling of the skull of the patient under examination. Unfortunately, the currently available EEG devices and their embedded software do not take this into account; instead, it is common to use a literature-based skull conduct…

The paper assesses quality measures for machine learning models using cross-validation.

eDCF estimates intrinsic dimension using local connectivity.