New estimator adapts to various error distributions.
problem Adapting to different error distributions in nonparametric regression.
method Introduces outrigger local polynomial estimator with modified weighted least squares.
result Minimax optimal over Hölder classes with multiplicative factor.
Study analyzes error in ReLU networks with local connections.
problem Improving neural network performance and understanding approximation errors.
method Analyzed approximation error of ReLU networks with local connections.
result Error estimate depends on depth and width of hidden layers.
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.
problem Ensuring local model validity in machine learning applications.
method Learning model error to estimate local validity using active learning.
result The proposed method can estimate local validity with a small amount of data.
New framework reduces private mean estimation error with optimal efficiency.
problem Locally private mean estimation of high-dimensional vectors.
method ProjUnit framework: random projections, normalization, and optimal algorithm execution in lower dimensions.
result Optimal error up to a 1+o(1)-factor with computational efficiency and low communication complexity.
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.
problem Improper local error estimates in UBU integrator for SDEs.
method Reconciles theory with practice by correcting local error estimates.
result Stronger assumptions needed for O(d1/4ε−1/2) steps in Wasserstein-2 distance. Improved locally private sparse estimation with multiple samples per user.
problem Challenges in high-dimensional locally private sparse estimation.
method Proposes a framework for user-level locally private sparse linear regression with multiple samples per user.
result Eliminates the dependency of dimensionality on error bounds, achieving tighter error bounds.
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.
problem Nonparametric estimation of drift function for diffusion processes from high-frequency discrete observations.
method Neural network-based estimator for drift function estimation.
result Derives a non-asymptotic convergence rate for the neural network estimator.
RQMC improves QMC by providing practical error bounds for financial applications.
problem Lack of practical error estimates in QMC methods.
method Combines Sobol LDS with randomized scrambling methods.
result RQMC outperforms standard QMC in convergence rates and provides error bounds.
New algorithm optimizes robust estimation under mixed local and global corruptions.
problem Combining local and global corruptions in robust statistics.
method Information-theoretic approach using sliced-Wasserstein metric.
result Optimal error achieved in polynomial time for stronger local perturbations.
Analyzes error sources in global feature effect estimation methods.
problem Unexplored error sources in global feature effect estimation methods.
method Systematic, estimator-level analysis of bias and variance.
result Holdout data is theoretically cleanest, but estimation variance depends on sample size and model characteristics.
Normalizing Flows improve prediction interval efficiency in CP.
problem Inefficient prediction intervals in CP due to non-uniform error distribution.
method Train a Normalizing Flow to optimize the distance metric between errors and inputs.
result Optimized prediction intervals are more efficient and valid.
We study the problem of estimating a set of d linear queries with respect to some unknown distribution p over a domain 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.
problem Minimizing KL divergence between true and estimated distributions.
method Construct minimax optimal private estimators, then focus on instance-optimality.
result Achieved instance-optimality up to constant factors for KL estimation.
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.
problem Training diffusion models is computationally expensive due to the curse of dimensionality.
method Localized neural networks and localized score matching loss to estimate low-dimensional score functions.
result Localized diffusion models can circumvent the curse of dimensionality with reduced sample complexity.
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.
problem Improving EEG source localization accuracy with unknown skull conductivity.
method Bayesian Approximation Error approach using conditional Gaussian regression, iterative optimization, and physics-informed learning.
result Clear improvements in EEG source localization accuracy and feasible estimates for unknown 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.
problem High-dimensional additive regression with heavy-tailed errors and transfer learning.
method Smooth backfitting estimator with local linear smoothing, followed by a two-stage estimation method.
result The method achieves the minimax optimal rate under certain conditions.
Active local learning uses fewer labels to predict near-optimal functions.
problem Efficiently predicting near-optimal functions with fewer labels.
method Active local learning algorithm for estimating functions with fewer labels.
result Algorithm makes significantly fewer label queries than traditional methods.
New schemes improve error estimates for sampling from non-log-concave distributions.
problem Improving sampling from non-log-concave distributions with super-linear drift growth.
method Developed tamed Euler and randomized Euler schemes with error estimates.
result Near-optimal error bounds for sampling and optimization problems.
A framework assesses the trustworthiness of probabilistic classifiers using local calibration error.
problem Assessing the trustworthiness of probabilistic classifiers beyond traditional metrics.
method I-trustworthy framework linking local calibration to trustworthiness; Kernel Local Calibration Error (KLCE) method for hypothesis testing.
result The effectiveness of the proposed test statistic demonstrated through simulated and real-world datasets.
Adaptive method improves prediction intervals with global coverage guarantees and local error distribution.
problem Global coverage guarantees of conformal regression are often violated by local error distributions.
method Adaptive Conformal Regression with Jackknife+ Rescaled Scores
result Improves local coverage without sacrificing global coverage, especially in low-data regimes.
The report studies ranking from pairwise comparisons in graphs, achieving optimal error bounds and proposing efficient algorithms.
problem Ranking items from pairwise comparisons in general graphs and graphs with locality.
method Maximum likelihood estimation (MLE) and preconditioned gradient descent for general graphs; divide-and-conquer algorithms for graphs with locality.
result MLE achieves optimal error bounds in general graphs and identifies conditions for locality.
Neural networks can approximate complex stochastic equations well.
problem Approximating general stochastic differential equations.
method Identified neural network classes approximating continuous functions.
result Neural stochastic differential equations can approximate general stochastic differential equations arbitrarily well.
Data processing inequalities link Fisher information to local differential privacy constraints.
problem Understanding how Fisher information scales with local differential privacy constraints.
method Developed data processing inequalities for Fisher information under local differential privacy.
result Implications for private estimation with optimal bounds and error rates.
For the problem of high-dimensional sparse linear regression, it is known that an ℓ0-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.
problem Community detection on sensitive network data with privacy constraints.
method Spectral clustering framework leveraging locally distributed privacy-preserved auxiliary networks via randomized response and adaptive weighting.
result TransNet delivers strong gains in community detection across various privacy levels and heterogeneity patterns.
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.
problem Generalization error in statistical learning theory.
method Uniform localized convergence framework.
result Optimal generalization error bounds for various learning problems.
Paper improves spectral learning of HMMs to avoid local optima and improve robustness.
problem Spectral learning of HMMs can get stuck in local optima and degrade due to unchecked error propagation.
method Developed a novel algorithm (PSHMM) and online learning variants to mitigate error propagation and nonstationarity.
result PSHMM provides more robust estimation and forecasting compared to SHMM and B-W algorithm.
Improved manifold-adaptive dimension estimator for better data complexity assessment.
problem Estimating intrinsic dimensionality of complex data.
method Revised and improved Farahmand-Szepesvári-Audibert (FSA) estimator, incorporating probability density function and median.
result Median-FSA estimator outperforms existing methods in accuracy and robustness.
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…
Bayesian method improves EEG source imaging accuracy by estimating skull conductivity.
problem Sensitivity of EEG source imaging to skull conductivity modeling.
method Bayesian uncertainty modeling to estimate skull conductivity and focal sources.
result Clear improvements in source localization accuracy and feasible skull conductivity estimates.
Optimal Gaussian noise mechanisms achieve nearly optimal error in unbiased mean estimation.
problem Efficiently estimating the mean of high-dimensional data while preserving privacy.
method Differential privacy mechanisms with Gaussian noise, focusing on optimal covariance.
result Gaussian noise mechanisms achieve nearly optimal error among all private unbiased mean estimation mechanisms.
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.
problem Evaluating model performance on unseen distributions using disparate scoring functions.
method Rigorously studied popular scoring functions (confidence, local manifold smoothness, model agreement) independently of mechanism choice.
result Simple model-agreement scores outperform confidence- and smoothness-based scores in realistic settings with compromised training data.
The paper assesses quality measures for machine learning models using cross-validation.
problem Evaluating the accuracy and robustness of quality measures for machine learning models.
method Cross-validation approach to estimate prediction error and quantify explained variation. Confidence bounds and local quality measures derived from residuals.
result The reliability and robustness of quality measures are assessed through numerical examples and confidence bounds.
eDCF estimates intrinsic dimension using local connectivity.
problem Challenges in estimating intrinsic dimension due to scale dependence.
method eDCF: a novel, scalable, and parallelizable method based on Connectivity Factor (CF).
result eDCF consistently matches leading estimators with comparable MAE and higher exact intrinsic dimension match rates.