Efficient classifier error estimation without re-training.
problem Estimating classifier error without re-training.
method Generalized resubstitution based on empirical measures.
result Consistent and asymptotically unbiased error estimation.
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48 results for “empirical error estimates”
Empirical error estimates improve graph sparsification reliability.
problem Uncertainty in sparsification error limits downstream computations reliability.
method Data-driven approach to compute empirical error estimates.
result Empirical error estimates provide theoretical guarantees and are computationally feasible.
Paper assesses error estimates of Random Forests classification.
problem Quantitative assessment of Random Forests error estimates.
method Theoretical and empirical investigation of various error estimation methods.
result Random Forests' error estimates are closer to true error rate than average prediction error.
Empirical median performs well in estimating location with varying scales.
problem Estimating location with varying scales in data.
method Analysis of empirical median as an estimator.
result Matching upper and lower bounds on estimation error.
Estimates the generalization error of deep neural networks without relying on capacity measures.
problem Understanding how generalization error scales with training data for deep neural networks.
method Derives estimates of generalization error for deep networks based on two assumptions: zero training error and error probability proportional to distance to nearest training point.
result Estimates the generalization error of DNNs as O(1/(δN^{1/d})), matching experimental behavior.
A neural network method estimates densities from characteristic functions.
problem Estimating fixed-horizon probability densities from empirical characteristic functions.
method Data-driven Fourier-mixture neural-network method trained in Fourier space.
result Competitive performance and clear gains on heavy-tailed targets.
Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Accesscs.LG
Improved sample complexity for diffusion models without needing empirical risk minimizers.
problem Theoretical limitations in sample complexity for diffusion models.
method Structured decomposition of score estimation error, eliminating dependence on neural network parameters.
result Achieved sample complexity bound of O(ε^(-4)) without empirical risk minimizer access.
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 -divergences.
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.
We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a bridge to connect the estimation error of the mean difference and the misclassificat…
Improved TD learning reduces batch sampling error.
problem TD learning can be inaccurate in batch settings due to action weighting.
method Introduced PSEC-TD(0) to correct action weighting using importance sampling.
result PSEC-TD(0) produces more accurate value function estimates.
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.
New estimator reduces kernel mean estimation error.
problem Kernel mean estimation in reproducing kernel Hilbert spaces.
method Corrupt data with known distributions and estimate kernel mean under the corrupted distribution.
result The marginalized kernel mean estimator achieves lower estimation error.
TSAW improves MCMC integral estimation with faster convergence.
problem Estimating integrals using MCMC with standard random walks is slow.
method Introduces TSAW to penalize overuse in finite-state adaptive sampling.
result TSAW-based estimators converge faster, achieving error.
The study analyzes robustness of estimators in linear models with adversarial errors.
problem Analyzing robustness of estimators in linear models with adversarial errors.
method Develops a general theory for minimum norm interpolating estimators and RERM in linear models without conditions on errors.
result Quantitative bound for the prediction error relating it to Rademacher complexity, norm of minimum norm interpolator of errors, and subdifferential size.
Meta learning of optimal classifier error rates allows an experimenter to empirically estimate the intrinsic ability of any estimator to discriminate between two populations, circumventing the difficult problem of estimating the optimal Bayes classifier. To this end we propose a weighted nearest neighbor (WNN) graph es…
Complexity Dependent Error Rates for Physics-informed Statistical Learning via the Small-ball Methodstat.ML
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.
New DP methods for estimating means and frequencies with varying privacy demands.
problem Estimating statistics with users having different privacy requirements.
method Proposes algorithms for empirical mean and frequency estimation under heterogeneous privacy constraints, considering both correlated and permuted datasets.
result Establishes theoretical performance guarantees for algorithms, achieving minimax optimality.
In this paper, we study the performance of extremum estimators from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. By adapting the classical concentration inequalities, we derive upper bounds on the empirical out-of-sample prediction e…
We extend a variational framework to estimate calibration errors for divergences.
problem Ensuring predicted probabilities match observed class frequencies in machine learning.
method Extend variational framework to divergences, separating over- and under-confidence.
result Avoids overestimation and separates over- and under-confidence.
New method offsets DML's error-compounding issue and provides more stable causal parameter estimates.
problem Estimating ATE from observational data with robustness and stability.
method Robust Causal Learning (RCL) method to offset DML's deficiencies.
result RCL estimators are more stable and perform better than DML and traditional estimators.
From only positive (P) and unlabeled (U) data, a binary classifier could be trained with PU learning, in which the state of the art is unbiased PU learning. However, if its model is very flexible, empirical risks on training data will go negative, and we will suffer from serious overfitting. In this paper, we propose a…
Proposes RCL method to improve ATE estimation from observational data.
problem Error-compounding issue and extreme estimates in DML estimators.
method Robust Causal Learning (RCL) method to offset DML deficiencies.
result RCL estimators are more stable and perform better than DML estimators.
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…
New estimators outperform maximum likelihood without hyper-parameter estimation.
problem Improving system identification performance without hyper-parameter estimation.
method Developed generalized Bayes and closed-form biased estimators using excess MSE.
result New estimators have comparable performance to empirical-Bayes-based regularized estimator.
The study sets lower bounds on MMSE for inferring sensitive features from noisy data.
problem Estimating sensitive features from noisy observations of correlated features.
method Adversarial evaluation framework based on MMSE estimation with theoretical lower bounds.
result Derives closed-form bounds for linear models, showing optimality in noise variance.
New method bounds high-dimensional regression without estimating design covariance.
problem High-dimensional linear regression with random design.
method Error-in-operator approach that incorporates design covariance into empirical risk minimization.
result Dimension-free bounds on excess prediction risk derived.
New measure of robustness for estimators, with tight bounds for Gaussian mean estimation.
problem Developing robust statistical estimators for datasets with noise or outliers.
method Introducing empirical sensitivity as a new robustness measure and proving lower bounds for Gaussian mean estimation.
result Empirical sensitivity bounds for optimal estimators are tight, showing obstructions on mean and variance.
Empirical Transfer Operators and Finite-Sample Change Detection for Noisy Expanding Interval Mapsstat.ML
Detect changes in noisy dynamical systems using empirical approximations and finite-sample bounds.
problem Change detection in noisy dynamical systems
method Partition-based empirical approximations and finite-state stationary distribution stability
result Finite-sample bound for empirical stationary density
Proposes a new calibration error estimator for deep neural networks.
problem Improves calibration of deep neural networks, especially for canonical calibration.
method Uses a Dirichlet kernel density estimate to create a low-bias, trainable calibration error estimator.
result Asymptotically converges to true calibration error, enabling efficient estimation and mini-batch updates.
Study robust linear regression with outliers, providing exact asymptotics for ERM performance.
problem Robust linear regression in high-dimension with outliers.
method Analyzes , , and Huber losses, providing asymptotic performance metrics.
result Optimally-regularised ERM is asymptotically consistent with simple calibration, but Huber loss requires norm calibration.
An important class of distance metrics proposed for training generative adversarial networks (GANs) is the integral probability metric (IPM), in which the neural net distance captures the practical GAN training via two neural networks. This paper investigates the minimax estimation problem of the neural net distance ba…
New method balances covariates for stable causal survival effect estimation.
problem Estimating causal survival effects in data with conditionally-independent censoring.
method Covariate-balancing approach to empirically stable and asymptotically efficient estimation.
result Validated theoretical results in synthetic and semi-synthetic data.
Estimates proper calibration errors and refinement terms in probabilistic predictions.
problem Lack of a general estimator for proper calibration errors and refinement terms with known statistical properties.
method Proposes a method for consistent, asymptotically unbiased estimation of proper calibration errors and refinement terms.
result Proves the relation between refinement and f-divergences, implying information monotonicity in neural networks.
Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on Factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, w…
CRUDE calibrates regression uncertainty without assuming specific error distributions.
problem Uncalibrated uncertainty estimates in regression models, especially for modern predictive tasks.
method CRUDE assumes error distributions have a constant shape, shifted and scaled by predicted mean and standard deviation.
result CRUDE produces sharper, better calibrated, and more accurate uncertainty estimates than existing methods.
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose the natural lasso estimator for the error variance, which maximizes a penalized …
The paper develops generalization bounds for deep compound Gaussian neural networks.
problem Developing theoretical guarantees for the performance of deep neural networks.
method Novel generalization error bounds using a compound Gaussian prior and Dudley's integral.
result Theoretical bounds show generalization error scales in signal dimension and in network size.
A new method estimates Bayes error for deep networks, suggesting they may have reached the limit.
problem Evaluating the performance of deep learning models and detecting overfitting.
method A simple and direct Bayes error estimator based on uncertainty of class assignments.
result Deep networks may have reached the Bayes error limit for benchmark datasets.
Lower Bounds and a Near-Optimal Shrinkage Estimator for Least Squares using Random Projectionsmath.OC
Improved estimator for least squares using random projections achieves smaller error.
problem Improving the accuracy of least squares solutions for large-scale problems.
method James-Stein estimator applied to Gaussian sketching of least squares problems.
result Upper and lower bounds match when SNR is small and data matrix is well-conditioned.
This paper introduces a class of k-nearest neighbor (-NN) estimators called bipartite plug-in (BPI) estimators for estimating integrals of non-linear functions of a probability density, such as Shannon entropy and Rényi entropy. The density is assumed to be smooth, have bounded support, and be uniformly bounded from…
Simple private estimators for mean and covariance outperform existing methods.
problem Private estimation of mean and covariance at small sample sizes.
method Differentially private estimators for multivariate sub-Gaussian data.
result Asymptotic error rates match theoretical bounds and outperform previous methods.
Ordinal regression is aimed at predicting an ordinal class label. In this paper, we consider its semi-supervised formulation, in which we have unlabeled data along with ordinal-labeled data to train an ordinal regressor. There are several metrics to evaluate the performance of ordinal regression, such as the mean absol…
Cross-validation estimates model performance on unseen data, not training data.
problem Understanding how cross-validation estimates prediction error and its limitations.
method Analyzing linear models and popular prediction error estimates, introducing nested cross-validation.
result Cross-validation estimates the average prediction error of models fit on other unseen training sets, not the model at hand.
In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for empirical risk minimizers. In the general setting, we prove sanity-check bounds in the spirit of \cite{KR99} \textquotedblleft\textit{bounds showing that the worst-case error of this estimate is not m…
MEVA aggregates model predictions to improve accuracy without needing model details.
problem Improving model accuracy by combining multiple models.
method Non-intrusive, data-driven framework that treats models as black boxes and optimizes aggregation methods.
result MVA outperforms MEA in estimating aggregated predictions, enhancing robustness and accuracy.
This work concerns estimation of multidimensional nonlinear regression models using multilayer perceptron (MLP). The main problem with such model is that we have to know the covariance matrix of the noise to get optimal estimator. however we show that, if we choose as cost function the logarithm of the determinant of t…
We provide sharp empirical estimates of expectation, variance and normal approximation for a class of statistics whose variation in any argument does not change too much when another argument is modified. Examples of such weak interactions are furnished by U- and V-statistics, Lipschitz L-statistics and various error f…