Upper bounds for CV errors apply to lasso and other models.
problem Bounding CV errors for lasso and similar models.
method Rademacher complexity and Orlicz- norm.
result Upper bounds are tight and stable for lasso.
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,291 papers · 148 categories
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48 results for “upper bound of generalization error”
Novel upper bound for unsupervised domain adaptation considers joint error.
problem Addressing the issue of mixing samples from different classes when matching marginal distributions.
method Proposes a general upper bound that penalizes undesirable joint error, uses constrained hypothesis space, and introduces cross margin discrepancy.
result Our proposal outperforms related approaches in image classification error rates on domain adaptation benchmarks.
New method improves understanding of machine learning model performance.
problem Understanding how well machine learning models generalize from training data to unseen data.
method Auxiliary Distribution Method to derive new generalization error bounds.
result Upper bounds on generalization errors are tighter and more applicable.
The paper bounds the mean absolute error in DNN vector-to-vector regression.
problem Bounding the mean absolute error in deep neural network based vector-to-vector regression.
method Error decomposition techniques in statistical learning theory and non-convex optimization theory were used to derive upper bounds for approximation, estimation, and optimization errors.
result Theoretical upper bounds for mean absolute error in DNN vector-to-vector regression were derived and validated experimentally.
Establishes upper bounds on generalization error in active learning.
problem Improving query algorithms in active learning.
method Derives upper bounds on generalization error using informativeness and representativeness query strategies.
result Validates the use of regularization techniques to ensure bounds' validity.
Study bounds graph neural networks' over-parameterized error.
problem Understanding graph neural networks' performance in over-parameterized regimes.
method Developed mean-field regime bounds for graph convolutional and message passing neural networks.
result Established upper bounds with a convergence rate of for generalization error.
This work bounds the generalization error of private algorithms for discrete data.
problem Bounding the generalization error of private algorithms for discrete data.
method Information-theoretic approach using relative entropy and the method of types.
result Explicit upper bounds on the generalization error of stable private algorithms for discrete data.
Paper bounds prediction error for misspecified Gaussian process models.
problem Guaranteeing model confidence for nonparametric Gaussian process regression.
method Derives an upper bound for mean square prediction error using pseudo-concave optimization.
result Upper bound for mean square prediction error of misspecified models.
New method corrects for random measurement error in causal discovery.
problem Measurement error invalidates causal discovery results.
method Upper bound for measurement error variance from covariance matrix, applied to constraint-based causal discovery.
result Corrected causal discovery results are more reproducible.
This paper establishes lower bounds for SGD's error, matching upper bounds.
problem Proving lower error bounds for SGD optimization algorithm.
method Analysis of mean square error for SGD with specific learning rates.
result Essentially matching lower and upper bounds for SGD's mean square error.
Paper bounds NMF's generalization error using Bayesian learning.
problem Unclear theoretical optimization of NMF as a learning machine.
method Real log canonical threshold and Bayesian learning applied to NMF.
result Generalization error of NMF can be smaller than regular models.
New lower bounds nearly match existing upper bounds for boosted classifiers.
problem Understanding the generalization performance of boosted classifiers.
method Margin-based lower bounds on boosted classifiers.
result Lower bounds nearly match the th margin bound, settling the generalization performance of boosted classifiers.
Study precise sample covariance error for Gaussian centered data.
problem Precise characterization of sample covariance error for Gaussian data.
method Developed a Random Duality Theory (RDT) framework to determine upper and lower bounds.
result Upper and lower bounds match in large-dimensional contexts, matching the spectral norm's limiting value.
Optimal transport bounds improve generalization in learning algorithms.
problem Understanding and improving generalization in machine learning.
method Using algorithmic transport cost and Wasserstein distance to derive upper bounds on generalization error.
result Generalization error decreases exponentially with the number of layers in deep neural networks.
This paper tightens the generalization error bound for graph embedding in non-Euclidean spaces.
problem High generalization error in non-Euclidean graph embedding, preventing practical applications.
method Novel upper bound of graph embedding's generalization error using local Rademacher complexity.
result The new bound is tighter and faster, allowing better performance in non-Euclidean spaces.
New bounds for sequential tests under power-one error levels.
problem Determining stopping times for sequential tests with power-one error levels.
method Proved two lower bounds for stopping times under specific conditions.
result Upper and lower bounds for sequential tests are shown to be tight.
Paper explores trade-off between convergence and stability in iterative algorithms.
problem Understanding the relationship between convergence and stability in iterative algorithms.
method Analyzes the overall performance of iterative algorithms in terms of training error and generalization error.
result Shows a fundamental trade-off between convergence and stability of iterative algorithms.
Fine-tunes deep neural networks to match theoretical bounds on generalization errors.
problem Improve generalization errors of deep neural networks by constraining weight norms.
method Proposes a two-stage renormalization procedure and a fine-grained SGD algorithm for training DNNs with constrained weights.
result Empirical generalization errors of DNNs are closer to theoretical bounds, improving accuracy.
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 paper analyzes GA of extremum estimators and applies it to penalized regression.
problem Analyzing the generalization ability of extremum estimators.
method Adapting classical concentration inequalities to derive upper bounds on GA.
result Demonstrates the GA of penalized regression estimates and its relation to bias-variance trade-off.
Jensen-Shannon Information Based Characterization of the Generalization Error of Learning Algorithmscs.IT
New bound on machine learning model performance using Jensen-Shannon information.
problem Understanding the performance of machine learning models.
method Proposes a new information-theoretic bound on generalization error.
result Shows that the new bound can be tighter than mutual information-based bounds under certain conditions.
Paper analyzes ECE bias and provides bounds for its estimation.
problem Understanding the estimation bias in ECE for machine learning models.
method Information-theoretic approach to analyze bias in uniform mass and uniform width binning strategies.
result Established upper bounds on ECE estimation bias and optimal number of bins.
The paper develops estimators for variance in graph structures using fused lasso.
problem Variance estimation in graph-structured problems.
method Developed linear time estimator for homoscedastic case and total variation regularization estimator for heteroscedastic case.
result Minimax rates and consistency for variance estimation in various graph structures.
Improved BO algorithms reduce prediction error under Gaussian noise.
problem Reducing prediction error in Bayesian optimization with Gaussian noise.
method Established new prediction error bounds for Gaussian process under frequentist setting.
result Proved improved convergence rates of cumulative regret for GP-UCB and GP-TS.
New bound on generalization error using mutual information.
problem Generalization error in supervised learning.
method Information-theoretic bound on mutual information between samples and predictions.
result Tighter characterization of generalization error.
This paper introduces a set of algorithms for Monte-Carlo Bayesian reinforcement learning. Firstly, Monte-Carlo estimation of upper bounds on the Bayes-optimal value function is employed to construct an optimistic policy. Secondly, gradient-based algorithms for approximate upper and lower bounds are introduced. Finally…
New research shows many batch selection methods for training work just as well as full batch training.
problem Finding optimal batch selection methods for training.
method Analysis of mini-batch Gradient Descent (GD) and Stochastic GD (SGD) with various batch selection rules.
result All mini-batch schedules, including deterministic ones, generalize optimally for smooth Lipschitz-convex/nonconvex/strongly-convex loss functions.
Study large deviations rates for SGD with strongly convex functions.
problem High probability metrics with SGD.
method Large deviations theory, generic gradient noise, strongly convex functions.
result Upper large deviations bound for SGD with strongly convex functions.
Paper finds the best way to estimate neural net distance from samples.
problem Estimating the neural net distance from samples.
method Developed minimax lower and upper bounds for the neural net distance.
result Lower and upper bounds match, validating the empirical neural net distance.
Investigates neural network approximation power with bounds.
problem Understanding neural network capacity for approximation.
method Established lower and upper bounds on network size and difference.
result Improved bounds for certain function classes.
Paper analyzes Gibbs and Langevin Monte Carlo for interpolation regime, showing generalization from low errors.
problem Analyzing Gibbs and Langevin Monte Carlo in overparameterized interpolation regime.
method Data-dependent bounds and stability under approximation with Langevin Monte Carlo.
result Generalization is signaled by small training errors in noisy regime, with bounds stable under approximation.
EBUCB framework achieves optimal regret with bounded approximate inference error.
problem Theoretical gap between practical performance and theoretical justification of Bayesian bandit algorithms with approximate inference.
method Enhanced Bayesian Upper Confidence Bound (EBUCB) framework that accommodates bandit problems with approximate inference.
result EBUCB achieves optimal regret order under certain conditions on inference error.
The study analyzes transfer learning using information theory.
problem Transfer learning in different distributions.
method Information-theoretic analysis, focusing on KL divergence.
result Upper bounds for general transfer learning algorithms and specific ERM.
Improved error bounds for Langevin MCMC with scaling.
problem Improving convergence rates of Langevin MCMC.
method Introducing scaling terms in underdamped Langevin equation and analyzing conditions for improved error bounds.
result Appropriate scaling improves error bounds in terms of condition number.
New algorithm for learning functions with bounds on error and sample complexity.
problem Learning -valued functions in a prediction model.
method General-purpose algorithm with upper and lower bounds on expected error and sample complexity.
result Improved bounds on sample complexity and agnostic learning conditions.
Upper bounds on Wasserstein distance for empirical measures in unbounded functional spaces.
problem Analyzing convergence and concentration of empirical measures in unbounded functional spaces.
method Generalized upper bounds using Wasserstein distance, covering large dimensional Euclidean spaces and Gaussian processes.
result Rate-optimal upper bounds for functional data distributions with specific decay rates.
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.
Bayesian bandit algorithms with approximate inference improve regret bounds in stochastic linear bandits.
problem Theoretical justification for Bayesian bandit algorithms with approximate inference in stochastic linear bandits.
method Proposed a theoretical framework to analyze approximate inference impact and conducted frequentist regret analysis on LinTS and LinBUCB.
result LinTS and LinBUCB preserve their original regret upper bounds with larger constant terms in approximate inference settings.
Study shows sample complexity for multicalibration is Θ(ε^-3) with polylogarithmic factors.
problem Minimizing Expected Calibration Error (ECE) for predictors with respect to a family of groups.
method Proved necessary and sufficient sample complexity of Θ(ε^-3) for multicalibration, using online-to-batch reduction and lower bounds.
result Sample complexity of multicalibration is Θ(ε^-3) with polylogarithmic factors, distinguishing it from marginal calibration.
The paper explores MAE as a loss function for DNN vector-to-vector regression, proving its advantages over MSE.
problem Improving loss function for deep neural network based vector-to-vector regression.
method Presenting performance bounds and new properties of MAE, deriving generalized upper bounds, and interpreting MAE as a Laplacian distribution.
result MAE is a more suitable loss function than MSE for DNN based vector-to-vector regression, especially when errors follow a Laplacian distribution.
The paper bounds generalization errors for deep neural networks with Markov datasets.
problem Bounding generalization errors for deep learning with Markov datasets.
method Developed new symmetrization inequalities for Markov chains, using spectral gap of the infinitesimal generator.
result Derived upper bounds on generalization errors for deep neural networks with Markov datasets.
The paper tightens bounds on covering numbers for deep ReLU networks.
problem Characterizing the capacity and performance of deep ReLU networks.
method Derives tight lower and upper bounds on metric entropy of ReLU networks.
result Establishes optimality in nonparametric regression via deep networks.
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.
Paper proposes deep neural networks for nonparametric regression from dependent data.
problem Nonparametric regression from strongly mixing observations.
method Minimum error entropy principle applied to deep neural networks.
result Deep neural networks achieve minimax optimal convergence rates for Gaussian errors.
Study shows depth improves generalization in deep learning models.
problem Understanding why and when depth improves generalization in deep learning.
method Implementation-agnostic state-transition model to analyze depth and generalization.
result Identifies geometric and semigroup mechanisms that keep entropy contribution saturated or polynomial, clarifying depth's statistical advantage.
The study establishes risk bounds for distributional regression estimators.
problem Estimating distributional regression models with nonparametric methods.
method Theoretical bounds for CRPS and MSE are derived for convex and non-convex constraints.
result Theoretical risk bounds are validated through experiments on simulated and real data.
Sharp bounds found on expert error in binary advice aggregation.
problem Aggregating binary advice from conditionally independent experts.
method Sharp upper and lower bounds on optimal error probability in asymmetric case.
result Sharp bounds recover and sharpen known results in symmetric case.
Paper establishes a universal growth rate for smooth surrogate losses in classification.
problem Analyzing growth rates of consistency bounds for various surrogate losses.
method Proves square-root growth rate for smooth margin-based losses; extends to multi-class classification.
result Demonstrates a universal square-root growth rate for smooth comp-sum and constrained losses.