Proposes a new bound on generalization error using conditional mutual information.
problem Improving the generalization error bound in machine learning.
method Combines error decomposition and conditional mutual information techniques.
result New bound is order-wise better than previous ones in a simple Gaussian setting.
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.
This work bounds classification error in machine learning for low Bayes error conditions.
problem Understanding the error mismatch between Bayes error and model-based classification error.
method Applying classification error bounds to study the relationship with Kullback-Leibler divergence and proposing a linear approximation for low Bayes error conditions.
result A linear approximation of the classification error bound for low Bayes error conditions is proposed.
This paper analyzes error bounds for biased SMC samplers in conditional sampling.
problem Analyzing error bounds for biased SMC samplers in conditional sampling.
method Develops a non-asymptotic error analysis for SMC samplers with biased mutation kernels.
result Derives the first non-asymptotic error bound for conditional sampling with score-based diffusion models.
The paper bounds estimation and prediction errors in time series using entropy.
problem Estimating and predicting errors in time series analysis.
method Information-theoretic approach focusing on conditional entropy.
result Generic bounds on estimation and prediction errors determined by conditional entropy.
Paper derives bounds on prediction errors using information theory.
problem Understanding maximum prediction errors in sequential data.
method Information-theoretic approach focusing on conditional entropy.
result Fundamental bounds on prediction errors depend on conditional entropy.
The article refines error bounds for various learning algorithms.
problem Achieving precise error rates for learning algorithms.
method General technique for obtaining bounds on error rates of sample-consistent classifiers.
result Refined bounds on error rates for several learning algorithms.
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.
We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes use of Curto and Fialkow's solutions for the truncated moment problem. The lower …
Paper analyzes convergence of two time-scale stochastic approximation using martingale approach.
problem Analyzing convergence of two time-scale stochastic approximation algorithms.
method Uses martingale approach to establish convergence conditions and rates.
result Establishes different rates of convergence for fast and slow subsystems.
New bounds on learning algorithm generalization error derived using information density.
problem Bounding the generalization error of learning algorithms.
method Exponential inequalities and information density/conditional information density.
result Novel bounds on average and tail probability of generalization error.
Study shows exponential error reduction in multiclass classification without bias-variance trade-off.
problem Multiclass classification with margin conditions.
method Analysis of classification error under hard-margin conditions.
result Exponential decrease in classification error without bias-variance trade-off.
Enhanced H H H -consistency bounds derived under relaxed conditions.
problem Quantifying the relationship between zero-one estimation error and surrogate loss estimation error.
method Relaxing the condition on the surrogate loss conditional regret and presenting a general framework for establishing enhanced H H H -consistency bounds. result Derivation of more favorable H H H -consistency bounds in various scenarios. Unified approach to error bounds for convex optimization problems.
problem Analyzing convergence rates of iterative methods for convex optimization.
method Unified framework for establishing error bounds for structured convex optimization problems.
result Unified error bounds for various optimization problems, including machine learning and statistics.
New bounds study class-specific generalization error in machine learning.
problem Existing generalization theories assume uniform class performance, but in practice, classes vary significantly.
method Developed novel information-theoretic bounds using KL divergence and CMI.
result Theoretical bounds accurately capture complex class-generalization error behavior.
Improved bounds on learning algorithms' performance using conditional mutual information.
problem Bounding the generalization error of learning algorithms.
method Introducing conditional mutual information and disintegrated mutual information to tighten bounds.
result New bounds are tighter than previous ones, especially for noisy, iterative algorithms.
This paper improves entropy bounds for ranking time-series complexity.
problem Ranking the complexity of time series processes.
method Building on information theoretic bounds, the paper improves the upper bound of conditional differential entropy using Hadamard's inequality and covariance matrix properties.
result The improved bounds can be used to rank the complexity of time series processes.
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.
Study rates of convergence for approximate solutions to linear ill-posed problems in Hilbert scales.
problem Linear ill-posed inverse problems with noisy data.
method Approximate reconstructions from random noisy data using regularization schemes in Hilbert scale.
result Explicitly established error bounds for smooth regression functions.
Paper derives uniform error bounds for Gaussian process regression for safer control applications.
problem Quantifying model error in Gaussian process regression for safety-critical applications.
method Employing Gaussian process distribution and continuity arguments, derive uniform error bounds under weaker assumptions.
result Derives novel uniform error bounds for Gaussian process regression under weaker assumptions.
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.
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.
Sharp 2-Wasserstein bounds for DDPMs derived from Föllmer process.
problem Sampling error bounds for DDPMs in 2-Wasserstein distance.
method Lipschitz-type conditions on score function, Föllmer process, and log-concave target distributions.
result Sharp upper bounds for DDPMs in 2-Wasserstein distance, optimal in dimension and steps.
Study improves least squares estimation for heavy-tailed errors.
problem Improving least squares estimation under heteroscedastic and heavy-tailed errors.
method Analyzes the rate of convergence of least squares estimator under bounded conditional variance and finitely many moments of errors.
result Upper bounds on rates of convergence of LSE for heavy-tailed errors are found.
Study selective classification with halfspaces, achieving error bounds under Gaussian distributions.
problem Modeling relationships in subsets of data defined by selection rules.
method Sparse linear classifiers for subsets defined by halfspaces, focusing on Gaussian feature distributions.
result First PAC-learning algorithm for homogeneous halfspace selectors with error guarantee $\bigO*{\sqrt{\mathrm{opt}}}$ .
Generalizes Barankin bound for vector cases in mean square error.
problem Achieving the lower bound of mean square error for vector estimates.
method Finite dimensional vector Riesz representation theorem and linear matrix inequality.
result Necessary and sufficient conditions for achieving the lower bound.
The paper provides mean-square error bounds for stochastic approximation algorithms.
problem Error bounds for recursive equations with Markovian disturbances.
method Analysis of mean-square error for stochastic approximation algorithms.
result Mean-square error achieves the optimal rate of O ( 1 / n ) O(1/n) O ( 1/ n ) under certain conditions. New error bounds for flow matching methods using deterministic sampling.
problem Improving the accuracy of flow matching methods for generating probability distributions.
method Derived error bounds for flow matching methods under deterministic sampling conditions.
result Presented error bounds for flow matching methods using L 2 L^2 L 2 loss and regularity conditions. Nonasymptotic error bounds and strong consistency rates for survival analysis methods.
problem Establishing reliable error bounds and consistency rates for survival analysis methods.
method Nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators in metric spaces.
result Rates of strong consistency match existing lower bounds for conditional CDF estimation.
This paper tackles worst-class error rate in classification tasks.
problem Minimizing worst-class error rate in classification tasks, especially in medical image classification.
method Designing a boosting approach to bound the worst-class error rate using Deep Neural Networks (DNNs).
result The proposed boosting approach lowers worst-class test error rates while avoiding overfitting.
This work extends SVM error bounds to weighted SVM and introduces hyperparameter selection methods.
problem Improving SVM performance through effective hyperparameter selection.
method Extending span error bound theory to weighted SVM and introducing hyperparameter selection methods.
result The span rule is the most effective method for weighted SVM hyperparameter selection and provides the best predictor of test error.
This paper tightens information-theoretic bounds on generalization errors.
problem Understanding the discrepancy between training and testing data losses.
method Investigates the tightness of information-theoretic bounds on generalization error.
result The individual sample mutual information bound can be asymptotically tight under specific assumptions.
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.
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 improves error bounds for sparse regression with heavy-tailed covariates.
problem Estimating sparse coefficients in linear regression with heavy-tailed covariates.
method Employed an ℓ 1 \ell_1 ℓ 1 -penalized Huber regression method. result Error bound identical to Gaussian case for L L L -subexponential covariates. New sampling algorithms for complex distributions without log-concavity.
problem Efficient sampling from complex, high-dimensional distributions.
method Randomized splitting Langevin Monte Carlo (RSLMC) algorithm.
result Uniform-in-time error bounds for RSLMC and RLMC algorithms.
Bounds on factual and counterfactual distributions under measurement error in discrete models.
problem Measurement errors in discrete data and their impact on inference.
method Expressing modeling assumptions as linear constraints and using linear programming to derive bounds.
result Sharp bounds on factual and counterfactual distributions for various models, including instrumental variable scenarios.
Hierarchical Federated Learning bounds generalize using Wasserstein distance.
problem Bounding generalization error in Federated Learning with hierarchical sampling.
method Introduced a hierarchical sampling framework and derived generalization bounds using Wasserstein distance.
result Recover and strictly imply existing CMI bounds for bounded losses.
SGD handles label noise with bounds improving over SGLD.
problem Label noise in non-convex optimization.
method Stochastic gradient descent with uniform dissipativity and smoothness conditions, using Wasserstein distance and algorithmic stability.
result Generalization error bounds with a rate of n − 2 / 3 n^{-2/3} n − 2/3 , better than SGLD's n − 1 / 2 n^{-1/2} n − 1/2 . 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.
Sharp bounds on uniform generalization errors in binary linear classification.
problem Understanding the uniform generalization errors in binary linear classification.
method Isoperimetric arguments, Poincaré and log-Sobolev inequalities for joint distributions.
result Sharp concentration bounds on uniform generalization errors, almost sure convergence in broad settings.
The study analyzes numerical stability in large language models using mixed-precision arithmetic.
problem Numerical stability of large language models using low-precision arithmetic.
method Developed a mixed-precision analysis of transformer inference, deriving bounds for condition numbers and forward error.
result Established that numerical stability is determined by the interplay between weight magnitude and the growth of the residual stream.
This paper develops fast rates for ERM and SA algorithms under error bound conditions.
problem Developing fast and adaptive optimization algorithms for statistical learning.
method Empirical Risk Minimization (ERM) and Stochastic Approximation (SA) algorithms with fast convergence rates under error bound conditions.
result Fast and adaptive convergence rates for ERM and SA algorithms, spanning from O ( 1 / n ) O(1/\sqrt{n}) O ( 1/ n ) to O ( 1 / n ) O(1/n) O ( 1/ n ) , depending on error bound conditions. PD-PINNs accelerate PINN training by incorporating task-specific dictionaries.
problem Training PINNs is slow and lacks theoretical error bounds.
method Integrates task-dependent dictionaries into PINNs to enhance convergence.
result PD-PINNs achieve faster convergence and bounded prediction errors.
Paper improves risk bounds for nonconvex-strongly-concave minimax problems.
problem Achieving sharper risk bounds for nonconvex-strongly-concave minimax problems.
method Using uniform localized convergence to derive high probability generalization error bounds.
result Derives n times faster excess primal risk bounds for popular algorithms.
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.
New bound matches exact generalization error for quadratic Gaussian problem.
problem Understanding generalization error in quadratic Gaussian problems.
method Information-theoretic approach with new ingredients.
result Exact tight bound for generalization error.
Improved bounds for MALA in non-convex sampling problems.
problem Sampling from non-convex distributions in high dimensions.
method Metropolis-adjusted Langevin algorithm (MALA) with improved bounds.
result MALA is faster than competitors in many challenging scenarios.