We propose a statistical adaptive procedure called SALSA for automatically scheduling the learning rate (step size) in stochastic gradient methods. SALSA first uses a smoothed stochastic line-search procedure to gradually increase the learning rate, then automatically switches to a statistical method to decrease the le…
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48 results for “statistical learning rate”
New federated learning protocols resist Byzantine failures and offer privacy guarantees.
problem Resisting Byzantine failures in federated learning.
method Proposes robust federated learning protocols with optimal statistical rates and privacy guarantees.
result Achieves nearly optimal statistical rates and tight rate in terms of all parameters for strongly convex losses.
Despite the development of numerous adaptive optimizers, tuning the learning rate of stochastic gradient methods remains a major roadblock to obtaining good practical performance in machine learning. Rather than changing the learning rate at each iteration, we propose an approach that automates the most common hand-tun…
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.
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.
Privacy Aware Learningstat.ML
We study statistical risk minimization problems under a privacy model in which the data is kept confidential even from the learner. In this local privacy framework, we establish sharp upper and lower bounds on the convergence rates of statistical estimation procedures. As a consequence, we exhibit a precise tradeoff be…
AdaDetectGPT improves text authorship detection with statistical guarantees.
problem Determining if text is authored by a human or an LLM.
method Adaptive learning of a witness function from training data to enhance logits-based detectors.
result AdaDetectGPT nearly uniformly improves text authorship detection, with up to 37% improvement.
Graph learning improves FXRP and FXSA with significant statistical arbitrage gains.
problem Improving FXRP and FXSA with complex multi-currency and interest rate relationships.
method Two-step graph learning approach: first, edge-level regression on spatiotemporal graph; second, stochastic optimization with constraints and risk-adjusted return maximization.
result Graph-learning method achieves higher information and Sortino ratios than benchmarks.
Near-optimal rates for multi-task learning with shared representations.
problem Approximation and statistical complexity of learning multiple operators.
method Multiple Neural Operators (MNO) architecture and comparison with DeepONet.
result Near-optimal upper and lower bounds for approximation and generalization.
In large-scale distributed learning, security issues have become increasingly important. Particularly in a decentralized environment, some computing units may behave abnormally, or even exhibit Byzantine failures -- arbitrary and potentially adversarial behavior. In this paper, we develop distributed learning algorithm…
The paper analyzes convergence in SGD with momentum and proposes a diagnostic test.
problem Detecting convergence in stochastic gradient descent with momentum.
method Analyzes the transient and stationary phases of SGD with momentum, constructs a statistical diagnostic test.
result The proposed diagnostic test effectively detects convergence in the stationary phase of SGD with momentum.
The paper introduces gapped scale-sensitive dimensions to improve learning rate bounds.
problem Improving lower bounds on rates of convergence in statistical and online learning.
method Introducing and analyzing gapped scale-sensitive dimensions for function classes.
result Gapped dimensions lead to stronger lower bounds on offset Rademacher averages.
New bounds on learning shared representations improve model performance and efficiency.
problem Improving model performance and efficiency through shared representations across clients.
method Established new upper and lower bounds on statistical error, designed a spectral estimator for non-convex least-squares solutions.
result Optimal statistical rate achieved when shared representation is well covered across clients.
Study shows multi-distribution learning has slower rates than single-task learning.
problem Understanding the statistical complexity of learning from heterogeneous sources.
method Structured hypothesis-testing framework to capture the statistical cost of certifying near-optimality under bounded noise.
result Learning across multiple distributions incurs slow rates scaling with , even under constant noise levels.
Study on distributional TD learning with linear approximations for better return estimation.
problem Estimating the return distribution of a policy in reinforcement learning.
method Finite-sample analysis of distributional TD learning with linear function approximation, using the linear-categorical Bellman equation and exponential stability arguments for products of random matrices.
result Sample complexity of linear distributional TD learning matches that of classic linear TD learning, indicating similar difficulty in estimating return distribution versus its expectation.
The speed with which a learning algorithm converges as it is presented with more data is a central problem in machine learning --- a fast rate of convergence means less data is needed for the same level of performance. The pursuit of fast rates in online and statistical learning has led to the discovery of many conditi…
New research shows unlabeled data is equally valuable as labeled data in certain semi-supervised learning scenarios.
problem Improving learning performance with limited labeled data.
method Statistical models with continuous parameters, showing equal utility of unlabeled data under specific conditions.
result The learning rate of semi-supervised learning scales similarly to supervised learning when unlabeled data is abundant.
Study improves estimation of functions from noisy data using convex penalties.
problem Estimating functions from noisy point evaluations of linear operators.
method Tikhonov regularization with convex and -homogeneous penalty functionals.
result Derives concentration rates for regularized solutions in symmetric Bregman distance.
We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Thus, it has minimal variance among all unbiased estimators and is asymptotically normally dis…
Novel mutual information bound improves statistical inference rates.
problem Improving statistical inference rates in Bayesian nonparametrics.
method Introduces a novel mutual information bound.
result Improved contraction rates for fractional posteriors.
SGDM accelerates faster than SGD with large batch sizes and permits broader learning rates.
problem Understanding the role of momentum in SGDM and its convergence rates.
method Analysis of SGDM convergence rates under strongly convex settings, including finite-sample rates and asymptotic normality of the averaged estimator.
result SGDM converges faster than SGD with large batch sizes and permits broader learning rates.
New methods tackle statistical inverse problems with random data.
problem Statistical inverse problems with random experimental design.
method Spectral regularization, regularization by projection, convex penalties.
result Minimax rates in expectation and probability for convergence.
Study optimizes learning rates for conditional mean embedding estimates.
problem Consistency of kernel ridge regression for conditional mean embedding.
method Adaptive statistical learning rate derived for misspecified setting.
result Upper bound matches optimal rates without assuming finite dimensionality.
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.
Boosting improves data fitting while maintaining fairness guarantees.
problem Ensuring fairness in data preprocessing.
method Boosting algorithm to learn sufficient statistics of exponential families.
result The learned distribution maintains fairness guarantees while fitting the data better.
SFS-DA method statistically tests FS reliability under domain adaptation.
problem Feature selection reliability under domain adaptation with limited target data.
method Selective Inference framework to control false positive rate and enhance true positive rate.
result SFS-DA method controls FPR below a pre-specified level (e.g., 0.05) while maximizing true positive rate.
Enhanced ROOT-SGD optimizes stochastic optimization with diminishing stepsizes.
problem Improving statistical efficiency in stochastic optimization.
method Integrates a diminishing stepsize strategy into ROOT-SGD.
result Achieves optimal convergence rates with improved stability and precision.
Error bound conditions (EBC) are properties that characterize the growth of an objective function when a point is moved away from the optimal set. They have recently received increasing attention in the field of optimization for developing optimization algorithms with fast convergence. However, the studies of EBC in st…
Paper introduces PTL-SI for statistical inference in TL-HDR, controlling FPR.
problem Quantifying statistical significance in TL-HDR with limited data.
method PTL-SI framework for valid -values in TL-HDR feature selection.
result Valid -values and controlled FPR in TL-HDR feature selection.
A review of statistical SSL methods showing improved classifier performance.
problem Forming classifiers from limited labeled data and many unlabeled data.
method Statistical approaches to semi-supervised learning.
result A classifier from partially labeled data can have lower expected error rate.
Multi-group learners suffer a penalty in transductive learning.
problem The penalty on multi-group learners in transductive learning.
method Analyzing the relationship between the number of groups and the error rate.
result The penalty can increase linearly with the number of groups, up to the square-root of the sample size.
We establish optimal rates for online regression for arbitrary classes of regression functions in terms of the sequential entropy introduced in (Rakhlin, Sridharan, Tewari, 2010). The optimal rates are shown to exhibit a phase transition analogous to the i.i.d./statistical learning case, studied in (Rakhlin, Sridharan,…
Proposes a more robust rating scale for banks.
problem Inconsistent rating scale validation leading to higher capital requirements.
method Develops a new rating scale that is statistically distinguishable and robust.
result Reduces the calibration probability of default, saving capital requirements.
New bounds on generalization error for distributed learning using rate-distortion theory.
problem Establishing upper bounds on generalization error for distributed learning algorithms.
method Using rate-distortion theory, the paper introduces new bounds that depend on the compressibility of each client's algorithm.
result The bounds suggest that the generalization error of the distributed setting decays faster than that of the centralized one with a factor of .
New approach uses PDE learning for faster RL fine-tuning.
problem Learning optimal control policy for diffusion process.
method Solves variational inequality based on HJB equations.
result Shows fine-tuning can be done via supervised regression.
Develops statistical methods for rates of change on Riemannian manifolds.
problem Statistical inference for rates of change in spatial processes over non-Euclidean domains.
method Formalizes smoothness and constructs differential processes for Riemannian manifolds, derives conditions for kernel existence, and develops predictive inference.
result Validates theoretical findings through simulation experiments for derivatives over polyhedral meshes.
Distribution learning via neural differential equations: a nonparametric statistical perspectivemath.ST
This work analyzes the statistical properties of neural ODEs for distribution learning.
problem Statistical properties of neural ODEs for distribution learning.
method General nonparametric statistical convergence analysis for distribution learning via neural ODE models.
result Established nearly minimax-optimal convergence rates for neural ODEs.
Smoothness Adaptivity in Constant-Depth Neural Networks: Optimal Rates via Smooth Activationsstat.ML
Smooth activations enable optimal error rates in neural networks for Sobolev function classes.
problem Achieving optimal approximation and estimation error rates for neural networks in Sobolev function classes.
method Study of neural networks with smooth activations, proving optimal rates via approximation and statistical properties.
result Constant-depth networks with smooth activations achieve optimal rates of approximation and estimation, demonstrating smoothness adaptivity.
The paper studies kernel smoothing and mean shift for directional data, deriving convergence rates and mode estimation.
problem Statistical and computational problems of kernel smoothing for directional data.
method Generalization of mean shift to directional data, derivation of convergence rates, and investigation of mode estimation.
result Statistical convergence rates of directional KDE and its derivatives, ascending property of directional mean shift, and mode estimation.
Study shows fast rates for inverse reinforcement learning with linear rewards.
problem Entropy-regularized min-max inverse reinforcement learning in finite-horizon MDPs.
method Structural and statistical analysis of Min-Max-IRL with pseudo-self-concordance.
result Both trajectory-level KL divergence and parameter error decay at .
A hypothesis test for the long-term calibration in rating systems with overlapping time windowsq-fin.RM
Statistical test verifies long-term rating system calibration with overlapping time windows.
problem Verifying supervisory requirements for overlapping time windows in rating systems.
method Analyzes long-run default rate distribution and correlation effects; presents conservative calibration test methods.
result Developed a test for individual and portfolio levels that can handle unknown variance.
Bounds for rating override ratesq-fin.RM
Overrides of credit ratings are important correctives of ratings that are determined by statistical rating models. Financial institutions and banking regulators agree on this because on the one hand errors with ratings of corporates or banks can have fatal consequences for the lending institutions and on the other hand…
New dynamics for SGD in small learning rate regime.
problem Improving stochastic gradient descent in small learning rate regime.
method Introducing stochastic modified flows and distribution dependent stochastic modified flows.
result Captures fluctuating dynamics of SGD in small learning rate - infinite width scaling regime.
Bayesian approach controls FDR in high-dimensional models.
problem High-dimensional variable selection and inference.
method Adapted Mirror Statistic to Bayesian framework for FDR control.
result Effective FDR control without data splitting.
Study controls error rates of binary classifiers using hypothesis testing.
problem Traditional binary classifiers have uncontrolled error rates.
method Combines binary classification with statistical hypothesis testing.
result Trained classifiers can be made to meet target error rate thresholds.
A new knockoff statistic using conditional prediction function improves variable selection in complex models.
problem Controlling false discovery rate in complex models with nonlinear relationships.
method Introducing a knockoff statistic based on the conditional prediction function for use with machine learning models.
result The CPF statistics provide superior power in detecting prognostic variables over existing knockoff statistics.
The rectified flow method is analyzed for its statistical properties.
problem Theoretical support for rectified flow methods is lacking.
method Empirical analysis of rectified flow's statistical properties using regression and density estimation.
result Convergence rates for rectified flow estimators are faster than for nonparametric regression and density estimation.
Improved fast rates for decision making with forward-KL regularization in contextual bandits.
problem Improving fast rates for decision making with forward-KL regularization in contextual bandits.
method Streamlined analysis of forward-KL-regularized offline CBs, exploiting the pessimism principle and convex-analytical pipeline.
result First upper bounds in tabular and general function approximation settings.