Improved uniform convergence bound with fat-shattering dimension reduces sample complexity gap.
problem Gap between upper and lower bounds on sample complexity for fat-shattering dimension.
method Provided an improved uniform convergence bound.
result Closed the gap between existing upper and lower bounds on sample complexity.
Estimates fat-shattering dimension of aggregated function classes.
problem Understanding the complexity of aggregated function classes.
method Analyzes fat-shattering dimension of k-fold aggregations of real-valued function classes. result Provides upper and lower bounds on fat-shattering dimension for linear and affine function classes.
New learning rule for quantum measurement classes overcomes uniform convergence issues.
problem Characterizing learnability of POVM hypothesis classes in quantum settings.
method Introduced a new learning rule called denoised ERM to address uniform convergence issues.
result Characterized learnability conditions and sample complexity bounds for POVM classes.
Study robust regression learning under adversarial attacks.
problem Understanding which function classes are learnable in the presence of adversarial attacks.
method Introduced a novel agnostic sample compression scheme and used fat-shattering dimension to construct adversarially robust sample compression schemes.
result Finite fat-shattering dimension classes are learnable in both realizable and agnostic settings.
The study provides a sample complexity estimate for multi-category classifiers with bounded variation.
problem Controlling the deviation between empirical and generalization performances of multi-category classifiers.
method Using the empirical L1-norm covering number and fat-shattering dimension, the study derives a sample size estimate for classifiers of bounded variation.
result The sample size estimate is sufficient for the performances to be close with high probability, improving the dependency on the number of classes.
Positive results for agnostic regression with various losses.
problem Agnostic regression with bounded sample compression.
method Generic and efficient sample compression schemes for real-valued functions.
result Exact and approximate compression schemes for specific losses.
New algorithms achieve near-optimal cumulative loss in nonparametric online learning and games.
problem Fast rates of convergence in nonparametric online regression and classification.
method Randomized proper learning algorithms, hierarchical aggregation, multi-scale extension, stability proof.
result Achieved near-optimal cumulative loss bounds for real-valued and binary games.
General lower bounds on neural network approximation in L^p norm.
problem Fundamental limits of neural network expressivity.
method General lower bound proof on approximation in L^p norm, applied to feed-forward neural networks.
result Neural networks can't approximate certain functions as well as previously thought.
Characterizes statistical complexity of realizable regression in PAC and online learning.
problem Understanding the statistical complexity of realizable regression in both PAC and online learning settings.
method Introduces minimax instance optimal learners, novel and combinatorial dimensions to characterize learnability.
result Characterizes which classes of real-valued predictors are learnable and provides necessary conditions for learnability.
New algorithm for learning functions with bounds on error and sample complexity.
problem Learning [0,1]-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.
New algorithm learns regression models privately under growth condition.
problem Private learning of nonparametric regression models.
method Novel filtering procedure to output stable hypotheses for nonparametric function classes.
result Established first nonparametric private learnability guarantee for diverging fat shattering dimensions.
New findings on neural networks with non-negative weights and low training error.
problem Does a low training error imply a small outer norm for two-layer neural networks?
method Covering number argument and fat-shattering dimension analysis.
result For non-negative output weights, low training error guarantees a well-controlled outer norm.
Improved robust learning model with tighter generalization bounds.
problem Adversarial robust learning in environments with limited corruptions.
method Model as a zero-sum game, using regret minimization and ERM oracles.
result Improved sample complexity for robust classifiers, handling infinite hypothesis classes.
Characterizes sample complexity for outcome indistinguishability in machine learning.
problem Outcome indistinguishability in machine learning, focusing on distinguishers and predictors.
method Sample complexity characterized by metric entropy of predictor and distinguisher classes, using dual Minkowski norms.
result Equivalence and tightness of sample complexity characterizations in distribution-specific and distribution-free settings.
Characterizes the sample complexity of list regression tasks.
problem Understanding the sample complexity of list learning tasks in regression.
method Introducing two combinatorial dimensions: k-OIG dimension and k-fat-shattering dimension.
result These dimensions characterize realizable and agnostic k-list regression.
Framework for private, noise-tolerant, and efficient learning algorithms.
problem Private and efficient learning of large-margin halfspaces in noisy environments.
method Simple framework using differential privacy and noise tolerance conditions.
result Noise-tolerant and private PAC learners for large-margin halfspaces with sample complexity independent of dimension.
Recent advances in large-margin classification of data residing in general metric spaces (rather than Hilbert spaces) enable classification under various natural metrics, such as string edit and earthmover distance. A general framework developed for this purpose by von Luxburg and Bousquet [JMLR, 2004] left open the qu…
Let F be a family of Borel measurable functions on a complete separable metric space. The gap (or fat-shattering) dimension of F is a combinatorial quantity that measures the extent to which functions f in F can separate finite sets of points at a predefined resolution gamma > 0. We establish a connection between the g…
The article introduces gamma-Psi-dimensions for margin multi-category classifiers.
problem Margin multi-category classifiers' generalization performance under minimal learnability hypotheses.
method Derives gamma-Psi-dimensions, handles capacity measures, and establishes upper bounds on metric entropies and Rademacher complexity.
result Gamma-Psi-dimensions improve over fat-shattering dimension and offer a promising alternative for multi-class to binary transitions.
New algorithm reduces online learning error for unknown feature distributions.
problem Oracle-efficient hybrid online learning with unknown feature and label distributions.
method Computational efficient online predictor using ERM oracle for finite-VC and fat-shattering classes.
result Oracle-efficient sublinear regret bounds for hybrid online learning with unknown feature generation.
In response to a 1997 problem of M. Vidyasagar, we state a criterion for PAC learnability of a concept class C under the family of all non-atomic (diffuse) measures on the domain Ω. The uniform Glivenko--Cantelli property with respect to non-atomic measures is no longer a necessary condition, and consisten…
Paper combines RL with policy regularization for inventory policies.
problem Optimizing inventory policies using RL and dynamic programming.
method Hybrid approach combining RL with policy regularization.
result Generalization guarantees for inventory policies using VC theory.
Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view to explore various aspects of smooth kernels related to their inferential proper…
Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on investigating the information-theoretic upper bounds of sample complexity - how ma…
New algorithm reduces prediction error in online learning without knowing base measure.
problem Smoothed online learning without knowledge of base measure.
method R-Cover algorithm based on recursive coverings.
result First algorithm to guarantee sublinear regret for agnostic smoothed online learning without prior knowledge of base measure.
Study public-data assisted private stochastic optimization with labeled or unlabeled public data.
problem Limits and capability of public-data assisted differentially private (PA-DP) algorithms in stochastic convex optimization.
method Lower bounds for PA-DP mean estimation and novel methods for leveraging public data in private supervised learning.
result Achieved dimension independent rate for GLM with unlabeled public data, showing optimality.
Comparative learning combines realizable and agnostic settings for two hypothesis classes, reducing sample complexity.
problem Learning with two hypothesis classes in a more general setting than single hypothesis classes.
method Introduces comparative learning, defines mutual VC dimension and Littlestone dimension, and applies insights to multiaccuracy and multicalibration.
result Sample complexity of comparative learning is characterized by mutual VC dimension and Littlestone dimension.