Study on kernel regression risk in high dimensions using Pinsker bound.
problem Kernel regression risk in high-dimensional inner product spaces.
method Investigation of Pinsker bound for kernel regression on sphere Sd with sample size n=αdγ(1+od(1)). result Exact minimax risk and Pinsker constant identified for kernel regression.
The paper develops inequalities for log-concave functions and related surface areas.
problem Understanding log-concave functions and their inequalities.
method Establishing new inequalities through f-divergences and functional affine surface areas.
result New inequalities on functional affine surface area and bounds for Kullback-Leibler divergence.
A central result in statistical theory is Pinsker's theorem, which characterizes the minimax rate in the normal means model of nonparametric estimation. In this paper, we present an extension to Pinsker's theorem where estimation is carried out under storage or communication constraints. In particular, we place limits …
New bounds for Neyman-Pearson region using f-divergences.
problem Bounding the Neyman-Pearson region for hypothesis testing.
method Establishing novel lower and upper bounds using f-divergences. result Best possible lower bound for the Neyman-Pearson boundary using hockey-stick f-divergences. TRM improves long-horizon LLM RL by masking divergent sequences.
problem Long-horizon reinforcement learning with LLMs suffers from off-policy mismatch and approximation errors.
method Derives and applies trust region bounds to control divergence, proposing Trust Region Masking.
result First non-vacuous monotonic improvement guarantees for long-horizon LLM-RL.
TRM improves long-horizon reinforcement learning for LLMs by masking divergent sequences.
problem Long-horizon reinforcement learning for LLMs suffers from off-policy mismatch and approximation errors.
method Derives and applies trust region bounds to control divergence, proposing Trust Region Masking.
result First non-vacuous monotonic improvement guarantees for long-horizon LLM-RL.
PAC-Bayesian set up involves a stochastic classifier characterized by a posterior distribution on a classifier set, offers a high probability bound on its averaged true risk and is robust to the training sample used. For a given posterior, this bound captures the trade off between averaged empirical risk and KL-diverge…
We unify f-divergences, Bregman divergences, surrogate loss bounds (regret bounds), proper scoring rules, matching losses, cost curves, ROC-curves and information. We do this by systematically studying integral and variational representations of these objects and in so doing identify their primitives which all are rela…
We formulate the notion of minimax estimation under storage or communication constraints, and prove an extension to Pinsker's theorem for nonparametric estimation over Sobolev ellipsoids. Placing limits on the number of bits used to encode any estimator, we give tight lower and upper bounds on the excess risk due to qu…
We propose a general variational framework of fair clustering, which integrates an original Kullback-Leibler (KL) fairness term with a large class of clustering objectives, including prototype or graph based. Fundamentally different from the existing combinatorial and spectral solutions, our variational multi-term appr…
Study bandwidth-limited training and inference of language models.
problem Training and inference of language models on scattered data with limited bandwidth.
method Analyzed two protocols: Federated Probe-Logit Distillation (FPLD) for training and Federated Conformal RAG (FC-RAG) for inference.
result Explicit high-probability KL-consistency rate and distribution-free marginal-coverage bound for Federated Conformal RAG.
CAST predicts distribution-valued time series by stabilizing and transporting simplex-supported successors.
problem Forecasting distribution-valued time series with structural failure modes.
method CAST (Causal Anchored Simplex Transport) uses successors retrieved from causal context, stabilized with a persistence anchor, and locally transported on ordered supports.
result CAST outperforms baselines on eleven public and simulated benchmarks, achieving best average rank on both one-step KL and autoregressive rollout JSD.
Causal inference is perhaps one of the most fundamental concepts in science, beginning originally from the works of some of the ancient philosophers, through today, but also weaved strongly in current work from statisticians, machine learning experts, and scientists from many other fields. This paper takes the perspect…
The study optimizes bounds for comparing training and population loss.
problem Optimizing bounds for comparing training and population loss.
method Derives generic information-theoretic and PAC-Bayesian generalization bounds using convex comparator functions.
result The tightest possible bound is obtained with the comparator being the convex conjugate of the CGF of the bounding distribution.
Introduces bounded scale measure and generalizes property A.
problem Defining property A for large scale spaces with bounded geometry.
method Introduces bounded scale measure, shows its coarse invariance, and generalizes property A.
result Definition of property A for large scale spaces with bounded scale measure is a coarse invariant.
Paper improves PAC-Bayes bounds for various loss types.
problem Improving PAC-Bayes bounds for different types of losses.
method Introducing new high-probability PAC-Bayes bounds for bounded and general tail behaviors losses, and extending to anytime-valid bounds.
result New fast-rate and mixed-rate bounds for losses with bounded ranges, and parameter-free bounds for losses with general tail behaviors.
Improved bounds for Monte Carlo Rademacher Averages using self-bounding functions.
problem Proving sharper concentration bounds for MCERA.
method Deriving new bounds through self-bounding functions and concentration of measure.
result Novel bounds depend on data-dependent quantities, improving over standard methods.
Study bounds on self-shrinkers with bounded HA for applications.
problem Understanding bounds on self-shrinkers with bounded HA.
method Integral and pointwise bounds on the second fundamental form of self-shrinkers.
result Gap and compactness results for self-shrinkers.
Investigates tight PAC-Bayes bounds for small datasets.
problem Tightening PAC-Bayes bounds for small data.
method Generic PAC-Bayes theorem, meta-learning, synthetic tasks.
result PAC-Bayes bounds are competitive with Chernoff bounds but not as tight.
Extends Fatou theorem to bounded harmonic maps.
problem Classical Fatou theorem for bounded harmonic functions.
method Extending theorem to bounded harmonic maps.
result Identifies bounded harmonic maps on unit disk with bounded measurable functions on boundary.
New bound relaxes uniform gradient norm assumptions for PAC-Bayesian bounds.
problem Generalization bounds with strict assumptions like uniformly bounded loss.
method Relax uniform bounds assumptions to on-average bounded loss and gradient norm.
result Proposes a new generalization bound with a surrogate of model complexity.
Jiang et al. (2020) found no uniformly tight generalization bounds for neural networks in the overparameterized setting.
problem Finding uniformly tight generalization bounds for neural networks in the overparameterized setting.
method Examined more than a dozen generalization bounds, proving that no bounds can be uniformly tight in the overparameterized setting.
result No generalization bounds can be uniformly tight in the overparameterized setting.
Willmore-type inequalities for bounded domains in manifolds with curvature bounds.
problem Establishing inequalities for bounded domains in manifolds with curvature bounds.
method Using asymptotic or integral Ricci curvature bounds to establish inequalities.
result Recovering a recent inequality of Jin-Yin.
Lower bounds on curvature integral for manifolds with curvature constraints.
problem Bounding curvature integrals under curvature constraints.
method Proving a lower bound for the curvature integral using dimension, upper curvature bounds, and injectivity radius.
result Uniformly bounded below integral of scalar curvature.
Paper improves SLCB regret bound for bounded noise.
problem Stochastic linear contextual bandits with bounded noise.
method Set-membership estimation (SME) and optimism in the face of uncertainty (OFU).
result Improved regret bound of O(logT). Study on CMC hypersurfaces with bounded index and area, proving multiplicity one convergence and bounds on genus.
problem Understanding CMC hypersurfaces with bounded index and area.
method Bubble-compactness theory for embedded CMC hypersurfaces in low dimensions.
result Minimal blow-ups are all catenoids, and bounds on genus provided.
Uniform entropy bound for Ricci shrinkers with bounded curvature.
problem Bounding entropy for Ricci shrinkers with specific curvature constraints.
method Establishing uniform entropy bounds for simply connected Ricci shrinkers with a finite second homotopy group and uniform curvature bounds.
result Uniform entropy bound for simply connected Ricci shrinkers with a finite second homotopy group and uniform curvature bounds.
New study on regret lower bounds for multi-agent multi-armed bandit problems.
problem Understanding the limits of performance in multi-agent multi-armed bandit problems.
method Comprehensive study on different settings, establishing tight lower bounds.
result First comprehensive study on regret lower bounds across various settings.
The paper improves PAC-Bayes bounds for losses with finite moments.
problem Bounding generalization for losses with heavy tails and finite moments.
method Truncation method and PAC-Bayes bounds for unbounded losses with heavy tails and bounded variance.
result Bounds interpolate between slow and fast rates depending on the moment.
Sharp lower bound for Hodge Laplacian on Kähler hyperbolic manifolds.
problem Finding a sharp lower bound for the spectrum of the Hodge Laplacian.
method Explicitly expressed in terms of the supremum norm of the 1-form.
result Explicit spectral lower bounds for bounded symmetric domains.
New bounds for SGD show improved performance in various settings.
problem Improving convergence bounds for SGD with random permutations.
method Analyzing convergence of SGD with random reshuffling and arbitrary permutations.
result Tighter lower bounds for weighted average iterates in both convex and strongly-convex cases.
Uniform bounds for eigenvalues of Hodge Laplacian on manifolds with lower Ricci curvature.
problem Establishing bounds for eigenvalues of Hodge Laplacian under lower Ricci curvature.
method Using geometric assumptions including lower Ricci curvature, injectivity radius, and diameter bounds.
result Uniform eigenvalue bounds for the Hodge Laplacian and connection Laplacian.
The paper honors Lai's contributions to multi-armed bandits and establishes new regret bounds.
problem Improving regret bounds in multi-armed bandit problems.
method Establishes non-asymptotic regret bounds for upper confidence bound indices.
result New regret bounds match Lai-Robbins lower bound.
New method to parametrize infinite Riemann surfaces with bounded triangulations.
problem Parametrizing infinite Riemann surfaces with bounded triangulations.
method Introducing bounded ideal triangulations and proving real-analyticity of the parametrization.
result Real-analytic parametrization of Teichmüller spaces for infinite surfaces with bounded triangulations.
We propose a general framework for studying adaptive regret bounds in the online learning framework, including model selection bounds and data-dependent bounds. Given a data- or model-dependent bound we ask, "Does there exist some algorithm achieving this bound?" We show that modifications to recently introduced sequen…
Triangulates surfaces with bounded energy using diffeomorphisms.
problem Triangulating surfaces with bounded Kolasinski--Menger energy.
method Uses bounded distortion diffeomorphisms of subsets of a plane.
result Triangulation with bounded number of triangles.
This paper analyzes regret bounds for Gaussian process Thompson sampling.
problem Analyzing the performance of Gaussian process Thompson sampling (GP-TS) in Bayesian optimization.
method The paper derives several regret bounds for GP-TS, including a lower bound, upper bounds on the second moment of cumulative regret, expected lenient regret, and improved cumulative regret.
result The paper provides improved regret upper bounds for GP-TS, showing that it suffers from a polynomial dependence on 1/δ with probability δ. New bounds on machine learning model generalization error moments.
problem Understanding the performance of machine learning models.
method Information-theoretic bounds on the moments of the generalization error of learning algorithms.
result Proposed bounds on generalization error moments and their high-probability bounds.
New PAC-Bayes bounds for unbounded losses using Cramér-Chernoff techniques.
problem Developing bounds for unbounded losses in PAC-Bayesian settings.
method Introducing a new PAC-Bayes oracle bound using Cramér-Chernoff bounds and controlling random variable tails.
result Our bounds generalize and improve upon previous results, providing more informative and potentially tighter bounds.
New tighter bounds for learning algorithms from Steinke & Zakynthinou's supersample setting.
problem Improving generalization bounds for machine learning algorithms.
method Information-theoretic approach using projected loss and Rademacher sequence.
result The new bounds are tighter than previous information-theoretic bounds.
New bound for neural networks with full-rank weights, independent of network width.
problem Understanding generalization of neural networks with full-rank weight matrices.
method Using Koopman operators to derive a tighter generalization bound for full-rank weight matrices.
result The bound is tighter than existing norm-based bounds when condition numbers are small.
Paper presents a reduction-based framework for conservative bandits and RL with improved lower and upper bounds.
problem Conservative bandits and reinforcement learning problems.
method Reduction technique to calculate necessary and sufficient budget from baseline policy.
result Improved lower and upper bounds for various conservative settings.
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.
New bounds for nearly-linear networks without training.
problem Generalization of neural networks close to linearity.
method Perturbation of linear networks to derive bounds.
result First non-vacuous bounds for neural nets.
For non-compact manifolds with boundary we prove that bounded geometry defined by coordinate-free curvature bounds is equivalent to bounded geometry defined using bounds on the metric tensor in geodesic coordinates. We produce a nice atlas with subordinate partition of unity on manifolds with boundary of bounded geomet…
The study sets lower bounds for eigenvalue sums of Laplacian on bounded domains and spheres.
problem Establishing lower bounds for eigenvalue sums of the Laplacian.
method Extending known results on eigenvalues of Laplacian for bounded domains, spheres, and surfaces.
result Improved lower bounds for eigenvalue sums, connecting to conjectures and extending known results.
New bounds for knot distances using Khovanov homology.
problem Calculating precise distances between knots.
method Using Khovanov homology to refine existing bounds.
result Improved bounds for Gordian distances of knots.
Compactness proven for CMC surfaces with bounded topology and boundary length.
problem Proving compactness of CMC surfaces with specific constraints.
method Graphical Ck compactness proof for surfaces with bounded topology, area, and boundary length. result Space of free boundary CMC surfaces is compact in the Ck graphical sense away from a finite set of points.