New algorithm optimizes PAC-Bayes bound without surrogate loss.
problem Mismatch between optimisation objective and generalisation bound in stochastic neural networks.
method Proposes a novel training algorithm that optimizes the PAC-Bayesian bound directly.
result Empirical results show improved performance over existing PAC-Bayesian training methods.
New PAC-Bayes training method improves model generalization for unbounded loss.
problem Improving generalization of complex models under unbounded loss.
method Established new PAC-Bayes bound for unbounded loss, jointly training prior and posterior.
result Outperforms existing PAC-Bayes training algorithms and matches ERM accuracy.
This research improves PAC-Bayesian bounds for classification tasks using convexified loss.
problem Deriving generalization bounds for classification tasks with non-convex loss functions.
method Shift focus to misclassification excess risk bounds for PAC-Bayesian classification using convex surrogate loss and leveraging PAC-Bayesian relative bounds in expectation.
result Improved PAC-Bayesian bounds for classification tasks with convex surrogate loss.
PAC-Bayesian theory applied to data-dependent hypothesis sets yields uniform generalization bounds.
problem Proving uniform generalization bounds for data-dependent hypothesis sets.
method Applying PAC-Bayesian framework on 'random sets' and considering data-dependent hypothesis sets.
result Data-dependent uniform generalization bounds are proven, providing tighter and unified results.
PAC-Bayesian matrix completion with a spectral scaled Student prior offers efficient inference.
problem Matrix completion with underlying low-rank structure.
method Spectral scaled Student prior and PAC-Bayesian bounds.
result Minimax-optimal oracle inequality for model misspecification and general sampling distribution.
This paper tackles non-vacuous generalization bounds in ReLU networks by resolving rescaling invariances.
problem Non-vacuous generalization guarantees for ReLU networks with rescaling invariances.
method Proposes a lifted representation to resolve rescaling invariances and studies KL-based rescaling-invariant PAC-Bayes bounds.
result KL-based rescaling-invariant PAC-Bayes bounds provide tighter guarantees and resolve discrepancies in network complexity.
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.
Recently the generalization error of deep neural networks has been analyzed through the PAC-Bayesian framework, for the case of fully connected layers. We adapt this approach to the convolutional setting.
Wide stochastic networks show Gaussian behavior and improve training with PAC-Bayesian methods.
problem Analyzing and training over-parameterised neural networks with large width.
method Establishing Gaussian behavior for a stochastic architecture, applying PAC-Bayesian training.
result PAC-Bayesian training on large but finite-width networks outperforms standard methods.
Unified treatment of PAC-Bayesian and information-theoretic generalization bounds.
problem Generalization capabilities of machine learning algorithms.
method PAC-Bayesian and information-theoretic perspectives.
result Unified treatment and modular structure of proofs.
New algorithm constructs PAC prediction sets for meta-learning.
problem Uncertainty quantification in safety-critical systems.
method Proposes a novel algorithm to construct PAC prediction sets.
result Prediction sets satisfy a PAC guarantee with high probability over future tasks.
Unified PAC-Bayesian framework for deep learning generalization.
problem Limitations of existing PAC-Bayesian norm-based bounds for deep neural networks.
method Unified framework using anisotropic Gaussian posteriors and sensitivity matrix.
result Comparable or tighter generalization bounds compared to state-of-the-art approaches.
Proposes a method to quantify uncertainty in predictions under covariate shift.
problem Uncertainty quantification challenges in machine learning with covariate shifts.
method Constructs PAC prediction sets with given importance weights and confidence intervals for weights.
result Algorithm gives prediction sets with the smallest average normalized size.
We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization risk bounds maximizes the Bayesian marginal likelihood. This provides an alternative explanatio…
We propose an algorithm combining calibrated prediction and generalization bounds from learning theory to construct confidence sets for deep neural networks with PAC guarantees---i.e., the confidence set for a given input contains the true label with high probability. We demonstrate how our approach can be used to cons…
We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of certain dependent random variables by expectations of the same functions of independent Bernoulli random variables. This …
Paper refines PAC-Bayes bounds for bandit problems.
problem Improving probabilistic bounds for off-policy learning.
method Optimizes PAC-Bayesian bounds using a new parameter optimization approach.
result Provides two parameter-free PAC-Bayes bounds that nearly match optimal rates.
We show that the class of strongly connected graphical models with treewidth at most k can be properly efficiently PAC-learnt with respect to the Kullback-Leibler Divergence. Previous approaches to this problem, such as those of Chow ([1]), and Ho gen ([7]) have shown that this class is PAC-learnable by reducing it to …
Paper analyzes error exponent in agnostic PAC learning.
problem Analyzing performance of agnostic PAC learning.
method Using error exponent from Information Theory to analyze PAC learning.
result Improved distribution-dependent error exponent for agnostic learning.
New PAC-Bayesian approach stabilizes actor-critic learning.
problem Training instability in actor-critic algorithms.
method Employing PAC-Bayesian bound as the critic training objective.
result Significant improvement in online learning performance.
New risk measures control subgroup imbalances, improving PAC-Bayesian bounds.
problem Insufficient risk bounds for subgroup imbalances in data.
method Introduce constrained f-entropic risk measures and derive PAC-Bayesian bounds.
result First disintegrated PAC-Bayesian guarantees beyond standard risks.
Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors. PAC-Bayesian methods overcome this problem by providing bounds that hold regardless …
New approach for off-policy learning in contextual bandits with performance guarantees.
problem Improving performance of logging policies in contextual bandits.
method PAC-Bayesian analysis of policy mixtures, providing tighter generalization bounds and tractable optimization algorithms.
result Proved tighter generalization bounds and demonstrated effectiveness in practical scenarios.
New PAC-Bayes meta-learning method improves few-shot learning accuracy and calibration.
problem Few-shot learning with limited data.
method PAC-Bayes framework extended to meta-learning, estimating task-specific posteriors.
result State-of-the-art calibration and classification results on benchmarks.
Paper develops PAC-Bayes bounds for unknown linear systems.
problem Learning controllers for unknown stochastic linear discrete-time systems.
method PAC-Bayes framework for data-dependent high probability bounds.
result Proposes efficient learning algorithms with theoretical guarantees.
PAC-Bayes bounds have been proposed to get risk estimates based on a training sample. In this paper the PAC-Bayes approach is combined with stability of the hypothesis learned by a Hilbert space valued algorithm. The PAC-Bayes setting is used with a Gaussian prior centered at the expected output. Thus a novelty of our …
Paper tightens PAC-Bayes bounds using coin-betting for better estimates.
problem Estimating mean of random elements with possibly S-dependent parameters.
method Refined PAC-Bayes proof strategy based on coin-betting framework.
result Derives tighter concentration inequalities for all sample sizes.
Unified framework for anytime-valid PAC-Bayes bounds.
problem Deriving time-uniform PAC-Bayes bounds for stochastic processes.
method Combines four tools: nonnegative supermartingales, method of mixtures, Donsker-Varadhan formula, and Ville's inequality.
result Unified PAC-Bayes theorem for a wide class of discrete stochastic processes.
In machine learning, Domain Adaptation (DA) arises when the distribution gen- erating the test (target) data differs from the one generating the learning (source) data. It is well known that DA is an hard task even under strong assumptions, among which the covariate-shift where the source and target distributions diver…
New hybrid RL algorithm outperforms model-free and model-based methods.
problem Improving reinforcement learning algorithms for MDPs.
method Combines model-free and model-based learning, with a PAC analysis.
result Outperforms both model-free and model-based methods in most cases.
PAC-Net prunes deep models for better transfer learning.
problem Improving transfer learning with over-parameterized models.
method Prune, Allocate, Calibrate (PAC) approach.
result PAC-Net achieves state-of-the-art performance in inductive transfer learning.
This work extends PAC-Bayesian learning guarantees to non-compact symmetries and non-invariant data.
problem Lack of theoretical guarantees explaining the benefits of symmetries in machine learning models.
method Adapting and tightening PAC-Bayes bounds for non-compact symmetries and non-invariant data distributions.
result Theoretical evidence that symmetric models are preferable for symmetric data, beyond compact groups and invariant distributions.
Paper proves L2 regression can learn k-juntas without distributional assumptions.
problem Learning k-juntas using L2 regression without distributional restrictions.
method L2 polynomial regression and minimum mean square estimation (MMSE).
result Agnostic PAC learning of k-juntas using L2 polynomial regression.
New PAC bound for meta-learning improves generalization guarantees.
problem Provide strong generalization guarantees in meta-learning.
method PAC-Bayes and uniform stability frameworks applied to gradient-based meta-learning.
result Derives a tighter PAC bound for gradient-based meta-learning.
New method learns robustly with less data, bridging theory and practice.
problem Adversarial robust learning with metric perturbation.
method Tolerant adversarial PAC-learning with perturb-and-smooth approach and compression-based algorithm.
result First PAC-type guarantees for popular adversarial learning techniques.
New method optimises learning via surrogate PAC-Bayes bounds.
problem Computational intractability of optimising generalisation bounds.
method Iteratively optimising surrogate training objectives derived from PAC-Bayes bounds.
result Iteratively optimising surrogates implies optimising original generalisation bounds.
The paper studies a stochastic majority vote approach to improve classifier accuracy.
problem Improving classifier accuracy over ensembles of classifiers.
method Minimizing a PAC-Bayes generalization bound with Dirichlet distributions.
result Achieves state-of-the-art accuracy and tight generalization bounds.
We present a comprehensive study of multilayer neural networks with binary activation, relying on the PAC-Bayesian theory. Our contributions are twofold: (i) we develop an end-to-end framework to train a binary activated deep neural network, (ii) we provide nonvacuous PAC-Bayesian generalization bounds for binary activ…
PAC-Bayesian bounds for MLPs with cross entropy loss validated.
problem Generalization bounds for MLPs with cross entropy loss.
method Introduced probabilistic explanations and proved PAC-Bayesian bounds using ELBO.
result MLPs with cross entropy loss inherently guarantee PAC-Bayesian generalization bounds.
New PAC-Bayes method updates priors without losing confidence information.
problem Lack of sequential prior updates in PAC-Bayes without losing confidence information.
method Recursive PAC-Bayes decomposition of expected loss.
result Sequential prior updates with no information loss.
New PAC-Bayesian framework for flexible meta-learning.
problem Limitations in transferring knowledge between tasks in meta-learning.
method PAC-Bayesian theory applied to learning the learning algorithm.
result Flexibility in meta-learning mechanisms and improved prediction quality.
This paper provides a PAC-Bayesian bound for CVaR in machine learning.
problem Learning algorithms minimizing CVaR of empirical loss.
method Generalization bound of PAC-Bayesian type, reducing CVaR estimation to expectation estimation.
result The bound is small when empirical CVaR is small, providing concentration inequalities for CVaR.
We develop a scoring and classification procedure based on the PAC-Bayesian approach and the AUC (Area Under Curve) criterion. We focus initially on the class of linear score functions. We derive PAC-Bayesian non-asymptotic bounds for two types of prior for the score parameters: a Gaussian prior, and a spike-and-slab p…
Unified derivation of PAC-Bayes and MI bounds for general VC classes with fast rates.
problem Generalization bounds for machine learning models with VC classes.
method Unified derivation of conditional PAC-Bayesian and mutual information bounds, including MAC-Bayesian bounds.
result Nontrivial bounds for general VC classes and faster rates for specific conditions.
Algorithm constructs prediction sets with PAC guarantees in label shift settings.
problem Reliable uncertainty quantification in the face of distribution shift.
method Estimates predicted probabilities and confusion matrix, then propagates uncertainty through Gaussian elimination to compute confidence intervals and construct prediction sets.
result Satisfies PAC guarantees and produces smaller, more informative prediction sets.
We consider the Domain Adaptation problem, also known as the covariate shift problem, where the distributions that generate the training and test data differ while retaining the same labeling function. This problem occurs across a large range of practical applications, and is related to the more general challenge of tr…
The developments of Rademacher complexity and PAC-Bayesian theory have been largely independent. One exception is the PAC-Bayes theorem of Kakade, Sridharan, and Tewari (2008), which is established via Rademacher complexity theory by viewing Gibbs classifiers as linear operators. The goal of this paper is to extend thi…
PAC-Wrap provides provable guarantees for semi-supervised anomaly detection.
problem Ensuring reliable anomaly detection in safety-critical applications.
method PAC-Wrap wraps around existing anomaly detection methods to provide PAC guarantees.
result PAC-Wrap effectively provides rigorous guarantees for various anomaly detectors.