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.
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.
Meta-learning bounds derived using PAC-Bayes theory for improved generalization.
problem Uncertainty in generalization performance for meta-learning with new tasks.
method PAC-Bayes relative entropy bounds and empirical risk minimization (ERM) method.
result Competitive generalization performance and rapid convergence with data-dependent prior.
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.
This paper improves meta-learning by developing new PAC-Bayes bounds.
problem Meta-learning generalization gap across multiple tasks.
method Upper bounding convex functions linking environment and task-level losses.
result New PAC-Bayes bounds for meta-learning with improved algorithms.
Efficient PAC learning for contrastive linear representations is achieved.
problem Efficient PAC learning for contrastive linear representations.
method Relaxing the problem to a semi-definite program and using Rademacher complexity.
result First efficient PAC learning algorithm for contrastive learning.
PAC-Bayesian framework for fairness in stochastic and deterministic classifiers.
problem Theoretical guarantees on fairness for balancing predictive risk and fairness constraints.
method PAC-Bayesian framework for both stochastic and deterministic classifiers, covering a broad class of fairness measures.
result Derives generalization bounds for fairness, demonstrating tightness with empirical evaluation.
PAC-Bayesian bounds estimate adversarial robustness.
problem Estimating robustness to imperceptible input perturbations.
method PAC-Bayesian framework for averaging over hypotheses.
result General bounds valid for any type of adversarial attacks.
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.
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…
Introduces PAC-Bayes bounds for understanding learning procedures.
problem Understanding the generalization ability of learning procedures.
method PAC-Bayesian bounds and their applications to neural networks.
result Simplified version of localization technique described.
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.
Paper develops PAC verification for hypothesis classes and statistical algorithms.
problem Verifying machine learning models interactively.
method Develops interactive proof for PAC verification, proves lower bounds, and introduces a generalization.
result Improved protocol for verifying unions of intervals and statistical query algorithms.
New PAC-Bayes bounds use Wasserstein distances to improve generalization.
problem Lack of geometric properties in existing PAC-Bayes bounds.
method Developed new PAC-Bayes bounds with Wasserstein distances.
result Optimization guarantees translate to good generalization abilities.
PAC-Bayes bound requires prior to place mass on high-performing predictors.
problem Explaining generalization in machine learning.
method Analyzing necessary conditions for PAC-Bayes bounds to provide meaningful generalization guarantees.
result Achieving a target generalisation level requires the prior to place sufficient mass on high-performing predictors.
The cold posterior effect is explored through PAC-Bayes bounds for small sample sizes.
problem The cold posterior effect in approximate Bayesian inference for small datasets.
method Investigation through PAC-Bayes generalization bounds, focusing on temperature parameter λ.
result The temperature parameter λ in PAC-Bayes bounds captures the cold posterior effect.
PAC-Bayesian theory applied to learning optimization algorithms with generalization guarantees.
problem Learning optimization algorithms with provable generalization guarantees and explicit trade-offs.
method PAC-Bayes theory applied to learning-to-optimize, reformulating the learning procedure into a one-dimensional minimization problem.
result Learned optimization algorithms outperform deterministic worst-case analysis algorithms, even in the limit case of guaranteed convergence.
PAC-Bayes framework fails on simple 1D linear classification task.
problem Proving the learnability of simple 1D linear classification tasks using PAC-Bayes bounds.
method Demonstrated a specific 1D linear classification task that PAC-Bayes cannot analyze.
result PAC-Bayes framework cannot prove learnability of simple 1D linear classification tasks.
New method reduces computational cost for estimating PAC-Bayes bounds.
problem High computational cost in estimating PAC-Bayes bounds.
method General alternative method that makes computational savings.
result Reduces computational cost on the order of the dataset size.
New empirical PAC-Bayes bound for Markov chains with finite state space.
problem Lack of empirical bounds for Markov chains with temporal dependence.
method Proved a new PAC-Bayes bound for Markov chains, providing an empirical pseudo-spectral gap.
result First fully empirical PAC-Bayes bound for Markov chains with finite state space.
New PAC-Bayesian bounds for multi-view learning using Rényi divergence.
problem Applying PAC-Bayesian theory to multi-view learning.
method Introducing novel PAC-Bayesian bounds based on Rényi divergence for multi-view learning.
result Efficient optimization algorithms that align with theoretical bounds.
The study examines how equivariance in networks affects generalization error using PAC-Bayesian bounds.
problem Understanding how equivariance in networks impacts generalization error.
method Utilized PAC-Bayesian analysis for equivariant networks, deriving norm-based bounds for generalization error.
result The bound indicates that using larger group size in the model improves generalization error.
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.
New PAC-Bayesian bounds provide practical guarantees for neural networks.
problem Loose derandomization step in PAC-Bayesian bounds for deterministic models.
method Introduce disintegrated PAC-Bayesian bounds for deterministic models.
result Significant practical improvement over state-of-the-art bounds.
Paper improves PAC-Bayesian bounds for linear regression.
problem Improving PAC-Bayesian error bounds for linear regression.
method Proposes a tighter error bound for linear regression that converges to the generalization loss with a well-chosen temperature parameter. Also applies to non-i.i.d. training data.
result Error bound applies to certain time series generated by dynamical models.
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.
The study improves PAC-Bayesian bounds for adversarial generative models.
problem Improving generalization bounds for adversarial generative models.
method Extending PAC-Bayesian theory to generative models, developing bounds for Wasserstein and total variation distances.
result New training objectives for Wasserstein and Energy-Based GANs.
Unified framework for deriving generalization bounds in supervised learning.
problem Generalization error bounds in supervised learning.
method Data Processing Inequality PAC-Bayesian framework.
result Unified bounds on binary Kullback-Leibler generalization gap for various divergences.
Algorithm constructs confidence sets for deep neural networks with PAC guarantees.
problem Ensuring reliable predictions for deep neural networks with high confidence.
method Combines calibrated prediction and learning theory bounds.
result Constructs PAC confidence sets for various deep models.
This work provides statistical guarantees for VAEs using PAC-Bayesian theory.
problem Theoretical properties of VAEs remain open questions.
method PAC-Bayesian theory to derive statistical guarantees.
result Upper bounds on Wasserstein distance between input and generative model.
New PAC-Bayesian bounds improve Sliced-Wasserstein distances.
problem Improving statistical properties of Sliced-Wasserstein distances.
method Leveraging PAC-Bayesian theory to provide bounds and learning procedures.
result PAC-Bayesian generalization bounds for adaptive SW distances.
This work uses PAC-Bayes for structured prediction with ILE, yielding insights and algorithms.
problem Structured prediction with interdependent outputs and implicit loss embeddings.
method PAC-Bayes perspective applied to ILE framework, deriving generalization bounds and learning algorithms.
result Two learning algorithms derived from PAC-Bayes bounds, analyzed and implemented.
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.
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.
The paper improves PAC-Bayes bounds for data-dependent predictors.
problem Guaranteeing the quality of predictions on unseen examples.
method Basic PAC-Bayes inequality for stochastic kernels, leading to various bounds.
result Validates PAC-Bayes bounds without fixed 'data-free' priors and bounded losses.
PAC-Bayesian bounds for stochastic LTI systems derived.
problem Error bounds for stochastic LTI systems.
method PAC-Bayesian theory applied to autonomous stochastic LTI models.
result Error bounds for stochastic LTI systems derived.
New PAC-Bayes bounds for heavy-tailed losses using supermartingales.
problem Extending PAC-Bayes bounds to heavy-tailed losses.
method Using supermartingales and bounded variance assumption.
result PAC-Bayes generalization bounds for heavy-tailed losses.
Enhances predictive models against misspecification and outliers.
problem Suboptimal generalization under misspecification and outliers.
method Combines PACm ensemble bounds with a generalized logarithm score function. result Produces predictive distributions resistant to both misspecification and outliers.
PAC learning simplified as bipartite matching.
problem Efficiently solving PAC learning problems.
method Transductive learning and one-inclusion graphs.
result PAC learning can be reduced to bipartite matching.
PACOH improves meta-learning with theoretical guarantees and practical efficiency.
problem Meta-learning's generalization to unseen tasks is poorly understood, especially with limited meta-training tasks.
method PAC-Bayesian framework for deriving generalization bounds and developing PAC-optimal meta-learning algorithms.
result PACOH yields state-of-the-art performance in predictive accuracy and uncertainty estimation.
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.
New algorithms minimize PAC-Bayesian C-Bound for majority voting, leading to scalable and accurate predictors.
problem Improving majority vote classifiers using PAC-Bayesian bounds.
method Directly optimizing PAC-Bayesian guarantees on the C-Bound with gradient descent.
result Self-bounding majority vote learning algorithms with scalable and accurate predictors.
Empirically, the PAC-Bayesian analysis is known to produce tight risk bounds for practical machine learning algorithms. However, in its naive form, it can only deal with stochastic predictors while such predictors are rarely used and deterministic predictors often performs well in practice. To fill this gap, we develop…
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.
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.
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…
New PAC-Bayes bounds for unbounded loss functions.
problem Generalization bounds for learning problems with unbounded loss functions.
method Introducing HYPE, a new notion for loss range, and deriving a novel PAC-Bayesian generalization bound.
result PAC-Bayes framework extended to unbounded loss functions.
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.