The Probably Approximately Correct (PAC) Bayes framework (McAllester, 1999) can incorporate knowledge about the learning algorithm and (data) distribution through the use of distribution-dependent priors, yielding tighter generalization bounds on data-dependent posteriors. Using this flexibility, however, is difficult,…
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48 results for “data-dependent priors”
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.
PriorGrad: Improving Conditional Denoising Diffusion Models with Data-Dependent Adaptive Priorstat.ML
PriorGrad improves speech synthesis models by using data-dependent adaptive priors.
problem Inefficiency in denoising diffusion models due to mismatch between prior and data distributions.
method Proposes PriorGrad, an adaptive prior derived from data statistics based on conditional information.
result PriorGrad achieves faster convergence and superior performance in speech synthesis models.
Generalization Guarantees for Representation Learning via Data-Dependent Gaussian Mixture Priorsstat.ML
The study improves representation learning bounds using data-dependent Gaussian mixtures.
problem Improving generalization in representation learning.
method Established bounds using relative entropy and MDL of latent variables.
result The approach significantly improves generalization over existing methods.
New data-dependent priors improve PAC-Bayes bounds.
problem Improving PAC-Bayes bounds for nonconvex learning.
method Using data to learn a conditional expectation of the posterior, given a subset of training data.
result Data-dependent oracle priors lead to stronger PAC-Bayes bounds.
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.
Optimal kernel in KR can be data-dependent, improving model performance.
problem Fixed kernel in KR limits model performance.
method Considered data-dependent kernels for KR, using posterior covariance.
result Data-dependent kernel choice leads to optimal performance.
TSFlow uses Gaussian processes to match priors for better time series forecasting.
problem Difficulties in aligning generative models' priors with time series data.
method Conditional flow matching (CFM) with Gaussian processes, optimal transport, and data-dependent priors.
result TSFlow produces high-quality unconditional samples and competitive forecasting results.
Framework evaluates the impact of prior knowledge in deep learning models.
problem Mitigating data-driven model shortcomings like data dependence and generalization ability.
method Model-agnostic framework inspired by interpretable machine learning, assessing data volume and estimation range effects.
result Complex relationship between data and knowledge, including dependence, synergistic, and substitution effects.
One of the major shortcomings of variational autoencoders is the inability to produce generations from the individual modalities of data originating from mixture distributions. This is primarily due to the use of a simple isotropic Gaussian as the prior for the latent code in the ancestral sampling procedure for the da…
Two data-dependent information metrics are developed to quantify the information of the prior and likelihood functions within a parametric Bayesian model, one of which is closely related to the reference priors from Berger, Bernardo, and Sun, and information measure introduced by Lindley. A combination of theoretical, …
In this paper we analyze a budgeted learning setting, in which the learner can only choose and observe a small subset of the attributes of each training example. We develop efficient algorithms for ridge and lasso linear regression, which utilize the geometry of the data by a novel data-dependent sampling scheme. When …
This paper presents eight PAC-Bayes bounds to analyze the generalization performance of multi-view classifiers. These bounds adopt data dependent Gaussian priors which emphasize classifiers with high view agreements. The center of the prior for the first two bounds is the origin, while the center of the prior for the t…
We show that Entropy-SGD (Chaudhari et al., 2017), when viewed as a learning algorithm, optimizes a PAC-Bayes bound on the risk of a Gibbs (posterior) classifier, i.e., a randomized classifier obtained by a risk-sensitive perturbation of the weights of a learned classifier. Entropy-SGD works by optimizing the bound's p…
In this work, we improve upon the stepwise analysis of noisy iterative learning algorithms initiated by Pensia, Jog, and Loh (2018) and recently extended by Bu, Zou, and Veeravalli (2019). Our main contributions are significantly improved mutual information bounds for Stochastic Gradient Langevin Dynamics via data-depe…
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.
Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost and it is difficult to design nonstationary GP priors in practice. In this paper, we propose a sparse Gaussian process model, EigenGP, based on the Karhunen-Loeve (KL) expan…
We present algorithms for topic modeling based on the geometry of cross-document word-frequency patterns. This perspective gains significance under the so called separability condition. This is a condition on existence of novel-words that are unique to each topic. We present a suite of highly efficient algorithms based…
Feed-forward neural networks can be understood as a combination of an intermediate representation and a linear hypothesis. While most previous works aim to diversify the representations, we explore the complementary direction by performing an adaptive and data-dependent regularization motivated by the empirical Bayes m…
Ensemble learning, the machine learning paradigm where multiple algorithms are combined, has exhibited promising perfomance in a variety of tasks. The present work focuses on unsupervised ensemble classification. The term unsupervised refers to the ensemble combiner who has no knowledge of the ground-truth labels that …
The paper studies multi-view representation learning with generalization guarantees and a new regularizer.
problem Distributed multi-view representation learning with correct estimation at a decoder.
method Generalization bounds using relative entropy and MDL, data-dependent Gaussian mixture priors.
result Data-dependent Gaussian mixture priors lead to good performance and outperform existing methods.
New method improves causal structure discovery with Prior-Fitted Networks.
problem Errors in likelihood estimation limit proper causal structure discovery.
method Amortized causal discovery with Prior-Fitted Networks.
result Significant gains in structure recovery compared to baselines.
A new learning method uses data to learn from large model sets.
problem Learning with large sets of candidate models where uniform convergence is hard.
method Data-dependent learning that incorporates empirical data less reliant on prior assumptions.
result Demonstrates improved generalization in various learning assumptions.
The Gibbs algorithm's generalization error is bounded, improving with prior volume in low temperatures.
problem Bounding the generalization error of the Gibbs algorithm in low temperature regimes.
method Analyzes the Gibbs algorithm's performance, extending known high-temperature bounds to low-temperature scenarios.
result With high probability, the generalization error decreases with the total prior volume of similar hypotheses.
This work proves generalization bounds for neural networks without Lipschitz assumptions.
problem Proving generalization guarantees for neural networks without Lipschitz continuity.
method Introduces a data-dependent fractal dimension and uses it to prove generalization bounds.
result Generalization bounds are proven without requiring Lipschitz continuity.
New KD-tree based method for private synthetic data generation.
problem Creating private synthetic data that accurately represents real data.
method KD-trees combined with noise perturbation for differentially private synthetic data generation.
result Our data-dependent approach improves utility over prior work and scales well.
We reformulate data-dependent constraints to ensure they are always met with high probability.
problem Ensuring fairness and stability in machine learning models with data-dependent constraints.
method Calibrated reformulation of constraints to guarantee satisfaction with a specified probability.
result Our method guarantees that fairness constraints are met at test time with high probability.
Improved flow-based models capture dependencies better with multi-scale autoregressive priors.
problem Limited expressiveness of flow-based models for long-range data dependencies.
method Introducing channel-wise dependencies through multi-scale autoregressive priors (mAR) in split coupling flow layers (mAR-SCF).
result Achieves state-of-the-art density estimation results on MNIST, CIFAR-10, and ImageNet.
New bounds use IPMs to improve generalization in machine learning.
problem Improving generalization bounds in machine learning.
method PAC-Bayes bounds with Integral Probability Metrics (IPM).
result Natural interpolation between worst-case and favorable cases.
We present a study of generalization for data-dependent hypothesis sets. We give a general learning guarantee for data-dependent hypothesis sets based on a notion of transductive Rademacher complexity. Our main result is a generalization bound for data-dependent hypothesis sets expressed in terms of a notion of hypothe…
New bounds explain modern machine learning algorithms' generalization.
problem Explaining generalization behavior of modern machine learning algorithms.
method Proposes a new complexity measure based on empirical Rademacher complexity of an algorithm- and data-dependent hypothesis class.
result Obtains novel bounds with finite fractal dimension, simplifies proofs, and recovers known results.
In this paper, we present a novel way to summarize the structure of large graphs, based on non-parametric estimation of edge density in directed multigraphs. Following coclustering approach, we use a clustering of the vertices, with a piecewise constant estimation of the density of the edges across the clusters, and ad…
A new data-adaptive prior stabilizes kernel learning in operators.
problem Learning kernels in operators from data is ill-posed due to nonlocal dependence.
method Introduces a data-adaptive prior to stabilize the Bayesian posterior mean.
result The data-adaptive prior achieves a stable posterior with small noise limits.
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.
Paper introduces data-dependent SSP for private linear and logistic regression.
problem Private linear and logistic regression with better performance.
method Data-dependent sufficient statistic perturbation (SSP) for linear and logistic regression.
result Data-dependent SSP outperforms state-of-the-art methods for linear and logistic regression.
The paper shows robustness and generalization are closely connected via data-dependent bounds.
problem Connecting robustness and generalization in machine learning.
method Data-dependent generalization bounds that reduce dependence on covering number and hypothesis space.
result Proves robustness implies generalization, with near-exponential improvements in various situations.
LLEB uses a learned prior to quantify neural network uncertainty.
problem Quantifying uncertainty in neural network predictions.
method LLEB uses a learnable prior as a normalizing flow to maximize the evidence lower bound.
result LLEB performs on par with existing approaches in uncertainty quantification.
A new approach uses partial likelihood to improve tree-based density estimation and inference.
problem Inference on tree-based models suffers from overfitting and reduced efficiency due to data-independent partitioning.
method Proposes a partial likelihood approach to data-dependent partitioning of tree-based models.
result Significant gains in estimation accuracy and computational efficiency from adopting partial likelihood.
This paper improves SSL methods using ensemble techniques with data-dependent weighted losses.
problem Improving SSL performance and robustness with large unlabeled data.
method Developed a framework for weighted cross-entropy losses in ensembling SSL methods without altering the backbone.
result Our method outperforms state-of-the-art SSL methods on ImageNet-1K, especially in few-shot learning.
New method certifies deep graph classifiers with tighter risk bounds.
problem Certifying the reliability of deep graph classifiers.
method Linearized deep assignment flows with random initial conditions, using PAC-Bayes risk certification.
result Computes tighter out-of-sample risk certificates efficiently.
New algorithm achieves data-dependent regret bounds in MDPs with unknown transitions.
problem Achieving best-of-both-worlds guarantees with data-dependent regret bounds in MDPs with unknown transitions.
method Optimistic follow-the-regularized-leader algorithm with new optimistic Q-function estimators and transition bonus.
result First-order, second-order, and path-length bounds with polylog(T) regret in the stochastic regime.
ZNMF improves facial recognition performance using data-dependent penalties.
problem Facial recognition performance in the Cambridge ORL database.
method ZNMF uses data-dependent auxiliary constraints to modify NMF.
result ZNMF outperforms other constrained NMF algorithms in facial recognition.
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.
Survey on new data-dependent bounds for neural networks.
problem Generalization of overparameterized neural networks.
method Extending PAC-Bayesian theory, refining complexity terms, and replacing information-theoretic terms with stability assumptions.
result Unified template inequality and comparison of bounds.
Deep ensembles mimic Bayesian averaging with learned priors.
problem Quantifying uncertainty in neural networks.
method Showed deep ensembles perform exact Bayesian averaging with an implicitly learned data-dependent prior.
result Deep ensembles are Bayesian and provide an explanation for their strong empirical performance.
New algorithm learns changing discrete distributions with minimal drift error.
problem Learning discrete distributions that change over time with limited past samples.
method Adaptive algorithm using data-dependent bounds to balance statistical and drift errors.
result Tighter statistical error bounds for drifting distributions with or without finite support.
Fast robust subspace tracking in sparse data-dependent noise with near-optimal delay.
problem Robustly tracking time-varying subspaces in the presence of sparse outliers.
method Introduces a fast mini-batch robust ST solution under mild assumptions.
result Provably correct subspace tracking with near-optimal delay and same time complexity as simple PCA.
Reweighting improves risk bounds in certain data regions.
problem Improving risk bounds in classification and heteroscedastic regression.
method Weighted empirical risk minimization with a data-dependent weight function.
result A weighted ERM estimator can achieve superior performance in specific sub-regions.