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 “prior dependence”
The paper highlights how machine learning calibrations can be biased by training data.
problem Machine learning calibrations can be biased by the training data, affecting downstream analyses.
method The paper examines simulation-based and data-based calibrations, highlighting their prior dependence and proposing solutions.
result A recently proposed Gaussian Ansatz approach can avoid some biases in simulation-based calibrations.
SIGMA prior enables federated learning for non-factorizable models.
problem Current FL methods assume conditional independence, limiting applicability to non-factorizable models.
method SIGMA prior approximates deep generative model to induce conditional independence structure.
result SIGMA prior expands FL applicability to fields requiring modeling dependencies.
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.
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.
We consider the stochastic multi-armed bandit problem with a prior distribution on the reward distributions. We are interested in studying prior-free and prior-dependent regret bounds, very much in the same spirit as the usual distribution-free and distribution-dependent bounds for the non-Bayesian stochastic bandit. B…
Bayesian model averaging (BMA) is the state of the art approach for overcoming model uncertainty. Yet, especially on small data sets, the results yielded by BMA might be sensitive to the prior over the models. Credal Model Averaging (CMA) addresses this problem by substituting the single prior over the models by a set …
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.
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.
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.
Prior-Dependent Allocations for Bayesian Fixed-Budget Best-Arm Identification in Structured Banditsstat.ML
Algorithm identifies best arm with prior info in structured bandits.
problem Bayesian fixed-budget best-arm identification in structured bandits.
method Prior-dependent allocations based on structure and prior information.
result Improved theoretical bounds and robust performance across diverse 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.
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.
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.
Bayesian models use hyperparameters to indirectly assign priors, and this work shows how these priors can be derived from maximum entropy principles.
problem Understanding the assumptions and dependencies in Bayesian hierarchical models.
method Demonstrates how canonical distributions and maximum entropy principles can be used to derive marginal priors in hierarchical models.
result Marginal priors in hierarchical models derived from maximum entropy principles have different constraints compared to the original priors.
We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and interchangeable Dirichlet process priors to learn the structure. The introduction of…
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.
Probabilistic neural networks are typically modeled with independent weight priors, which do not capture weight correlations in the prior and do not provide a parsimonious interface to express properties in function space. A desirable class of priors would represent weights compactly, capture correlations between weigh…
The empirically successful Thompson Sampling algorithm for stochastic bandits has drawn much interest in understanding its theoretical properties. One important benefit of the algorithm is that it allows domain knowledge to be conveniently encoded as a prior distribution to balance exploration and exploitation more eff…
Providing meaningful privacy to users of location based services is particularly challenging when multiple locations are revealed in a short period of time. This is primarily due to the tremendous degree of dependence that can be anticipated between points. We propose a Rényi differentially private framework for boundi…
Bayesian convolutional deep sets improve ambiguity in stationary process modeling.
problem Ambiguity in translation equivariant functional representations due to insufficient data points.
method Introduce Bayesian convolutional deep sets with task-dependent stationary prior.
result Improves representation quality compared to kernel smoother and non-parametric models.
Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropriate priors when exchangeability assumptions do not hold, and instead …
Recursive PAC-Bayes: A Frequentist Approach to Sequential Prior Updates with No Information Losscs.LG
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.
Thompson sampling used for linear bandits with normal-gamma priors.
problem Optimizing decisions in uncertain environments with linear dependencies and unknown parameters.
method Bayesian Thompson sampling with multivariate normal-gamma priors.
result Derivation of a Bayesian regret bound for the approach.
The vast majority of optimization and online learning algorithms today require some prior information about the data (often in the form of bounds on gradients or on the optimal parameter value). When this information is not available, these algorithms require laborious manual tuning of various hyperparameters, motivati…
Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Spacecs.LG
Unified framework for convergence of discrete diffusion models without state space size dependence.
problem Fundamental limitations in existing convergence theory for discrete diffusion models, especially under singular priors and large vocabularies.
method Unified adjoint-equation-based framework that establishes dimension-free convergence guarantees in any integral probability metric (IPM).
result First dimension-free convergence bounds applicable to both masked and uniform priors, free of state space size .
Spike-and-slab priors are popular Bayesian solutions for high-dimensional linear regression problems. Previous theoretical studies on spike-and-slab methods focus on specific prior formulations and use prior-dependent conditions and analyses, and thus can not be generalized directly. In this paper, we propose a class o…
In many problem settings, parameter vectors are not merely sparse but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity." Classical sparse regression methods, such as the lasso and automatic relevance determination (ARD), which model par…
New method uses quotient predictor space for better PAC-Bayes bounds, reducing KL divergence and improving model performance.
problem Overparameterized models with continuous symmetries can lead to biased predictions.
method Perform PAC-Bayesian analysis on quotient predictor space, constructing a canonical prior that reflects model's implicit bias.
result The new prior reduces KL divergence and improves model performance in experiments.
While Bayesian methods are praised for their ability to incorporate useful prior knowledge, in practice, convenient priors that allow for computationally cheap or tractable inference are commonly used. In this paper, we investigate the following question: for a given model, is it possible to compute an inference result…
The study optimizes Gaussian process approximations for finite-rank models.
problem Posterior behavior of finite-rank approximations differs from parent GP priors.
method Locally supported basis expansions with dependent Gaussian coefficients.
result Finite-rank expansions inherit the same posterior contraction rate as parent GP priors.
New method adapts DLMs to intrinsic data dependence without prior knowledge.
problem Understanding how unmasking schedules affect DLM generation quality.
method Adapts unmasking schedule to target data distribution's dependence structure.
result Sampling convergence guarantees improve for low-complexity distributions.
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, …
DALI improves inference for GANs by matching prior and conditional distributions.
problem Effective inference for generative adversarial models (GANs).
method Explicitly matches prior and conditional distributions in data and code spaces, constraining dependency structure.
result Significantly improves reconstruction and generation compared to other GAN inference models.
Transforming Causality: Transformer-Based Temporal Causal Discovery with Prior Knowledge Integrationcs.LG
Transformer-based method for causal discovery with prior knowledge integration.
problem Complex nonlinear dependencies and spurious correlations in time series data.
method Multi-layer Transformer forecaster with gradient-based causal structure extraction and attention masking for prior knowledge integration.
result Significant improvement in causal discovery and causal lag estimation compared to state-of-the-art methods.
RBM models reveal how hidden unit tail behavior affects pattern reconstruction.
problem Understanding how the tail behavior of hidden units in RBMs influences pattern reconstruction.
method Identified an effective energy function for RBMs and studied its local minima.
result The ability to reconstruct patterns depends on the tail behavior of the hidden unit prior distribution.
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…
Model-based free-breathing cardiac MRI reconstruction using deep learned \& STORM priors: MoDL-STORMcs.LG
We introduce a model-based reconstruction framework with deep learned (DL) and smoothness regularization on manifolds (STORM) priors to recover free breathing and ungated (FBU) cardiac MRI from highly undersampled measurements. The DL priors enable us to exploit the local correlations, while the STORM prior enables us …
The study finds that memorization is necessary or harmful depending on the prior distribution and noise level.
problem The impact of memorization on generalization in overparameterized models.
method An overparameterized linear model with general priors in a Bayesian setup.
result Explicit conditions for optimal generalization based on the prior distribution and noise level.
This paper explores minimax-Bayes solutions for reinforcement learning problems.
problem How to select appropriate priors for decision making under uncertainty in sequential decision making.
method Study of minimax-Bayes solutions for various reinforcement learning problems.
result Minimax policies are more robust than standard priors.
This paper relaxes the common prior assumption in the public and private information game of Morris and Shin (2000, 2004). For the generalized game, where the agent's prior expectations are heterogenous, it derives a sharp condition for the emergence of unique/multiple equilibria. This condition indicates that unique e…
We consider the scenario where the parameters of a probabilistic model are expected to vary over time. We construct a novel prior distribution that promotes sparsity and adapts the strength of correlation between parameters at successive timesteps, based on the data. We derive approximate variational inference procedur…
Develops probabilistic models for gene regulatory network inference.
problem Challenges in reconstructing gene regulatory networks from genome-wide data.
method Two complementary frameworks: PMF-GRN and GLM-Prior.
result Probabilistic inference refines regulatory estimates with quantified uncertainty.
Bayesian neural networks with dependent weights converge to Gaussian mixtures.
problem Limitations of standard Gaussian priors in neural networks.
method Posterior analysis with Gaussian likelihood for networks with dependent weights.
result Posterior distribution identified in the wide-width limit, ensuring invertibility of random covariance matrix.
MetaTS learns to explore better by meta-learning prior from bandit instances.
problem Efficient exploration in bandit problems.
method MetaThompson Sampling (MetaTS) that meta-learns the prior from bandit instances.
result MetaTS quickly adapts to unknown prior and achieves better exploration.
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.
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.
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…