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.
One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary conditions. We construct multi-output Gaussian process priors with realizations in the so…
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.
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.
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…
Novel approach for estimating conditional expectations using Bayesian quadrature.
problem Estimating conditional expectations with costly evaluations.
method Probabilistic numerical methods incorporating prior smoothness knowledge.
result Fast convergence rate and uncertainty quantification.
Paper shows how meta-learning can reduce prior learning cost.
problem Learning the prior in meta-learning with fast rates.
method Examined Gibbs algorithm in meta-learning context.
result Bernstein's condition holds at meta level, reducing prior learning cost.
Imagine that measurements are made at times t0 and t1 of the trajectory of a physical system whose governing laws are given approximately by a class A of so-called {\em prior vector fields}. Because the physical laws are not known precisely, it might be that the measurements are not realised by the integ…
We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the convergence rates. Under similar "prior mass and testing" conditions considered in the literature, the rat…
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…
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…
This work shows that Gaussian is the only prior for optimal linear estimation in L1 loss.
problem Optimal linear estimation of a random variable from noisy observations under L1 fidelity criterion. method Analyzes the conditions under which the conditional median is a linear estimator and identifies the Gaussian distribution as the only prior that induces linearity.
result Gaussian is the only prior distribution that induces linearity in the conditional median for L1 loss. New framework uses score-based priors to solve ill-conditioned polynomial equations, improving signal recovery from noisy data.
problem Recovering signals from low-order moments in inverse problems, especially ill-conditioned polynomial equations.
method Integrates score-based diffusion priors with moment-based estimators to regularize and solve nonlinear inverse problems.
result Diffusion priors improve recovery from third-order moments and make super-resolution MTD feasible.
Generative models produce realistic objects in many domains, including text, image, video, and audio synthesis. Most popular models---Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs)---usually employ a standard Gaussian distribution as a prior. Previous works show that the richer family of pri…
Develops methods for constructing likelihoods and priors for Bayesian networks.
problem Learning parameters and structure of Bayesian networks from limited data.
method Introduces assumptions for constructing likelihoods and priors from small assessments.
result Allows construction of likelihoods and priors for a wide range of network structures.
A new meta-learning method using shared variational inference.
problem Meta-learning with uncertainty over model parameters.
method Shared amortized variational inference network for conditional prior and posterior.
result Prevents collapse of conditional prior to Dirac delta function.
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.
New method uses Gaussian processes for solving linear PDEs with boundary conditions.
problem Solving linear PDEs with boundary conditions.
method Boundary Ehrenpreis--Palamodov Gaussian Processes (B-EPGPs).
result Significant accuracy and resource improvements over existing methods.
It is well-known that the distribution over functions induced through a zero-mean iid prior distribution over the parameters of a multi-layer perceptron (MLP) converges to a Gaussian process (GP), under mild conditions. We extend this result firstly to independent priors with general zero or non-zero means, and secondl…
CW-Gen models improve probabilistic time series forecasting by incorporating prior information.
problem Challenges in probabilistic forecasting of multivariate time series due to non-stationarity, inter-variable dependencies, and distribution shifts.
method CW-Gen framework that incorporates prior information through conditional whitening. JMCE learns conditional mean and covariance, improving sample quality.
result CW-Gen consistently enhances predictive performance, capturing non-stationary dynamics and inter-variable correlations more effectively than prior-free approaches.
Improved compressed sensing using a generator that learns from measurements.
problem Signal recovery accuracy in compressed sensing.
method Proposes a framework that uses measurement-conditional generative models to refine signal estimation.
result Uniformly superior performance with up to an order of magnitude reduction in reconstruction error.
Rényi Neural Processes replace KL divergence with Rényi divergence to improve NP performance.
problem Parameterization coupling in Neural Processes leads to prior misspecification.
method Propose Rényi Neural Processes (RNP) by replacing KL divergence with Rényi divergence.
result Significant performance improvements in real-world problems, including better log-likelihoods.
In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. This characterisation shows that it is indeed a well-chosen condition being equivalent to several previously used alternative notions of no-arbitrage and …
Ens-CGP synthesizes ensemble-based inference with Gaussian processes.
problem Ensemble-based inference and Gaussian process modeling.
method Formulates Ens-CGP as a conditional Gaussian process for ensemble moments.
result Ens-CGP provides a unified probabilistic foundation for Kalman-type methods.
C-t3VAE improves class representation in long-tailed generative models.
problem Latent geometric bias in VAEs under class imbalance.
method Per-class Student's t-distribution priors, closed-form objective, equal-weight latent mixture.
result Consistently lower FID scores and better class-balanced generation for severely imbalanced datasets.
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.
Proposes a method to learn conditional VAEs from datasets with missing covariates.
problem Learning conditional VAEs from datasets with missing covariates.
method Augments conditional VAEs with a prior distribution for missing covariates and estimates their posterior using amortised variational inference.
result The proposed method outperforms previous methods in learning conditional VAEs from non-temporal, temporal, and longitudinal datasets.
Prediction of future states of the environment and interacting agents is a key competence required for autonomous agents to operate successfully in the real world. Prior work for structured sequence prediction based on latent variable models imposes a uni-modal standard Gaussian prior on the latent variables. This indu…
This paper establishes for the first time the predictive performance of speed priors and their computational complexity. A speed prior is essentially a probability distribution that puts low probability on strings that are not efficiently computable. We propose a variant to the original speed prior (Schmidhuber, 2002),…
We derive and approximate the conjugate prior of Dirichlet and beta distributions.
problem Intractability of conjugate prior for Dirichlet and beta distributions.
method Derive conjugate prior, define closed-form approximation, and provide algorithm.
result Closed-form approximation enables fully tractable Bayesian treatment.
Corrected and improved simulation methods for Dirichlet-Laplace prior.
problem Incorrect sampling order in original MCMC method for DL prior.
method Provided two solutions: correction and alternative algorithm.
result Improved simulation methods for DL prior without affecting theoretical results.
We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the functional relationship between the task variables and the parameters of this con…
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 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.
Study improves convergence rates for GVI under prior misspecification.
problem Improving convergence rates for GVI under prior misspecification.
method Proves rates of convergence and robustness to prior misspecification in GVI framework.
result Establishes sufficient conditions for existence and uniqueness of GVI posteriors.
Model approximates market prices and returns without prior market dynamics.
problem Simultaneously approximate market prices and log returns.
method GDN model of Kratsios and Papon (2022) for generalized Ornstein-Uhlenbeck process.
result Universal approximation guarantees for conditional distributions and contingent claims.
TGD improves conditional sampling by concentrating computation on promising trajectories.
problem Efficiently training-free conditional sampling with diffusion priors.
method Tempered Guided Diffusion (TGD) using annealed sequential Monte Carlo.
result TGD yields a consistent particle approximation to the posterior as the number of particles grows.
We formulate a new class of conditional generative models based on probability flows. Trained with maximum likelihood, it provides efficient inference and sampling from class-conditionals or the joint distribution, and does not require a priori knowledge of the number of classes or the relationships between classes. Th…
New method learns fusion rules from few images using granular ball priors.
problem Challenges in supervised learning for image fusion with limited data.
method Introduces incomplete priors and Granular Ball Pixel Computation (GBPC) algorithm.
result Lightweight neural network learns effective fusion rules from few images.
This paper presents a Bayesian image segmentation model based on Potts prior and loopy belief propagation. The proposed Bayesian model involves several terms, including the pairwise interactions of Potts models, and the average vectors and covariant matrices of Gauss distributions in color image modeling. These terms a…
Bayesian framework uses AI-generated data to improve parameter estimation.
problem Parameter estimation in models with unknown or unspecified likelihood.
method Exponentially tilted empirical likelihood with Dirichlet process posterior.
result AI-generated data can provide useful regularization for parameter estimation.
The paper examines conditions for linearity in a conditional mean estimator under vector Poisson noise.
problem Conditions for linearity of the conditional mean estimator in vector Poisson noise.
method Analyzes prior distributions and their impact on the conditional mean estimator's linearity.
result The only prior distribution that induces linearity is a product gamma distribution, and non-zero dark current parameter prevents linearity.
Weak diffusion priors can still perform well in inverse problems.
problem Using mismatched or low-fidelity diffusion priors in inverse problems.
method Extensive experiments and theoretical analysis combining Bayesian-consistency theory and local-correlation analysis.
result Weak priors succeed when measurements are highly informative, and they fail in other regimes.
Proposes sampling from reverse diffusion posteriors for contextual bandits.
problem Complex distributions in contextual bandits.
method Approximate posterior sampling with a diffusion model prior using Laplace approximation.
result Empirically consistent and efficient approximations for contextual bandits.
Study high-dimensional Bayesian linear regression using variational inference.
problem High-dimensional Bayesian linear regression with product priors.
method Non-linear large deviations theory and variational inference.
result Unique optimizer in variational problem governs posterior distribution under separation condition.
This paper formulates an utility indifference pricing model for investors trading in a discrete time financial market under non-dominated model uncertainty. The investors preferences are described by strictly increasing concave random functions defined on the positive axis. We prove that under suitable conditions the m…
Bayesian method uses deep learning prior for CT reconstruction.
problem Imaging inverse problems in CT reconstruction.
method SA-Roundtrip prior with HMC-pCN sampler.
result Outperforms state-of-the-art methods in CT reconstruction.
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…