Variational Bayes (VB) methods have emerged as a fast and computationally-efficient alternative to Markov chain Monte Carlo (MCMC) methods for scalable Bayesian estimation of mixed multinomial logit (MMNL) models. It has been established that VB is substantially faster than MCMC at practically no compromises in predict…
The study examines MCMC methods for arbitrary objectives and finds likelihood sharpness impacts performance and regularization.
problem Limitations of MCMC methods for arbitrary objective functions.
method Two-block MCMC framework with Metropolis-Hastings and Gibbs sampling, exploring likelihood curvature and sharpness.
result Likelihood sharpness governs in-sample performance and regularization inferred by training data.
New MCMC method corrects bias without extra cost.
problem Correcting bias in MCMC algorithms without additional computational cost.
method Generalized Markov Chain Importance Sampling methods.
result Proposed methods are more efficient than Metropolis-Hastings versions.
Paper proposes an alternative to MCMC for sampling in energy-based models.
problem Difficulty in generating samples from the current energy function in contrastive approaches.
method Viewing the evolution of the modeling distribution as the evolution of the energy function and samples from this distribution along a time-dependent vector field.
result The proposed method efficiently matches the current distribution in a finite time, unlike MCMC.
Performing exact Bayesian inference for complex models is computationally intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are expensive for large datasets and high-dimensional models. A standard approach to mitigate this complexity consists i…
Improved Bayesian computation for imaging problems using a new MCMC method.
problem Challenges in Bayesian computation for imaging inverse problems due to high dimensionality and non-smoothness.
method Introduces a new accelerated proximal MCMC method (ls SK-ROCK) that combines data augmentation and relaxation with proximal MCMC.
result The method converges faster and achieves better accuracy than state-of-the-art approaches.
New method for MCMC models without perfect or sequential samplers.
problem Bayesian inference for complex models with intractable terms.
method Utilizes tractable independence model to construct unbiased estimates.
result Scalable method for high-dimensional models.
New MCMC method learns sparse preconditioner for high-dimensional problems.
problem High-dimensional sampling with complex correlation structures.
method Adaptive MCMC with sparse preconditioner using online PCA.
result Significant reduction in computational complexity and improved performance.
Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a domain. Structure learning forms one of the inference challenges of statistical graphi…
This paper proposes a method to train energy-based models using variational auto-encoders for efficient sampling.
problem Training energy-based models by maximum likelihood is challenging due to intractable partition functions and difficult sampling from the model distribution.
method The authors propose using a variational auto-encoder to initialize finite-step MCMC sampling, specifically Langevin dynamics, to train the energy-based model.
result The proposed method enables training energy-based models using maximum likelihood, generating samples comparable to GANs and EBMs.
Normalized random measures (NRMs) provide a broad class of discrete random measures that are often used as priors for Bayesian nonparametric models. Dirichlet process is a well-known example of NRMs. Most of posterior inference methods for NRM mixture models rely on MCMC methods since they are easy to implement and the…
It is well known that Markov chain Monte Carlo (MCMC) methods scale poorly with dataset size. A popular class of methods for solving this issue is stochastic gradient MCMC. These methods use a noisy estimate of the gradient of the log posterior, which reduces the per iteration computational cost of the algorithm. Despi…
It is challenging to develop stochastic gradient based scalable inference for deep discrete latent variable models (LVMs), due to the difficulties in not only computing the gradients, but also adapting the step sizes to different latent factors and hidden layers. For the Poisson gamma belief network (PGBN), a recently …
Bayesian structure learning improved using GFlowNets.
problem Inferring Bayesian network structure from data.
method Using Generative Flow Networks (GFlowNets) for approximating posterior DAG distributions.
result DAG-GFlowNet provides an accurate approximation of the posterior over DAGs.
A D-Wave quantum annealer (QA) having a 2048 qubit lattice, with no missing qubits and couplings, allowed embedding of a complete graph of a Restricted Boltzmann Machine (RBM). A handwritten digit OptDigits data set having 8x7 pixels of visible units was used to train the RBM using a classical Contrastive Divergence. E…
A new method uses MCMC-assisted normalizing flows for efficient Bayesian sampling.
problem Sampling from complex posterior distributions in Bayesian statistics.
method Training a normalizing flow using direct KL divergence and MCMC assistance.
result The method improves sampling efficiency for complicated posterior distributions.
Many Markov Chain Monte Carlo (MCMC) methods leverage gradient information of the potential function of target distribution to explore sample space efficiently. However, computing gradients can often be computationally expensive for large scale applications, such as those in contemporary machine learning. Stochastic Gr…
Accelerates MCMC sampling for large-scale problems using machine learning.
problem Efficiently sampling large-scale Bayesian inference problems with high computational cost.
method Integrates low-fidelity machine learning models into a multilevel MCMC framework.
result Significantly accelerates multilevel sampling by a factor of two with similar accuracy.
SVI and GP surrogates improve calibration of ABMs in epidemiology.
problem Calibrating stochastic ABMs in epidemiology is computationally expensive.
method Stein Variational Inference (SVI) with Gaussian process (GP) surrogates.
result SVI maintains comparable predictive accuracy and calibration effectiveness to MCMC.
Stein variational gradient descent improves inference in Gaussian process models.
problem Inference in Gaussian process models with non-Gaussian likelihoods and large data volumes is computationally intensive and inaccurate with traditional methods.
method Stein variational gradient descent (SVGD) for non-parametric inference.
result SVGD monotonically decreases the Kullback-Leibler divergence from the sampling distribution to the true posterior.
Fast variational Bayes methods improve geospatial data analysis speed and accuracy.
problem Inaccurate and slow variational Bayes methods for large geospatial data.
method Combination of calculus of variations, closed-form gradient updates, and linear response corrections.
result Comparable accuracy to spNNGP with reduced computational costs and faster speed.
New algorithm tunes SGMCMC hyperparameters for scalable Bayesian inference.
problem Tuning hyperparameters for SGMCMC is challenging due to lack of principled methods.
method Proposes a bandit-based algorithm using Stein discrepancies to tune hyperparameters.
result The method effectively tunes SGMCMC hyperparameters for various applications.
New MCMC methods improve efficiency for large network inference.
problem Efficiency of Metropolis within Gibbs for large networks.
method Combination of split Hamiltonian Monte Carlo and Firefly Monte Carlo.
result New methods outperform Metropolis within Gibbs on synthetic and real networks.
Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed acyclic graph (DAG) is highly challenging mainly due to the vast number of possible…
A new variational method speeds up Bayesian phylogenetic inference.
problem Slow and inefficient MCMC methods in Bayesian phylogenetic inference.
method Combining subsplit Bayesian networks with variational inference for efficient tree topology and branch length estimation.
result Variational approach provides competitive performance with significantly fewer iterations.
A new algorithm PBNN improves scalability of Bayesian Neural Networks.
problem Scalability issues in Neural Network posterior sampling with large datasets.
method Penalty Bayesian Neural Networks (PBNN) using subsampled batch data.
result PBNN achieves good predictive performance with small mini-batch sizes.
New KSDs control moments in approximations, improving diagnostics and tests.
problem Inability of standard KSDs to control moment convergence.
method Developed alternative diffusion KSDs under sufficient conditions.
result First KSDs to exactly characterize q-Wasserstein convergence.
Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run independent MCMC algorithms targeting the corresponding subposterior, can spread…
TADDAA improves accuracy diagnostics for variational approximations.
problem Challenges in evaluating the accuracy of variational approximations.
method Uses many short parallel MCMC chains to obtain lower bounds on the error of each posterior functional of interest.
result Validates the practical utility and computational efficiency of TADDAA on various models.
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.
New algorithms improve MPBART for HIV patient data.
problem Improving inference for multinomial outcomes in HIV patient data.
method Introduced two new algorithms for fitting MPBART.
result Better performance in MCMC convergence and predictive accuracy.
ChEES-HMC improves SMC samplers' efficiency and speed.
problem Efficiently sampling from complex posterior distributions.
method Incorporating ChEES-HMC into SMC samplers.
result ChEES-HMC outperforms NUTS in speed and efficiency.
A new Metropolis-Hastings algorithm uses Gaussian Processes to speed up sampling from complex models.
problem Sampling from computationally expensive probabilistic models.
method Two-stage Metropolis-Hastings algorithm with a Gaussian Process surrogate model.
result The approach learns the target distribution while sampling, eliminating the need for pre-training.
SGBD algorithm improves robustness in Bayesian sampling.
problem Inefficiency of existing MCMC algorithms in large datasets.
method Extends Barker MCMC to stochastic gradient framework, introducing bias-corrected version.
result SGBD is more robust to hyperparameter tuning and gradient noise.
Unified framework for MCMC algorithms simplifies their design and application.
problem Diverse MCMC algorithms with varying principles and applications.
method Involutive MCMC (iMCMC) framework unifying MCMC approaches.
result Unified view of MCMC algorithms facilitates the development of new and more efficient algorithms.
The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets…
New samplers improve compositional generation with diffusion models.
problem Improving compositional generation with diffusion models.
method Score-based interpretation, energy-based parameterization, Metropolis-corrected samplers.
result New samplers enable successful compositional generation across various tasks.
Semi-Implicit Variational Inference (SIVI) is improved with SIVI-SM using score matching.
problem Intractable densities in variational distributions hinder SIVI training.
method SIVI-SM uses score matching to handle intractable densities in a minimax formulation.
result SIVI-SM outperforms ELBO-based SIVI methods in Bayesian inference tasks.
EP-GFlowNets parallelize GFlowNet training for large-scale Bayesian inference.
problem Prohibitive repeated evaluations of unnormalized distributions for large-scale posterior sampling.
method Divide-and-conquer approach with server learning from local models.
result EP-GFlowNets enable efficient parallel and federated Bayesian inference.
Proposes a new method for fiducial inference using autoencoders.
problem Computational difficulty in extracting generalized fiducial distributions.
method Designs a fiducial autoencoder (FAE) to generate generalized fiducial samples and applies approximate fiducial computation (AFC) to improve accuracy.
result Effective and accurate fiducial inference achieved through FAE and AFC.
Unified framework for MCMC and machine learning problems.
problem Intersection of MCMC and machine learning problems.
method Unified framework integrating various MCMC and machine learning techniques.
result Translation and generalization of theory and methods.
JaxSGMC simplifies SG-MCMC for Bayesian deep learning.
problem Uncertainty quantification in deep learning models.
method Modular stochastic gradient MCMC in JAX.
result Facilitates trustworthy neural network predictions.
Paper proposes first unlearning algorithm for MCMC models.
problem Enforcing right to be forgotten in AI causes high costs for data deletion.
method Converts MCMC unlearning to explicit optimization problem, designs MCMC influence function.
result MCMC unlearning does not compromise generalizability of models.
Stochastic gradient Hamiltonian Monte Carlo (SGHMC) is an efficient method for sampling from continuous distributions. It is a faster alternative to HMC: instead of using the whole dataset at each iteration, SGHMC uses only a subsample. This improves performance, but introduces bias that can cause SGHMC to converge to …
Stochastic EM with biased MCMC improves inference stability.
problem Intractable E-step in EM algorithm.
method Stochastic approximation with biased MCMC.
result ULA is more stable and sometimes faster than MALA.
A VB method for high-dimensional regression with student-t priors achieves nearly optimal performance and computational efficiency.
problem High-dimensional linear model inferences with heavy-tailed shrinkage priors.
method Variational Bayesian (VB) procedure for high-dimensional linear models with student-t priors.
result The VB method achieves nearly optimal contraction rate and computational efficiency, outperforming MCMC methods.
It is known that the Langevin dynamics used in MCMC is the gradient flow of the KL divergence on the Wasserstein space, which helps convergence analysis and inspires recent particle-based variational inference methods (ParVIs). But no more MCMC dynamics is understood in this way. In this work, by developing novel conce…
VPR improves posterior uncertainty quantification by combining VI and predictive resampling.
problem Inaccurate posterior sampling with MCMC due to computational constraints.
method Variational predictive resampling (VPR) that uses VI's predictive strength and imputes future observations.
result VPR converges to the exact Bayesian posterior in a Gaussian location model and improves uncertainty quantification.