Machine learning techniques improve Bayesian computation for complex data.
problem Infeasible posterior computation in high-dimensional models.
method Improving posterior computation using machine learning techniques.
result Potential to enhance Bayesian computation efficiency.
This Chapter, "Overview of Approximate Bayesian Computation", is to appear as the first chapter in the forthcoming Handbook of Approximate Bayesian Computation (2018). It details the main ideas and concepts behind ABC methods with many examples and illustrations.
QBC uses quantum computers to speed up Bayesian computation.
problem Exponential speed-up in Bayesian computation.
method Quantum von Neumann measurement for simulating ML algorithms.
result Quantum versions of regression, Gaussian processes, and SGD.
The paper proposes using path signatures for better inference in time series data.
problem Simulation models with time series data often lack tractable likelihood functions.
method Approximate Bayesian Computation with path signatures to handle sequential data.
result Theoretical guarantees on the resultant posteriors for Bayesian parameter inference.
This paper considers the computational power of constant size, dynamic Bayesian networks. Although discrete dynamic Bayesian networks are no more powerful than hidden Markov models, dynamic Bayesian networks with continuous random variables and discrete children of continuous parents are capable of performing Turing-co…
Bayesian methods enhance deep learning models by improving reliability and uncertainty.
problem Improving reliability and uncertainty awareness in deep learning models.
method Approximate Bayesian inference techniques, including SG-MCMC and VI, applied to deep learning models.
result Enhanced posterior inference for deep learning models, particularly in neural networks and generative models.
Bayesian Deep Learning tackles inverse problems with neural networks and approximate computations.
problem Solving inverse problems with indirect measurements and uncertainties.
method Bayesian Deep Learning, using neural networks and approximate computations.
result Effective solutions for inverse problems using Bayesian Deep Learning.
New algorithm tackles big data Bayesian problems with latent variables.
problem Bayesian computing for large-scale problems with missing data and dimension jumping.
method Extended stochastic gradient MCMC with latent variables.
result Highly scalable and more efficient than traditional MCMC algorithms.
Bayesian optimization has emerged as a strong candidate tool for global optimization of functions with expensive evaluation costs. However, due to the dynamic nature of research in Bayesian approaches, and the evolution of computing technology, using Bayesian optimization in a parallel computing environment remains a c…
New BNN architectures reduce computational cost for uncertainty quantification.
problem High computational cost in Bayesian neural networks.
method Partial trace-class Bayesian neural networks (PaTraC BNNs).
result Comparable uncertainty quantification with fewer parameters.
A new method for efficient computation of Knowledge Gradient in Bayesian optimization.
problem Efficient computation of the Knowledge Gradient for Bayesian optimization.
method One-shot Hybrid KG, a new approach combining previous ideas.
result The new method is cheap to compute and preserves theoretical properties of previous methods.
A new method improves robustness and efficiency of Bayesian LOO-CV.
problem Computational expense and unreliability of classical LOO-CV in high-dimensional Bayesian models.
method Proposes a mixture estimator to compute Bayesian LOO-CV criteria with finite asymptotic variance.
result Improved robustness and efficiency in high-dimensional problems.
Explosive growth in data and availability of cheap computing resources have sparked increasing interest in Big learning, an emerging subfield that studies scalable machine learning algorithms, systems, and applications with Big Data. Bayesian methods represent one important class of statistic methods for machine learni…
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge, etc. The Bayesian formalism to inverse problems avoids most of the difficulties en…
Piecewise constant denoising can be solved either by deterministic optimization approaches, based on the Potts model, or by stochastic Bayesian procedures. The former lead to low computational time but require the selection of a regularization parameter, whose value significantly impacts the achieved solution, and whos…
Bayesian design improves experimental optimization.
problem Computational challenges limit BED practical use.
method Recent advances in BED have reduced computational burdens.
result Effective BED design is now feasible.
Bayesian optimization has become a popular method for high-throughput computing, like the design of computer experiments or hyperparameter tuning of expensive models, where sample efficiency is mandatory. In these applications, distributed and scalable architectures are a necessity. However, Bayesian optimization is mo…
New method improves ABC for Bayesian model comparison.
problem Comparing complex models with observed data.
method Approximate Bayesian Computation with posterior density estimation.
result Efficiently assigns high posterior probabilities to ground-truth models.
Gradient-EM Bayesian meta-learning accelerates adaptation with reduced computation and improved robustness.
problem Efficient and robust adaptation to new tasks with uncertainty assessment.
method Extends Bayesian meta-learning with gradient-EM algorithm, decoupling inner-update from meta-update.
result Improves accuracy with less computation cost and enhanced robustness to uncertainty.
A new Bayesian image segmentation algorithm is proposed by combining a loopy belief propagation with an inverse real space renormalization group transformation to reduce the computational time. In results of our experiment, we observe that the proposed method can reduce the computational time to less than one-tenth of …
Many applications in Bayesian statistics are extremely computationally intensive. However, they are often inherently parallel, making them prime targets for modern massively parallel processors. Multi-core and distributed computing is widely applied in the Bayesian community, however, very little attention has been giv…
Approximate Bayesian computation (ABC) is a method for Bayesian inference when the likelihood is unavailable but simulating from the model is possible. However, many ABC algorithms require a large number of simulations, which can be costly. To reduce the computational cost, Bayesian optimisation (BO) and surrogate mode…
Improved ABC method using Gaussian processes for more efficient simulations and uncertainty quantification.
problem Efficiently simulate and quantify uncertainty in ABC methods.
method Batch-sequential Bayesian experimental design, numerical method for uncertainty quantification, improved GP modeling assumptions.
result Improved framework for ABC methods that quantifies uncertainty and parallelizes simulations.
Paper proposes efficient method for evaluating Bayesian models in imaging.
problem Evaluation of Bayesian models in imaging when ground truth is unavailable.
method Novel combination of Bayesian cross-validation and data fission for unsupervised model selection and misspecification detection.
result Achieved excellent selection and detection accuracy with low computational cost.
This paper provides efficient algorithms for computing entropy and KL divergence in Bayesian networks.
problem Computing entropy and KL divergence for Bayesian networks efficiently.
method Leveraging the graphical structure of Bayesian networks, the paper provides computationally efficient algorithms.
result Reduces computational complexity of KL divergence from cubic to quadratic for Gaussian BNs.
We introduce new definitions of universal and superuniversal computable codes, which are based on a code's ability to approximate Kolmogorov complexity within the prescribed margin for all individual sequences from a given set. Such sets of sequences may be singled out almost surely with respect to certain probability …
A new framework for efficient Bayesian network inference.
problem High-dimensional Bayesian networks are hard to infer due to computational scaling.
method Directed convex subgraphs and minimal d-decomposition tree for decomposition, enabling parallel computation.
result The method reduces computational cost and enables parallel computation.
Efficiently discovers Bayesian network structure with reduced memory usage.
problem Bayesian network structure discovery is NP-hard and memory-intensive.
method Progressively leveled scoring approach with hierarchical computation.
result Achieved processing of a 28-variable Bayesian network using only memory.
Bayesian data sketching speeds up inference for large functional data.
problem Slow posterior computations in Bayesian varying coefficient models for large data.
method Compress functional response and predictor matrix using random linear transformation.
result Fully model-based Bayesian inference on compressed data.
This paper examines how neural architectures support amortized Bayesian inference and its performance under varying conditions.
problem Understanding and evaluating amortized inference under signal-to-noise variation and distribution shift.
method Statistical analysis of neural architectures including feedforward networks, Deep Sets, and Transformers.
result Neural architectures support amortized Bayesian inference, offering controlled generalization error and robustness under varying conditions.
Efficient algorithm for Bayesian networks reduces marginal probability distribution computation.
problem Exact computation of marginal probability distribution is NP-hard for categorical variables in Bayesian networks.
method Divide-and-conquer approach exploiting graphical properties of Bayesian networks.
result Novel algorithm outperforms state-of-the-art methods in classification and cancer subtype identification.
Improved Bayesian inference for neuronal ensemble inference reduces computational cost.
problem Efficient inference of neuronal ensembles from activity data.
method Modified MCMC algorithm with simulated annealing for hyperparameter control.
result Our method reduces computational cost while maintaining or improving inference accuracy.
Develops a new Bayesian inference method for discrete data.
problem Computational challenges in discrete state spaces, especially intractable likelihoods.
method Uses a discrete Fisher divergence to update beliefs about model parameters, circumventing the intractable normalising constant.
result Establishes statistical properties of the generalised posterior and proposes a calibration approach.
Bayesian neural networks (BNN) can estimate the uncertainty in predictions, as opposed to non-Bayesian neural networks (NNs). However, BNNs have been far less widely used than non-Bayesian NNs in practice since they need iterative NN executions to predict a result for one data, and it gives rise to prohibitive computat…
Due to the need for robust uncertainty quantification, Bayesian neural learning has gained attention in the era of deep learning and big data. Markov Chain Monte-Carlo (MCMC) methods typically implement Bayesian inference which faces several challenges given a large number of parameters, complex and multimodal posterio…
Stochastic Volatility in Mean models with heavy-tailed distributions using Hidden Markov Models
problem Accurate inference for Stochastic Volatility in Mean models with heavy-tailed distributions
method Numerically stable estimation procedure and parallel computing
result Significant reduction in computational times
The paper connects ABC to GBI, suggesting ABC as a robustification strategy.
problem Approximate Bayesian Computation struggles with tractability in complex simulators.
method Reinterpreting ABC as an implicitly defined error model and suggesting GBI.
result ABC can be seen as a robustification strategy for approximating Bayesian posteriors.
Bayesian optimization reduces computational effort in aircraft design optimization.
problem High computational cost in industrial aircraft design optimization.
method Constrained Bayesian optimization (Super Efficient Global Optimization with Mixture of Experts)
result Significant computational efficiency improvements over existing Isight optimizers.
GBC methods compute expected utility without needing the model's density.
problem Computing expected utility in complex models.
method Density-free generative method using quantile neural estimator.
result Efficient estimation of expected utility from simulated data.
GSSBO reduces GP fitting time in Bayesian optimization.
problem High computational cost of fitting Gaussian process surrogate models in Bayesian optimization.
method Gradient-based sample selection to reduce the number of samples used in GP fitting.
result Sublinear regret bounds and significant reduction in computational cost.
Paper proposes a learning-based sparse Bayesian method for accurate off-grid DOA estimation.
problem One-bit off-grid direction of arrival (DOA) estimation in a single snapshot scenario.
method Formulated off-grid DOA estimation model, used Sparse Bayesian framework, proposed Learning-based Sparse Bayesian approach.
result Improved computational efficiency and accuracy in off-grid DOA estimation.
Information-theoretic Bayesian optimisation techniques have demonstrated state-of-the-art performance in tackling important global optimisation problems. However, current information-theoretic approaches require many approximations in implementation, introduce often-prohibitive computational overhead and limit the choi…
Extends Bayesian theory to handle complex interdependencies in multidimensional event spaces.
problem Complex interdependencies between events and hypotheses sets in real-world systems.
method Developed a mathematical formalism for modeling complex relationships through rigorous derivation and validated using analytical proofs, simulations, and case studies.
result MDSE theory improves prediction accuracy by 15-20% compared to standard Bayesian methods in high interdimensionality datasets.
Proposes a new method to improve Bayesian computation accuracy using flexible classification.
problem Bayesian computations accuracy check using rank-based simulation-based calibration has limitations.
method Replaces marginal rank test with a flexible classification approach that learns from data.
result Improves statistical power and provides an interpretable divergence measure of miscalibration.
BaMANI uses ensemble learning to improve Bayesian network inference.
problem Bayesian network inference's reliance on specific algorithms can obscure causal relationships.
method Developed an ensemble learning approach to marginalize algorithm impact.
result Improved accuracy and reliability of causal network predictions.
GPU-accelerated BART speeds up Bayesian regression.
problem Long running time of BART makes it impractical for large datasets.
method GPU-enabled implementation of BART.
result BART is now 200x faster on GPUs.
We harness the power of Bayesian emulation techniques, designed to aid the analysis of complex computer models, to examine the structure of complex Bayesian analyses themselves. These techniques facilitate robust Bayesian analyses and/or sensitivity analyses of complex problems, and hence allow global exploration of th…
A scalable parallel BO method for asynchronous settings.
problem Expensive-to-evaluate problems in machine learning.
method Simple and scalable Bayesian optimization method for asynchronous parallel settings.
result Demonstrated promising performance on benchmark functions and hyperparameter optimization.