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Approximate Bayesian Inference
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Extremely popular for statistical inference, Bayesian methods are also becoming popular in machine learning and artificial intelligence problems. Bayesian estimators are often implemented by Monte Carlo methods, such as the Metropolis–Hastings algorithm of the Gibbs sampler. These algorithms target the exact posterior distribution. However, many of the modern models in statistics are simply too complex to use such methodologies. In machine learning, the volume of the data used in practice makes Monte Carlo methods too slow to be useful. On the other hand, these applications often do not require an exact knowledge of the posterior. This has motivated the development of a new generation of algorithms that are fast enough to handle huge datasets but that often target an approximation of the posterior. This book gathers 18 research papers written by Approximate Bayesian Inference specialists and provides an overview of the recent advances in these algorithms. This includes optimization-based methods (such as variational approximations) and simulation-based methods (such as ABC or Monte Carlo algorithms). The theoretical aspects of Approximate Bayesian Inference are covered, specifically the PAC–Bayes bounds and regret analysis. Applications for challenging computational problems in astrophysics, finance, medical data analysis, and computer vision area also presented.
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Keywords
- approximate Bayesian computation
- approximate Bayesian computation (ABC)
- Bayesian inference
- Bayesian sampling
- bayesian statistics
- Bethe free energy
- bifurcation
- complex systems
- control variates
- data imputation
- data streams
- deep learning
- differential evolution
- differential privacy (DP)
- discrete state space
- dynamical systems
- Edward–Sokal coupling
- Entropy
- ergodicity
- expectation-propagation
- factor graphs
- fixed-form variational Bayes
- Gaussian
- generalisation bounds
- Gibbs posterior
- gradient descent
- greedy algorithm
- Hamilton Monte Carlo
- hyperparameters
- integrated nested laplace approximation
- Kullback–Leibler divergence
- Langevin dynamics
- Langevin Monte Carlo
- Laplace approximations
- Machine learning
- Markov chain
- Markov chain Monte Carlo
- Markov kernels
- Mathematics & science
- MCMC
- MCMC-SAEM
- mean-field
- message passing
- meta-learning
- Monte Carlo integration
- network modeling
- network variability
- neural networks
- no free lunch theorems
- non-reversible dynamics
- online learning
- online optimization
- PAC-Bayes
- PAC-Bayes theory
- PAC–Bayes theory
- particle flow
- principal curves
- priors
- probably approximately correct
- Reference, information & interdisciplinary subjects
- regret bounds
- Research & information: general
- Riemann Manifold Hamiltonian Monte Carlo
- robustness
- sequential learning
- sequential Monte Carlo
- sleeping experts
- sparse vector technique (SVT)
- statistical learning theory
- Statistical mechanics
- Stiefel manifold
- stochastic gradients
- stochastic volatility
- thinning
- variable flow
- variational approximations
- variational Bayes
- variational free energy
- variational inference
- variational message passing
Links
DOI: 10.3390/books978-3-0365-3790-0Editions