Approximate Bayesian Inference
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...
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| 格式: | Online |
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| 語言: | 英语 |
| 出版: |
MDPI - Multidisciplinary Digital Publishing Institute
2022
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| 在線閱讀: | ONIX_20220621_9783036537894_138 |
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| _version_ | 1869514106439991296 |
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| collection | Directory of Open Access Books |
| description | 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. |
| format | Online |
| id | doab-20.500.12854ir-84560 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-845602024-03-28T03:32:01Z Approximate Bayesian Inference Alquier, Pierre bifurcation dynamical systems Edward–Sokal coupling mean-field Kullback–Leibler divergence variational inference Bayesian statistics machine learning variational approximations PAC-Bayes expectation-propagation Markov chain Monte Carlo Langevin Monte Carlo sequential Monte Carlo Laplace approximations approximate Bayesian computation Gibbs posterior MCMC stochastic gradients neural networks Approximate Bayesian Computation differential evolution Markov kernels discrete state space ergodicity Markov chain probably approximately correct variational Bayes Bayesian inference Markov Chain Monte Carlo Sequential Monte Carlo Riemann Manifold Hamiltonian Monte Carlo integrated nested laplace approximation fixed-form variational Bayes stochastic volatility network modeling network variability Stiefel manifold MCMC-SAEM data imputation Bethe free energy factor graphs message passing variational free energy variational message passing approximate Bayesian computation (ABC) differential privacy (DP) sparse vector technique (SVT) Gaussian particle flow variable flow Langevin dynamics Hamilton Monte Carlo non-reversible dynamics control variates thinning meta-learning hyperparameters priors online learning online optimization gradient descent statistical learning theory PAC–Bayes theory deep learning generalisation bounds Bayesian sampling Monte Carlo integration PAC-Bayes theory no free lunch theorems sequential learning principal curves data streams regret bounds greedy algorithm sleeping experts entropy robustness statistical mechanics complex systems thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science 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. 2022-06-21T08:42:21Z 2022-06-21T08:42:21Z 2022 book ONIX_20220621_9783036537894_138 9783036537894 9783036537900 https://directory.doabooks.org/handle/20.500.12854/84560 eng application/octet-stream Attribution 4.0 International https://mdpi.com/books/pdfview/book/5544 https://mdpi.com/books/pdfview/book/5544 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-0365-3790-0 10.3390/books978-3-0365-3790-0 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783036537894 9783036537900 508 Basel open access |
| spellingShingle | bifurcation dynamical systems Edward–Sokal coupling mean-field Kullback–Leibler divergence variational inference Bayesian statistics machine learning variational approximations PAC-Bayes expectation-propagation Markov chain Monte Carlo Langevin Monte Carlo sequential Monte Carlo Laplace approximations approximate Bayesian computation Gibbs posterior MCMC stochastic gradients neural networks Approximate Bayesian Computation differential evolution Markov kernels discrete state space ergodicity Markov chain probably approximately correct variational Bayes Bayesian inference Markov Chain Monte Carlo Sequential Monte Carlo Riemann Manifold Hamiltonian Monte Carlo integrated nested laplace approximation fixed-form variational Bayes stochastic volatility network modeling network variability Stiefel manifold MCMC-SAEM data imputation Bethe free energy factor graphs message passing variational free energy variational message passing approximate Bayesian computation (ABC) differential privacy (DP) sparse vector technique (SVT) Gaussian particle flow variable flow Langevin dynamics Hamilton Monte Carlo non-reversible dynamics control variates thinning meta-learning hyperparameters priors online learning online optimization gradient descent statistical learning theory PAC–Bayes theory deep learning generalisation bounds Bayesian sampling Monte Carlo integration PAC-Bayes theory no free lunch theorems sequential learning principal curves data streams regret bounds greedy algorithm sleeping experts entropy robustness statistical mechanics complex systems thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science Approximate Bayesian Inference |
| title | Approximate Bayesian Inference |
| title_full | Approximate Bayesian Inference |
| title_fullStr | Approximate Bayesian Inference |
| title_full_unstemmed | Approximate Bayesian Inference |
| title_short | Approximate Bayesian Inference |
| title_sort | approximate bayesian inference |
| topic | bifurcation dynamical systems Edward–Sokal coupling mean-field Kullback–Leibler divergence variational inference Bayesian statistics machine learning variational approximations PAC-Bayes expectation-propagation Markov chain Monte Carlo Langevin Monte Carlo sequential Monte Carlo Laplace approximations approximate Bayesian computation Gibbs posterior MCMC stochastic gradients neural networks Approximate Bayesian Computation differential evolution Markov kernels discrete state space ergodicity Markov chain probably approximately correct variational Bayes Bayesian inference Markov Chain Monte Carlo Sequential Monte Carlo Riemann Manifold Hamiltonian Monte Carlo integrated nested laplace approximation fixed-form variational Bayes stochastic volatility network modeling network variability Stiefel manifold MCMC-SAEM data imputation Bethe free energy factor graphs message passing variational free energy variational message passing approximate Bayesian computation (ABC) differential privacy (DP) sparse vector technique (SVT) Gaussian particle flow variable flow Langevin dynamics Hamilton Monte Carlo non-reversible dynamics control variates thinning meta-learning hyperparameters priors online learning online optimization gradient descent statistical learning theory PAC–Bayes theory deep learning generalisation bounds Bayesian sampling Monte Carlo integration PAC-Bayes theory no free lunch theorems sequential learning principal curves data streams regret bounds greedy algorithm sleeping experts entropy robustness statistical mechanics complex systems thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| topic_facet | bifurcation dynamical systems Edward–Sokal coupling mean-field Kullback–Leibler divergence variational inference Bayesian statistics machine learning variational approximations PAC-Bayes expectation-propagation Markov chain Monte Carlo Langevin Monte Carlo sequential Monte Carlo Laplace approximations approximate Bayesian computation Gibbs posterior MCMC stochastic gradients neural networks Approximate Bayesian Computation differential evolution Markov kernels discrete state space ergodicity Markov chain probably approximately correct variational Bayes Bayesian inference Markov Chain Monte Carlo Sequential Monte Carlo Riemann Manifold Hamiltonian Monte Carlo integrated nested laplace approximation fixed-form variational Bayes stochastic volatility network modeling network variability Stiefel manifold MCMC-SAEM data imputation Bethe free energy factor graphs message passing variational free energy variational message passing approximate Bayesian computation (ABC) differential privacy (DP) sparse vector technique (SVT) Gaussian particle flow variable flow Langevin dynamics Hamilton Monte Carlo non-reversible dynamics control variates thinning meta-learning hyperparameters priors online learning online optimization gradient descent statistical learning theory PAC–Bayes theory deep learning generalisation bounds Bayesian sampling Monte Carlo integration PAC-Bayes theory no free lunch theorems sequential learning principal curves data streams regret bounds greedy algorithm sleeping experts entropy robustness statistical mechanics complex systems thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| url | ONIX_20220621_9783036537894_138 |