Variational MCMC
We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly because this approximation tends to underestimate the true varianc...
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| Format: | Conference item |
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Morgan Kaufmann
2001
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| _version_ | 1826278457766576128 |
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| author | de Freitas, N Hojen−Sorensen, P Jordan, M Russell, S |
| author_facet | de Freitas, N Hojen−Sorensen, P Jordan, M Russell, S |
| author_sort | de Freitas, N |
| collection | OXFORD |
| description | We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly because this approximation tends to underestimate the true variance and other features of the data. We solve this problem by introducing more sophisticated MCMC algorithms. One of these algorithms is a mixture of two MCMC kernels: a random walk Metropolis kernel and a blockMetropolis-Hastings (MH) kernel with a variational approximation as proposaldistribution. The MH kernel allows one to locate regions of high probability efficiently. The Metropolis kernel allows us to explore the vicinity of these regions. This algorithm outperforms variationalapproximations because it yields slightly better estimates of the mean and considerably better estimates of higher moments, such as covariances. It also outperforms standard MCMC algorithms because it locates theregions of high probability quickly, thus speeding up convergence. We demonstrate this algorithm on the problem of Bayesian parameter estimation for logistic (sigmoid) belief networks. |
| first_indexed | 2024-03-06T23:44:13Z |
| format | Conference item |
| id | oxford-uuid:70593df6-27df-43c8-b446-a688b374d185 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:44:13Z |
| publishDate | 2001 |
| publisher | Morgan Kaufmann |
| record_format | dspace |
| spelling | oxford-uuid:70593df6-27df-43c8-b446-a688b374d1852022-03-26T19:36:31ZVariational MCMCConference itemhttp://purl.org/coar/resource_type/c_5794uuid:70593df6-27df-43c8-b446-a688b374d185Department of Computer ScienceMorgan Kaufmann2001de Freitas, NHojen−Sorensen, PJordan, MRussell, SWe propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly because this approximation tends to underestimate the true variance and other features of the data. We solve this problem by introducing more sophisticated MCMC algorithms. One of these algorithms is a mixture of two MCMC kernels: a random walk Metropolis kernel and a blockMetropolis-Hastings (MH) kernel with a variational approximation as proposaldistribution. The MH kernel allows one to locate regions of high probability efficiently. The Metropolis kernel allows us to explore the vicinity of these regions. This algorithm outperforms variationalapproximations because it yields slightly better estimates of the mean and considerably better estimates of higher moments, such as covariances. It also outperforms standard MCMC algorithms because it locates theregions of high probability quickly, thus speeding up convergence. We demonstrate this algorithm on the problem of Bayesian parameter estimation for logistic (sigmoid) belief networks. |
| spellingShingle | de Freitas, N Hojen−Sorensen, P Jordan, M Russell, S Variational MCMC |
| title | Variational MCMC |
| title_full | Variational MCMC |
| title_fullStr | Variational MCMC |
| title_full_unstemmed | Variational MCMC |
| title_short | Variational MCMC |
| title_sort | variational mcmc |
| work_keys_str_mv | AT defreitasn variationalmcmc AT hojensorensenp variationalmcmc AT jordanm variationalmcmc AT russells variationalmcmc |