Amortized Monte Carlo integration
Current approaches to amortizing Bayesian inference focus solely on approximating the posterior distribution. Typically, this approximation is, in turn, used to calculate expectations for one or more target functions{—}a computational pipeline which is inefficient when the target function(s) are kno...
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| Format: | Conference item |
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Proceedings of Machine Learning Research
2019
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| _version_ | 1797092935093714944 |
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| author | Goliński, A Wood, F Rainforth, T |
| author_facet | Goliński, A Wood, F Rainforth, T |
| author_sort | Goliński, A |
| collection | OXFORD |
| description | Current approaches to amortizing Bayesian inference focus solely on approximating the posterior distribution. Typically, this approximation is, in turn, used to calculate expectations for one or more target functions{—}a computational pipeline which is inefficient when the target function(s) are known upfront. In this paper, we address this inefficiency by introducing AMCI, a method for amortizing Monte Carlo integration directly. AMCI operates similarly to amortized inference but produces three distinct amortized proposals, each tailored to a different component of the overall expectation calculation. At runtime, samples are produced separately from each amortized proposal, before being combined to an overall estimate of the expectation. We show that while existing approaches are fundamentally limited in the level of accuracy they can achieve, AMCI can theoretically produce arbitrarily small errors for any integrable target function using only a single sample from each proposal at runtime. We further show that it is able to empirically outperform the theoretically optimal selfnormalized importance sampler on a number of example problems. Furthermore, AMCI allows not only for amortizing over datasets but also amortizing over target functions. |
| first_indexed | 2024-03-07T03:53:09Z |
| format | Conference item |
| id | oxford-uuid:c1f71e0c-42d8-4e50-9c49-715e6ed3a15f |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:53:09Z |
| publishDate | 2019 |
| publisher | Proceedings of Machine Learning Research |
| record_format | dspace |
| spelling | oxford-uuid:c1f71e0c-42d8-4e50-9c49-715e6ed3a15f2022-03-27T06:05:32ZAmortized Monte Carlo integrationConference itemhttp://purl.org/coar/resource_type/c_5794uuid:c1f71e0c-42d8-4e50-9c49-715e6ed3a15fSymplectic Elements at OxfordProceedings of Machine Learning Research2019Goliński, AWood, FRainforth, TCurrent approaches to amortizing Bayesian inference focus solely on approximating the posterior distribution. Typically, this approximation is, in turn, used to calculate expectations for one or more target functions{—}a computational pipeline which is inefficient when the target function(s) are known upfront. In this paper, we address this inefficiency by introducing AMCI, a method for amortizing Monte Carlo integration directly. AMCI operates similarly to amortized inference but produces three distinct amortized proposals, each tailored to a different component of the overall expectation calculation. At runtime, samples are produced separately from each amortized proposal, before being combined to an overall estimate of the expectation. We show that while existing approaches are fundamentally limited in the level of accuracy they can achieve, AMCI can theoretically produce arbitrarily small errors for any integrable target function using only a single sample from each proposal at runtime. We further show that it is able to empirically outperform the theoretically optimal selfnormalized importance sampler on a number of example problems. Furthermore, AMCI allows not only for amortizing over datasets but also amortizing over target functions. |
| spellingShingle | Goliński, A Wood, F Rainforth, T Amortized Monte Carlo integration |
| title | Amortized Monte Carlo integration |
| title_full | Amortized Monte Carlo integration |
| title_fullStr | Amortized Monte Carlo integration |
| title_full_unstemmed | Amortized Monte Carlo integration |
| title_short | Amortized Monte Carlo integration |
| title_sort | amortized monte carlo integration |
| work_keys_str_mv | AT golinskia amortizedmontecarlointegration AT woodf amortizedmontecarlointegration AT rainfortht amortizedmontecarlointegration |