Sampling from Non-smooth Distributions Through Langevin Diffusion
In this paper, we propose proximal splitting-type algorithms for sampling from distributions whose densities are not necessarily smooth nor log-concave. Our approach brings together tools from, on the one hand, variational analysis and non-smooth optimization, and on the other hand, stochastic diffu...
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| Vydáno v: | Methodology and computing in applied probability Ročník 23; číslo 4; s. 1173 - 1201 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York
Springer US
01.12.2021
Springer Nature B.V Springer Verlag |
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| ISSN: | 1387-5841, 1573-7713 |
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| Abstract | In this paper, we propose proximal splitting-type algorithms for sampling from distributions whose densities are not necessarily smooth nor log-concave. Our approach brings together tools from, on the one hand, variational analysis and non-smooth optimization, and on the other hand, stochastic diffusion equations, and in particular the Langevin diffusion. We establish in particular consistency guarantees of our algorithms seen as discretization schemes in this context. These algorithms are then applied to compute the exponentially weighted aggregates for regression problems involving non-smooth penalties that are commonly used to promote some notion of simplicity/complexity. Some popular penalties are detailed and implemented on some numerical experiments. |
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| AbstractList | In this paper, we propose proximal splitting-type algorithms for sampling from distributions whose densities are not necessarily smooth nor log-concave. Our approach brings together tools from, on the one hand, variational analysis and non-smooth optimization, and on the other hand, stochastic diffusion equations, and in particular the Langevin diffusion. We establish in particular consistency guarantees of our algorithms seen as discretization schemes in this context. These algorithms are then applied to compute the exponentially weighted aggregates for regression problems involving non-smooth penalties that are commonly used to promote some notion of simplicity/complexity. Some popular penalties are detailed and implemented on some numerical experiments. |
| Author | Luu, Tung Duy Chesneau, Christophe Fadili, Jalal |
| Author_xml | – sequence: 1 givenname: Tung Duy surname: Luu fullname: Luu, Tung Duy organization: Normandie University, ENSICAEN, UNICAEN, CNRS, GREYC – sequence: 2 givenname: Jalal surname: Fadili fullname: Fadili, Jalal organization: Normandie University, ENSICAEN, UNICAEN, CNRS, GREYC – sequence: 3 givenname: Christophe surname: Chesneau fullname: Chesneau, Christophe email: christophe.chesneau@unicaen.fr organization: Normandie University, UNICAEN, CNRS, LMNO |
| BackLink | https://hal.science/hal-02896662$$DView record in HAL |
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| CitedBy_id | crossref_primary_10_1016_j_amc_2023_128377 crossref_primary_10_1093_imanum_drad038 crossref_primary_10_1287_moor_2022_0307 crossref_primary_10_1007_s11222_023_10254_y crossref_primary_10_1137_23M1581807 crossref_primary_10_1137_23M1582345 crossref_primary_10_1109_TSP_2023_3247142 |
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| Keywords | 65C30 Langevin diffusion Exponentially weighted aggregation Proximal splitting Monte-Carlo 65C05 Non-smooth distributions 65C60 65C50 |
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| Title | Sampling from Non-smooth Distributions Through Langevin Diffusion |
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