A hierarchy of convex relaxations for the total variation distance
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915556216537088 |
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| author | Lasserre, Jean-Bernard |
| author_facet | Lasserre, Jean-Bernard |
| contents | Given two measures $μ$, $ν$ on Rd that satisfy Carleman's condition, we provide a numerical scheme to approximate as closely as desired the total variation distance between $μ$ and $ν$. It consists of solving a sequence (hierarchy) of convex relaxations whose associated sequence of optimal values converges to the total variation distance, an additional illustration of the versatility of the Moment-SOS hierarchy. Indeed each relaxation in the hierarchy is a semidefinite program whose size increases with the number of involved moments. It has an optimal solution which is a couple of degree-2n pseudo-moments which converge, as n grows, to moments of the Hahn-Jordan decomposition of $μ$-$ν$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01086 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A hierarchy of convex relaxations for the total variation distance Lasserre, Jean-Bernard Optimization and Control Given two measures $μ$, $ν$ on Rd that satisfy Carleman's condition, we provide a numerical scheme to approximate as closely as desired the total variation distance between $μ$ and $ν$. It consists of solving a sequence (hierarchy) of convex relaxations whose associated sequence of optimal values converges to the total variation distance, an additional illustration of the versatility of the Moment-SOS hierarchy. Indeed each relaxation in the hierarchy is a semidefinite program whose size increases with the number of involved moments. It has an optimal solution which is a couple of degree-2n pseudo-moments which converge, as n grows, to moments of the Hahn-Jordan decomposition of $μ$-$ν$. |
| title | A hierarchy of convex relaxations for the total variation distance |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.01086 |