Convex relaxation for the generalized maximum-entropy sampling problem
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908810126295040 |
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| author | Ponte, Gabriel Fampa, Marcia Lee, Jon |
| author_facet | Ponte, Gabriel Fampa, Marcia Lee, Jon |
| contents | The generalized maximum-entropy sampling problem (GMESP) is to select an order-$s$ principal submatrix from an order-$n$ covariance matrix, to maximize the product of its $t$ greatest eigenvalues, $0<t\leq s <n$. Introduced more than 25 years ago, GMESP is a natural generalization of two fundamental problems in statistical design theory: (i) maximum-entropy sampling problem (MESP); (ii) binary D-optimality (D-Opt). In the general case, it can be motivated by a selection problem in the context of principal component analysis (PCA).
We introduce the first convex-optimization based relaxation for GMESP, study its behavior, compare it to an earlier spectral bound, and demonstrate its use in a branch-and-bound scheme. We find that such an approach is practical when $s-t$ is very small. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01390 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convex relaxation for the generalized maximum-entropy sampling problem Ponte, Gabriel Fampa, Marcia Lee, Jon Statistics Theory Optimization and Control The generalized maximum-entropy sampling problem (GMESP) is to select an order-$s$ principal submatrix from an order-$n$ covariance matrix, to maximize the product of its $t$ greatest eigenvalues, $0<t\leq s <n$. Introduced more than 25 years ago, GMESP is a natural generalization of two fundamental problems in statistical design theory: (i) maximum-entropy sampling problem (MESP); (ii) binary D-optimality (D-Opt). In the general case, it can be motivated by a selection problem in the context of principal component analysis (PCA). We introduce the first convex-optimization based relaxation for GMESP, study its behavior, compare it to an earlier spectral bound, and demonstrate its use in a branch-and-bound scheme. We find that such an approach is practical when $s-t$ is very small. |
| title | Convex relaxation for the generalized maximum-entropy sampling problem |
| topic | Statistics Theory Optimization and Control |
| url | https://arxiv.org/abs/2404.01390 |