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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2202.03572 |
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| _version_ | 1866911765552431104 |
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| author | Krivitsky, Pavel N. Kuvelkar, Alina R. Hunter, David R. |
| author_facet | Krivitsky, Pavel N. Kuvelkar, Alina R. Hunter, David R. |
| contents | This article discusses the problem of determining whether a given point, or set of points, lies within the convex hull of another set of points in $d$ dimensions. This problem arises naturally in a statistical context when using a particular approximation to the loglikelihood function for an exponential family model; in particular, we discuss the application to network models here. While the convex hull question may be solved via a simple linear program, this approach is not well known in the statistical literature. Furthermore, this article details several substantial improvements to the convex hull-testing algorithm currently implemented in the widely used 'ergm' package for network modeling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_03572 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Likelihood-based Inference for Exponential-Family Random Graph Models via Linear Programming Krivitsky, Pavel N. Kuvelkar, Alina R. Hunter, David R. Computation This article discusses the problem of determining whether a given point, or set of points, lies within the convex hull of another set of points in $d$ dimensions. This problem arises naturally in a statistical context when using a particular approximation to the loglikelihood function for an exponential family model; in particular, we discuss the application to network models here. While the convex hull question may be solved via a simple linear program, this approach is not well known in the statistical literature. Furthermore, this article details several substantial improvements to the convex hull-testing algorithm currently implemented in the widely used 'ergm' package for network modeling. |
| title | Likelihood-based Inference for Exponential-Family Random Graph Models via Linear Programming |
| topic | Computation |
| url | https://arxiv.org/abs/2202.03572 |