Polynomial time guarantees for sampling based posterior inference in high-dimensional generalised linear models
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866911070817353728 |
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| author | Altmeyer, Randolf |
| author_facet | Altmeyer, Randolf |
| contents | The problem of computing posterior functionals in general high-dimensional statistical models with possibly non-log-concave likelihood functions is considered. Based on the proof strategy of Nickl and Wang (2022), but using only local likelihood conditions and without relying on M-estimation theory, nonasymptotic statistical and computational guarantees are provided for a gradient based MCMC algorithm. Given a suitable initialiser, these guarantees scale polynomially in key algorithmic quantities. The abstract results are applied to several concrete statistical models, including density estimation, nonparametric regression with generalised linear models and a canonical statistical non-linear inverse problem from PDEs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_13296 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Polynomial time guarantees for sampling based posterior inference in high-dimensional generalised linear models Altmeyer, Randolf Statistics Theory Numerical Analysis Analysis of PDEs Probability Computation 62F15, 62G05, 65C05 The problem of computing posterior functionals in general high-dimensional statistical models with possibly non-log-concave likelihood functions is considered. Based on the proof strategy of Nickl and Wang (2022), but using only local likelihood conditions and without relying on M-estimation theory, nonasymptotic statistical and computational guarantees are provided for a gradient based MCMC algorithm. Given a suitable initialiser, these guarantees scale polynomially in key algorithmic quantities. The abstract results are applied to several concrete statistical models, including density estimation, nonparametric regression with generalised linear models and a canonical statistical non-linear inverse problem from PDEs. |
| title | Polynomial time guarantees for sampling based posterior inference in high-dimensional generalised linear models |
| topic | Statistics Theory Numerical Analysis Analysis of PDEs Probability Computation 62F15, 62G05, 65C05 |
| url | https://arxiv.org/abs/2208.13296 |