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Polynomial time guarantees for sampling based posterior inference in high-dimensional generalised linear models
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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.
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Large sample scaling analysis of the Zig-Zag algorithm for Bayesian inference
For large datasets, the Zig-Zag sampler with control variates draws effectively independent posterior samples at O(1) cost per sample in stationarity, while vanilla sub-sampling and canonical Zig-Zag cost O(n).
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