Hessian Matrix Inversion in 10^10 Dimensions with Parametric Bootstraps
summary
Claims a practical way to get marginalized Hessian rows for hyperparameters when latent fields reach 10^10 dimensions, using a generative model and MAP reconstructions plus residuals as a parametric bootstrap to approximate posterior averages. Gradient and Gauss–Newton vector products come from backprop through n‑body simulation code, avoiding full Cholesky. MCMC is dismissed as infeasible (thousands of steps per independent sample); finite‑difference Hessian on paired seeds removes sampling noise and recovers unbiased power‑spectrum estimates with errors that fall as samples increase.
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chapters (7)
- 0:00Start
- 1:12Marginals in high dimensions
- 22:05How can we sample from p?
- 27:12Hessian after marginalization
- 28:21Applications to cosmology problems
- 29:53Reconstructing the power spectrum from MLE
- 31:29Summary
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