MathDB5 problems
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The target-complexity conjecture for Gaussian mixture variational inference
Let the sampling problem have a target density whose complexity may be measured, for example, by its number of modes, and let the problem dimension be the number of variables in th…
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Dashti–Stuart conjecture on MAP estimators for Banach-space Gaussian inverse problems
Dashti–Stuart conjecture. Assume that the conditions in Assumption hold. Then:
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Convergence of graph posteriors and optimal kernel bandwidth selection
Graph-posterior convergence conjecture. The convergence of the graph posteriors to the ground truth posterior, together with guidelines for choosing the kernel bandwidth optimally…
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Conjecture that randomised misfit posteriors approximate the ideal posterior
Randomised misfit posterior conjecture. The ideal deterministic posterior is well approximated by the random posterior.
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Positive spectral gap conjecture for the gpCN Metropolis algorithm
Positive spectral gap conjecture. The gpCN Metropolis targeting $$ has a strictly positive spectral gap whenever the pCN Metropolis has one.