A hybrid VI-HMC method runs expensive Hamiltonian Monte Carlo only on the neural network parameters most responsible for predictive uncertainty, cutting sampling cost while approximating full HMC posteriors.
Exact active subspace Metropolis-Hastings, with applications to the Lorenz-96 system
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abstract
We consider the application of active subspaces to inform a Metropolis-Hastings algorithm, thereby aggressively reducing the computational dimension of the sampling problem. We show that the original formulation, as proposed by Constantine, Kent, and Bui-Thanh (SIAM J. Sci. Comput., 38(5):A2779-A2805, 2016), possesses asymptotic bias. Using pseudo-marginal arguments, we develop an asymptotically unbiased variant. Our algorithm is applied to a synthetic multimodal target distribution as well as a Bayesian formulation of a parameter inference problem for a Lorenz-96 system.
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Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators
A hybrid VI-HMC method runs expensive Hamiltonian Monte Carlo only on the neural network parameters most responsible for predictive uncertainty, cutting sampling cost while approximating full HMC posteriors.