Hadamard Langevin dynamics supplies a smooth nonconvex reparameterization of the l1-prior that exactly preserves the posterior marginal together with the first rigorous existence, uniqueness, ergodicity, and discretization-convergence theory for the resulting diffusion.
We have µ(z) = −M(z)∇H(z) + 1 2 1 x/η = −M(z)∇H(z) + divM(z)−1(M(z))
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Hadamard Langevin dynamics for sampling the l1-prior
Hadamard Langevin dynamics supplies a smooth nonconvex reparameterization of the l1-prior that exactly preserves the posterior marginal together with the first rigorous existence, uniqueness, ergodicity, and discretization-convergence theory for the resulting diffusion.