Eric Moulines Ecole Polytechnique Invertible-ﬂow non equilibrium sampling Abstract : Simultaneously sampling from a complex distribution with intractable normalizing con- stant and approximating expectations under this distribution is a challenging problem. We introduce a novel scheme, inspired by the the non-equilibrium sampling introduced by (Rotskoﬀ and Vanden- Eijnden (2019), called Invertible Flow Non Equilibrium Sampling (InFine). InFine departs from classical Sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) approaches. InFine constructs unbiased estimators of expectations and in particular of normalizing constants by combin- ing the orbits of a deterministic transform started from random initializations. When this transform is chosen as an appropriate integrator of a conformal Hamiltonian system, these orbits are optimization paths. InFine is also naturally suited to design new MCMC sampling schemes by selecting samples on the optimization paths.Additionally, InFine can be used to construct an Evidence Lower Bound (ELBO) leading to a new class of Variational AutoEncoders (VAE).

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Eric Moulines

Ecole Polytechnique

Invertible-flow non equilibrium sampling

Abstract : Simultaneously sampling from a complex distribution with intractable normalizing con-stant and approximating expectations under this distribution is a challenging problem. We introducea novel scheme, inspired by the the non-equilibrium sampling introduced by (Rotskoff and Vanden-Eijnden (2019), called Invertible Flow Non Equilibrium Sampling (InFine). InFine departs fromclassical Sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) approaches. InFineconstructs unbiased estimators of expectations and in particular of normalizing constants by combin-ing the orbits of a deterministic transform started from random initializations. When this transform ischosen as an appropriate integrator of a conformal Hamiltonian system, these orbits are optimizationpaths. InFine is also naturally suited to design new MCMC sampling schemes by selecting sampleson the optimization paths.Additionally, InFine can be used to construct an Evidence Lower Bound(ELBO) leading to a new class of Variational AutoEncoders (VAE).