Simultaneously sampling from a complex distribution with intractable normalizing constant and approximating expectations under this distribution is a notoriously challenging problem. We introduce a novel scheme, Invertible Flow Non Equilibrium Sampling (InFine), which 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 combining 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).

翻译：同时从复杂分布中采集样本,在这种分布中难以实现常态正常化,期望接近一致,这是一个众所周知的挑战性问题。我们引入了一个新颖的计划,即“不可逆流动非平衡抽样(InFine)”,它脱离了古典的蒙泰卡洛序列(SMC)和Markov连锁蒙特卡洛(MCMC)方法。InFine通过将随机初始化开始的确定性变换轨道结合起来,构建了对预期的公正估计,特别是使常数正常化。当这种变换被选为符合要求的汉密尔顿系统的适当综合器时,这些轨道是优化路径。在Fine中,通过在优化路径上选择样本,自然也适合设计新的MCMCMC取样计划。此外,InFine还可以用来构建一个证据更低的声调(ELBO),导致一个新的Variational Autoccers (VAE) 类别。