Transport maps can ease the sampling of distributions with non-trivial geometries by transforming them into distributions that are easier to handle. The potential of this approach has risen with the development of Normalizing Flows (NF) which are maps parameterized with deep neural networks trained to push a reference distribution towards a target. NF-enhanced samplers recently proposed blend (Markov chain) Monte Carlo methods with either (i) proposal draws from the flow or (ii) a flow-based reparametrization. In both cases, the quality of the learned transport conditions performance. The present work clarifies for the first time the relative strengths and weaknesses of these two approaches. Our study concludes that multimodal targets can reliability be handled with flow-based proposals up to moderately high dimensions. In contrast, methods relying on reparametrization struggle with multimodality but are more robust otherwise in high-dimensional settings and under poor training. To further illustrate the influence of target-proposal adequacy, we also derive a new quantitative bound for the mixing time of the Independent Metropolis-Hastings sampler.
翻译:运输图可以通过将非三角地理分布图转化为易于处理的分布图来方便对非三角地理分布分布的抽样。随着标准化流动(NF)的开发,这一方法的潜力已经提高。这些流动图的开发是经过深层神经网络培训,将参考分布推向目标的参数化的地图。NF增强的采样者最近提议了混合(Markov链)蒙特卡洛方法,其中(一) 提案取自流动或(二) 以流动为基础的再平衡,(二) 提案取自流动或(二) 以流动为基础的再平衡。在这两种情况下,学习的运输条件的绩效的质量。目前的工作首次澄清了这两种方法的相对优缺点。我们的研究得出结论,多式联运目标可以可靠地用流基建议处理,最高可达到中等高的尺寸。相比之下,依赖多式联运的再平衡斗争的方法在高维度环境中和训练不足的情况下更为健全。为了进一步说明目标建议是否充分的影响,我们还为独立大都会采样器的混合时间定出新的定量。