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：传输地图能够简化具有非平凡几何结构的分布采样，通过将其转化为更易处理的分布。随着归一化流（Normalizing Flows, NF）的发展，这一方法的潜力显著提升——归一化流是由深度神经网络参数化的映射，旨在将参考分布推向目标分布。近期提出的NF增强采样器将（马尔可夫链）蒙特卡洛方法与以下两种策略相结合：（i）从流中生成提议采样，或（ii）基于流的重参数化。在这两种情况下，学习得到的传输质量直接影响性能。本研究首次厘清了这两种方法的相对优势与局限性。我们的结论表明，对于中等维度的多模态目标，基于流的提议方法能够可靠处理；而依赖重参数化的方法在多模态场景中表现不佳，但在高维设置或训练不足的情况下更具鲁棒性。为进一步说明目标-提议适配性的影响，我们还推导出独立梅特罗波利斯-黑斯廷斯（Independent Metropolis-Hastings）采样器混合时间的新定量界。