Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models, such as normalizing flows and generative adversarial networks, characterize conditional distributions by learning a transport map that pushes forward a simple reference (e.g., a standard Gaussian) to a target distribution. While these approaches successfully describe many non-Gaussian problems, their performance is often limited by parametric bias and the reliability of gradient-based (adversarial) optimizers to learn these transformations. This work proposes a non-parametric generative model that iteratively maps reference samples to the target. The model uses block-triangular transport maps, whose components are shown to characterize conditionals of the target distribution. These maps arise from solving an optimal transport problem with a weighted $L^2$ cost function, thereby extending the data-driven approach in [Trigila and Tabak, 2016] for conditional sampling. The proposed approach is demonstrated on a two dimensional example and on a parameter inference problem involving nonlinear ODEs.

翻译：条件分布采样是贝叶斯推断和密度估计中的基本任务。生成模型（如归一化流和生成对抗网络）通过学习将简单参考分布（例如标准高斯分布）推送到目标分布的传输映射来表征条件分布。尽管这些方法成功描述了许多非高斯问题，但其性能常受限于参数偏差以及基于梯度（对抗）优化器学习这些变换的可靠性。本文提出一种非参数生成模型，通过迭代方式将参考样本映射至目标。该模型使用块三角传输映射，其各分量被证明可表征目标分布的条件分布。这些映射来源于求解加权L2成本函数的最优传输问题，从而扩展了[Trigila and Tabak, 2016]中用于条件采样的数据驱动方法。所提方法在二维示例以及涉及非线性常微分方程的参数推断问题上进行了验证。