We propose a linear-complexity method for sampling from truncated multivariate normal (TMVN) distributions with high fidelity by applying nearest-neighbor approximations to a product-of-conditionals decomposition of the TMVN density. To make the sequential sampling based on the decomposition feasible, we introduce a novel method that avoids the intractable high-dimensional TMVN distribution by sampling sequentially from $m$-dimensional TMVN distributions, where $m$ is a tuning parameter controlling the fidelity. This allows us to overcome the existing methods' crucial problem of rapidly decreasing acceptance rates for increasing dimension. Throughout our experiments with up to tens of thousands of dimensions, we can produce high-fidelity samples with $m$ in the dozens, achieving superior scalability compared to existing state-of-the-art methods. We study a tetrachloroethylene concentration dataset that has $3{,}971$ observed responses and $20{,}730$ undetected responses, together modeled as a partially censored Gaussian process, where our method enables posterior inference for the censored responses through sampling a $20{,}730$-dimensional TMVN distribution.

翻译：我们提出了一种线性复杂度方法，通过将最近邻近似应用于截断多元正态分布密度的条件乘积分解，实现高保真度的截断多元正态分布采样。为使基于该分解的序列采样可行，我们引入了一种创新方法：通过从$m$维截断多元正态分布中顺序采样来规避高维截断多元正态分布的计算难题，其中$m$是控制保真度的调节参数。该方法克服了现有方法在维度增加时接受率急剧下降的关键问题。在高达数万维度的实验中，我们仅需数十量级的$m$值即可生成高保真样本，相比现有最先进方法展现出更优的可扩展性。我们研究了一个包含3,971个观测响应和20,730个未检出响应的四氯乙烯浓度数据集，该数据集被建模为部分删失的高斯过程。我们的方法通过采样20,730维截断多元正态分布，实现了对删失响应的后验推断。