In this paper, we describe a method for estimating the joint probability density from data samples by assuming that the underlying distribution can be decomposed as a mixture of product densities with few mixture components. Prior works have used such a decomposition to estimate the joint density from lower-dimensional marginals, which can be estimated more reliably with the same number of samples. We combine two key ideas: dictionaries to represent 1-D densities, and random projections to estimate the joint distribution from 1-D marginals, explored separately in prior work. Our algorithm benefits from improved sample complexity over the previous dictionary-based approach by using 1-D marginals for reconstruction. We evaluate the performance of our method on estimating synthetic probability densities and compare it with the previous dictionary-based approach and Gaussian Mixture Models (GMMs). Our algorithm outperforms these other approaches in all the experimental settings.

翻译：本文描述了一种从数据样本中估计联合概率密度的方法，其核心假设是底层分布可分解为少量混合分量的乘积密度混合体。已有研究利用这种分解从较低维边缘分布（在相同样本量下可更可靠地估计）中估计联合密度。我们综合了两项关键思想：用字典表示一维密度，以及通过一维边缘分布估计联合分布的随机投影方法——这两者此前被独立探索。与先前基于字典的方法相比，我们的算法通过使用一维边缘分布进行重构，显著降低了样本复杂度。我们在合成概率密度估计任务上评估了方法性能，并与先前基于字典的方法及高斯混合模型进行了对比。实验结果表明，本算法在所有测试场景中均优于其他方法。