提出新方法破解退化高斯混合模型的可识别性难题。
Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing
- 通过稀疏正则化和分段仿射变换建模提升可识别性。
- 在合成与图像数据上成功恢复真实潜变量，验证有效性。
- 适合从事因果表示学习、潜变量建模的研究者参考。
因果表示学习（CRL）旨在从高维观测中识别潜在变量，即使变量间存在依赖关系。本文研究潜在变量服从可能退化的高斯混合分布，且仅通过分段仿射混合函数观测的情况。针对概率密度函数因退化而未定义的挑战，提出了逐步强化的可识别性结果。为实现排列与缩放意义下的可识别性，采用对学习表示施加稀疏正则化的方法。基于理论分析，提出两阶段估计方法，在学习表示中强制稀疏性和高斯性。在合成数据和图像数据上的实验表明，该方法能有效恢复真实潜变量。
原文摘要 · Abstract (English)
Causal representation learning (CRL) aims to identify the underlying latent variables from high-dimensional observations, even when variables are dependent with each other. We study this problem for latent variables that follow a potentially degenerate Gaussian mixture distribution and that are only observed through the transformation via a piecewise affine mixing function. We provide a series of progressively stronger identifiability results for this challenging setting in which the probability density functions are ill-defined because of the potential degeneracy. For identifiability up to permutation and scaling, we leverage a sparsity regularization on the learned representation. Based on our theoretical results, we propose a two-stage method to estimate the latent variables by enforcing sparsity and Gaussianity in the learned representations. Experiments on synthetic and image data highlight our method's effectiveness in recovering the ground-truth latent variables.
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