Prevalent in biological applications (e.g., human phenotype measurements), multimodal datasets can provide valuable insights into the underlying biological mechanisms. However, current machine learning models designed to analyze such datasets still lack interpretability and theoretical guarantees, which are essential to biological applications. Recent advances in causal representation learning have shown promise in uncovering the interpretable latent causal variables with formal theoretical certificates. Unfortunately, existing works for multimodal distributions either rely on restrictive parametric assumptions or provide rather coarse identification results, limiting their applicability to biological research which favors a detailed understanding of the mechanisms. In this work, we aim to develop flexible identification conditions for multimodal data and principled methods to facilitate the understanding of biological datasets. Theoretically, we consider a flexible nonparametric latent distribution (c.f., parametric assumptions in prior work) permitting causal relationships across potentially different modalities. We establish identifiability guarantees for each latent component, extending the subspace identification results from prior work. Our key theoretical ingredient is the structural sparsity of the causal connections among distinct modalities, which, as we will discuss, is natural for a large collection of biological systems. Empirically, we propose a practical framework to instantiate our theoretical insights. We demonstrate the effectiveness of our approach through extensive experiments on both numerical and synthetic datasets. Results on a real-world human phenotype dataset are consistent with established medical research, validating our theoretical and methodological framework.

翻译：在生物学应用（例如人类表型测量）中普遍存在的多模态数据集能够为潜在生物学机制提供有价值的洞见。然而，当前用于分析此类数据集的机器学习模型仍缺乏可解释性和理论保证，而这些特性对生物学应用至关重要。因果表征学习的最新进展已显示出通过形式化理论证明揭示可解释潜在因果变量的潜力。遗憾的是，现有针对多模态分布的研究要么依赖于限制性参数假设，要么仅提供较为粗略的识别结果，限制了其在偏好机制细节理解的生物学研究中的适用性。本研究旨在为多模态数据开发灵活的识别条件与原则性方法，以促进对生物数据集的理解。理论上，我们考虑一种灵活的非参数潜在分布（相较于先前工作中的参数假设），允许跨潜在不同模态的因果关系。我们为每个潜在成分建立了可识别性保证，扩展了先前工作中的子空间识别结果。我们关键的理论要素是不同模态间因果连接的结构稀疏性，正如我们将讨论的，这对于大量生物系统而言是自然存在的。实证方面，我们提出了一个实践框架来实现我们的理论洞见。通过在数值和合成数据集上的大量实验，我们证明了所提方法的有效性。在真实世界人类表型数据集上的结果与既有医学研究一致，验证了我们的理论与方法框架。