Causal representation learning algorithms discover lower-dimensional representations of data that admit a decipherable interpretation of cause and effect; as achieving such interpretable representations is challenging, many causal learning algorithms utilize elements indicating prior information, such as (linear) structural causal models, interventional data, or weak supervision. Unfortunately, in exploratory causal representation learning, such elements and prior information may not be available or warranted. Alternatively, scientific datasets often have multiple modalities or physics-based constraints, and the use of such scientific, multimodal data has been shown to improve disentanglement in fully unsupervised settings. Consequently, we introduce a causal representation learning algorithm (causalPIMA) that can use multimodal data and known physics to discover important features with causal relationships. Our innovative algorithm utilizes a new differentiable parametrization to learn a directed acyclic graph (DAG) together with a latent space of a variational autoencoder in an end-to-end differentiable framework via a single, tractable evidence lower bound loss function. We place a Gaussian mixture prior on the latent space and identify each of the mixtures with an outcome of the DAG nodes; this novel identification enables feature discovery with causal relationships. Tested against a synthetic and a scientific dataset, our results demonstrate the capability of learning an interpretable causal structure while simultaneously discovering key features in a fully unsupervised setting.

翻译：因果表示学习算法旨在发现数据中具有可解释因果关系的低维表示；由于实现此类可解释表示颇具挑战性，许多因果学习算法会利用携带先验信息的要素（如线性结构因果模型、干预数据或弱监督信号）。然而在探索性因果表示学习中，这些要素与先验信息可能难以获取或无法保证。另一方面，科学数据集通常具有多模态特征或基于物理的约束，研究表明运用此类科学多模态数据可在完全无监督场景下提升解缠效果。为此，我们提出一种能利用多模态数据与已知物理规律的因果表示学习算法（causalPIMA），用于发现蕴含因果关系的核心特征。该创新算法采用新型可微分参数化方法，通过单一且可计算的证据下界损失函数，在端到端可微分框架中同步学习有向无环图（DAG）与变分自编码器的潜在空间。我们在潜在空间上施加高斯混合先验，并将每个混合分量与DAG节点的某种结果相关联；这一新颖的对应关系实现了具有因果关系的特征挖掘。在合成数据集与科学数据集上的实验表明，该算法能够在完全无监督场景下同时学习可解释的因果结构并发现关键特征。