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：因果表征学习算法能够发现数据中具有可解释因果关系的低维表征；由于实现此类可解释表征具有挑战性，许多因果学习算法利用包含先验信息的元素，例如（线性）结构因果模型、干预数据或弱监督。然而，在探索性因果表征学习中，此类元素和先验信息可能无法获取或无法保证。另一方面，科学数据集通常包含多种模态或基于物理的约束，且此类科学多模态数据的应用已被证明能够在完全无监督场景下提升解耦效果。为此，我们提出一种因果表征学习算法（causalPIMA），该算法可利用多模态数据和已知物理规律发现具有因果关系的关键特征。我们的创新算法采用一种新的可微参数化方法，通过单一可计算的证据下界损失函数，在端到端可微框架中联合学习有向无环图（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节点的结果相对应；这种新颖的对应关系实现了具有因果关系的关键特征发现。在合成数据集与科学数据集上的测试结果表明，该算法能够在完全无监督环境下同时学习可解释的因果结构与发现关键特征。