Continuous Causal Component and Structure Discovery from Time Series

Causal representation learning aims to infer a small set of causally related latent variables and to model their causal relationships in order to explain high-dimensional observed data. Recent studies have made progress in identifying causal representations from time series by hypothesizing temporal structures among latent components. However, these methods are constrained by the observation scale and sampling regularity, as they typically assume that latent components evolve at discrete time steps. Moreover, they do not explicitly identify the causal graph among latent components, which limits the interpretability of the learned representations. To address these limitations, we propose Continuous Causal Component and Structure Discovery (C3SD). We theoretically show that latent causal components and their causal relationships can be identified up to permutation equivalence by modeling synchronous sparsity in the mapping between latent components and observed variables. Building on this result, C3SD employs a dual sparsity-induced autoencoder to infer latent causal components, together with an adaptive group lasso to jointly structure the encoding and decoding matrices. In addition, a neural ordinary differential equation–based joint autoencoder models the continuous-time causal dynamics of the latent components and recovers their underlying dynamical causal structure. Extensive experiments demonstrate that C3SD effectively identifies latent components and the causal mechanisms driving their continuous temporal evolution, particularly in sparsely and irregularly sampled time series.