  Causal discovery from time-series data has been a central task in machine
learning. Recently, Granger causality inference is gaining momentum due to its
good explainability and high compatibility with emerging deep neural networks.
However, most existing methods assume structured input data and degenerate
greatly when encountering data with randomly missing entries or non-uniform
sampling frequencies, which hampers their applications in real scenarios. To
address this issue, here we present CUTS, a neural Granger causal discovery
algorithm to jointly impute unobserved data points and build causal graphs, via
plugging in two mutually boosting modules in an iterative framework: (i) Latent
data prediction stage: designs a Delayed Supervision Graph Neural Network
(DSGNN) to hallucinate and register unstructured data which might be of high
dimension and with complex distribution; (ii) Causal graph fitting stage:
builds a causal adjacency matrix with imputed data under sparse penalty.
Experiments show that CUTS effectively infers causal graphs from unstructured
time-series data, with significantly superior performance to existing methods.
Our approach constitutes a promising step towards applying causal discovery to
real applications with non-ideal observations.
