Local Independence Testing for Point Processes
This addresses a technical bottleneck in causal inference for point processes, particularly in handling latent confounders, but is incremental as it builds on existing expansion techniques.
The paper tackled the problem of testing local independence for point processes in causal structure learning, which previously required strong model assumptions like Hawkes processes without latent confounders, and introduced an expansion-based method that approximates marginalized intensities arbitrarily well, showing improved performance in real and simulated data.
Constraint based causal structure learning for point processes require empirical tests of local independence. Existing tests require strong model assumptions, e.g. that the true data generating model is a Hawkes process with no latent confounders. Even when restricting attention to Hawkes processes, latent confounders are a major technical difficulty because a marginalized process will generally not be a Hawkes process itself. We introduce an expansion similar to Volterra expansions as a tool to represent marginalized intensities. Our main theoretical result is that such expansions can approximate the true marginalized intensity arbitrarily well. Based on this we propose a test of local independence and investigate its properties in real and simulated data.