Generator Identification for Linear SDEs with Additive and Multiplicative Noise

Published: 21 Sept 2023, Last Modified: 01 Jan 2024NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: Linear SDE, Identification, Causal inference
Abstract: In this paper, we present conditions for identifying the generator of a linear stochastic differential equation (SDE) from the distribution of its solution process with a given fixed initial state. These identifiability conditions are crucial in causal inference using linear SDEs as they enable the identification of the post-intervention distributions from its observational distribution. Specifically, we derive a sufficient and necessary condition for identifying the generator of linear SDEs with additive noise, as well as a sufficient condition for identifying the generator of linear SDEs with multiplicative noise. We show that the conditions derived for both types of SDEs are generic. Moreover, we offer geometric interpretations of the derived identifiability conditions to enhance their understanding. To validate our theoretical results, we perform a series of simulations, which support and substantiate the established findings.
Supplementary Material: zip
Submission Number: 5668