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One of the most important problems in science is understanding causation. This problem is particularly challenging when causation has to be inferred from observational data only. A further challenge of this problem is if the observed data were generated in the presence of latent confounders. In this paper, we propose a method for detecting confounders in multivariate time series using a recently introduced concept referred to as differential causal effect (DCE). The solution is based on feature-based Gaussian processes that are not only used for estimating the DCE of the observed time series but also for estimating the latent confounders. We demonstrate the performance of the proposed method with several examples. They show that the proposed approach can detect confounders and can accurately estimate causal strengths.

Estimation of time-varying graph topologies from graph signals

Y. Liu, C. Cui (January 2023, Conference record IEEE International Conference on Acoustics Speech and Signal Processing)

In science and engineering, we often deal with signals that are acquired from time-varying systems represented by dynamic graphs. We observe these signals, and the interest is in finding the time-varying topology of the graphs. We propose two Bayesian methods for estimating these topologies without assuming any specific functional relationships among the signals on the graphs. The two methods exploit Gaussian processes, where the first method uses the length scale of the kernel and relies on variational inference for optimization, and the second method is based on derivatives of the functions and Monte Carlo sampling. Both methods estimate the time-varying topologies of the graphs sequentially. We provide numerical tests that show the performance of the methods in two settings.

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