Xiang Lyu

Kazi Tasnim Zinat, Yun Zhou, Xiang Lyu et al.

Inferring causal relationships between event pairs in a temporal sequence is applicable in many domains such as healthcare, manufacturing, and transportation. Most existing work on causal inference primarily focuses on event types within the designated domain, without considering the impact of exogenous out-of-domain interventions. In real-world settings, these out-of-domain interventions can significantly alter causal dynamics. To address this gap, we propose a new causal framework to define average treatment effect (ATE), beyond independent and identically distributed (i.i.d.) data in classic Rubin's causal framework, to capture the causal relation shift between events of temporal process under out-of-domain intervention. We design an unbiased ATE estimator, and devise a Transformer-based neural network model to handle both long-range temporal dependencies and local patterns while integrating out-of-domain intervention information into process modeling. Extensive experiments on both simulated and real-world datasets demonstrate that our method outperforms baselines in ATE estimation and goodness-of-fit under out-of-domain-augmented point processes.

Xiang Lyu, Will Wei Sun, Zhaoran Wang et al.

We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. A critical challenge in the estimation and inference of this model is the fact that its penalized maximum likelihood estimation involves minimizing a non-convex objective function. To address it, this paper makes two contributions: (i) In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with an optimal statistical rate of convergence. (ii) We propose a de-biased statistical inference procedure for testing hypotheses on the true support of the sparse precision matrices, and employ it for testing a growing number of hypothesis with false discovery rate (FDR) control. The asymptotic normality of our test statistic and the consistency of FDR control procedure are established. Our theoretical results are backed up by thorough numerical studies and our real applications on neuroimaging studies of Autism spectrum disorder and users' advertising click analysis bring new scientific findings and business insights. The proposed methods are encoded into a publicly available R package Tlasso.