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If $X,Y,Z$ denote sets of random variables, two different data sources may contain samples from $P_{X,Y}$ and $P_{Y,Z}$, respectively. We argue that causal discovery can help inferring properties of the `unobserved joint distributions'…
Nonparametric series regression often involves specification search over the tuning parameter, i.e., evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences…
A tacit assumption in classical linear regression problems is the full knowledge of the existing link between the covariates and responses. In Unlinked Linear Regression (ULR) this link is either partially or completely missing. While the…
Anomaly detection on attributed networks aims to find the nodes whose behaviors are significantly different from other majority nodes. Generally, network data contains information about relationships between entities, and the anomaly is…
Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. However, the theoretical aspects, e.g., identifiability and asymptotic properties of statistical estimation are still obscure. This paper…
We consider processes on social networks that can potentially involve three factors: homophily, or the formation of social ties due to matching individual traits; social contagion, also known as social influence; and the causal effect of an…
Many real-world decision-making tasks require learning causal relationships between a set of variables. Traditional causal discovery methods, however, require that all variables are observed, which is often not feasible in practical…
Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent…
Many scientific and engineering challenges -- ranging from pharmacokinetic drug dosage allocation and personalized medicine to marketing mix (4Ps) recommendations -- require an understanding of the unobserved heterogeneity in order to…
Random-effects meta-analyses are very commonly used in medical statistics. Recent methodological developments include multivariate (multiple outcomes) and network (multiple treatments) meta-analysis. Here we provide a new model and…
This paper proposes a statistical inference method for assessing treatment effects with dyadic data. Under the assumption that the treatments follow an exchangeable distribution, our approach allows for the presence of any unobserved…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
Statistical inference of directed relations given some unspecified interventions (i.e., the intervention targets are unknown) is challenging. In this article, we test hypothesized directed relations with unspecified interventions. First, we…
Homophily is a graph property describing the tendency of edges to connect similar nodes. There are several measures used for assessing homophily but all are known to have certain drawbacks: in particular, they cannot be reliably used for…
This paper develops new methods for causal inference in observational studies on a single large network of interconnected units, addressing two key challenges: long-range dependence among units and the presence of general interference. We…
Difference-in-differences (DiD) is a cornerstone of causal inference, yet extending it to functional outcomes is not a routine scalar generalization; rather, it entails three fundamental challenges in identification, inference, and…
Recently, there has been great interest in estimating the conditional average treatment effect using flexible machine learning methods. However, in practice, investigators often have working hypotheses about effect heterogeneity across…
In many applications, it is often of practical and scientific interest to detect anomaly events in a streaming sequence of high-dimensional or non-Euclidean observations. We study a non-parametric framework that utilizes nearest neighbor…
Statistical inference with nonresponse is quite challenging, especially when the response mechanism is nonignorable. In this case, the validity of statistical inference depends on untestable correct specification of the response model. To…
This paper considers a network formation model when links are potentially misclassified. We focus on a game-theoretical model of strategic network formation with incomplete information, in which the linking decisions depend on agents'…