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This research addresses the challenge of conducting interpretable causal inference between a binary treatment and its resulting outcome when not all confounders are known. Confounders are factors that have an influence on both the treatment…

We address the problem of integrating data from multiple, possibly biased, observational and interventional studies, to eventually compute counterfactuals in structural causal models. We start from the case of a single observational dataset…

Unobserved confounding is a fundamental challenge for estimating causal effects. To address unobserved confounding, recent literature has turned to two different approaches -- proxy variables and the use of multiple treatments. The first…

In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…

We argue that the selective inclusion of data points based on latent objectives is common in practical situations, such as music sequences. Since this selection process often distorts statistical analysis, previous work primarily views it…

Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in…

Control variables are included in regression analyses to estimate the causal effect of a treatment on an outcome. In this paper, we argue that the estimated effect sizes of controls are unlikely to have a causal interpretation themselves,…

The research is about a systematic investigation on the following issues. First, we construct different outcome regression-based estimators for conditional average treatment effect under, respectively, true (oracle), parametric,…

This paper considers linear panel data models where the dependence of the regressors and the unobservables is modelled through a factor structure. The asymptotic setting is such that the number of time periods and the sample size both go to…

The increasing availability of experimental data has intensified interest in calibrating stochastic models, raising fundamental questions about parameter identifiability. Structural identifiability determines whether parameters can be…

Describing statistical dependencies is foundational to empirical scientific research. For uncovering intricate and possibly non-linear dependencies between a single target variable and several source variables within a system, a principled…

This dissertation focuses on modern causal inference under uncertainty and data restrictions, with applications to neoadjuvant clinical trials, distributed data networks, and robust individualized decision making. In the first project, we…

Mixtures of factor analysers (MFA) models represent a popular tool for finding structure in data, particularly high-dimensional data. While in most applications the number of clusters, and especially the number of latent factors within…

We study the identification of binary choice models with fixed effects. We propose a condition called sign saturation and show that this condition is sufficient for identifying the model. In particular, this condition can guarantee…

Network data often exhibit block structures characterized by clusters of nodes with similar patterns of edge formation. When such relational data are complemented by additional information on exogenous node partitions, these sources of…

Promising results have driven a recent surge of interest in continuous optimization methods for Bayesian network structure learning from observational data. However, there are theoretical limitations on the identifiability of underlying…

This paper develops a general causal inference method for treatment effects models with noisily measured confounders. The key feature is that a large set of noisy measurements are linked with the underlying latent confounders through an…

Partial identification approaches are a flexible and robust alternative to standard point-identification approaches in general instrumental variable models. However, this flexibility comes at the cost of a ``curse of cardinality'': the…

Structural parameter identifiability is a property of a differential model with parameters that allows for the parameters to be determined from the model equations in the absence of noise. One of the standard approaches to assessing this…

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…