Omar Faruque successfuly defends his PhD Proposal!

Causal analysis of observational data has become a central research area for understanding complex natural and socio-technical systems. Domains such as climate, healthcare, transportation, energy, and finance generate rich temporal and spatiotemporal datasets that capture the evolution of dynamic processes. Analyzing these data through a causal lens is crucial not only for scientific interpretation of underlying mechanisms but also for informing robust policy and decision-making. The first step in studying such systems is the development of holistic causal graphs that can represent the underlying causal mechanisms and then quantifying the impacts of these causal relations. However, observational data in these domains typically exhibit nonlinearity, nonstationarity, spatial heterogeneity, autocorrelation, time-varying confounding, and diverse noise distributions, posing significant challenges for existing causal methods.

This thesis addresses these challenges through three integrated contributions. First, we propose the Transformer-Integrated Temporal Causal Discovery (TTCD) framework, designed to uncover both contemporaneous and lagged causal relations from nonstationary time series. TTCD features a Non-Stationary Feature Learner to extract robust features, combining temporal and frequency-domain attention with dynamic non-stationarity profiling. A custom Causal Structure Learner then infers the underlying causal graph from these latent features, without strong assumptions about the underlying noise or data generation process.

Second, we extend causal discovery to spatiotemporal data, which often arise in gridded representations of physical and biological systems. As important phenomena in scientific domains are naturally represented as spatiotemporal data, it is required to analyze causal relations from both spatial and temporal modality. To tackle the high dimensionality, local spatial interference, and long-range dependencies inherent in these datasets, we develop a hybrid autoencoder architecture that integrates Graph Convolutional Networks (GCNs) with a Causal Graph Transformer. Unlike prior approaches that rely on strong structural assumptions, static graphs, or supervised signals, this model dynamically learns adjacency structures, avoiding these assumptions. The proposed method captures local connectivity through GCNs and long-range dependencies through the attention-based causal graph transformer.

Finally, we address the problem of causal inference in spatiotemporal systems with hidden confounders, where standard approaches are invalidated by unobserved factors, spatial interference, time-varying confounding, and spillover effects. We introduce a deep learning based potential outcome framework for inferring causal effects of applied treatments from spatiotemporal data in the presence of hidden confounders. The proposed model utilizes the causal graph diffusion technique to estimate unobserved confounders, taking spatial and temporal dynamics into account, and then predicts the factual and counterfactual outcomes of the applied treatment by controlling time-varying confounding with the help of a latent factor model.

Together, these contributions establish a unified framework for causal discovery and inference in temporal and spatiotemporal settings, advancing methodological capabilities while providing practical tools for scientific and policy applications. By applying the proposed methods to datasets from climate, healthcare, and other natural systems, this work seeks to enhance the reliability, interpretability, and actionability of causal analysis in complex real-world domains.

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