This dissertation develops structured statistical learning and inference methods for complex scientific data. Here, structure refers to problem-specific patterns that can be modeled to improve learning or inference: cluster-specific abundance and presence--absence patterns in microbiome compositions, modular organization in high-dimensional conditional dependence networks, and the conditional predictive structure among outcomes, covariates, and black-box predictions. Modeling such structure can improve clustering, network learning, and inference while preserving interpretability and statistical validity.

The first part studies model-based clustering of microbiome compositional data. We develop an Ising-Dirichlet mixture model for zero-inflated compositions, where each cluster has a presence--absence dependence structure and a nonzero abundance profile. The method is designed to improve clustering with limited samples by using information from both taxon occurrence patterns and relative abundance variation. Simulations and a resistant potato starch study show improved clustering accuracy and interpretable microbiome subgroups.

The second part studies variable clustering in high-dimensional graphical models. We develop a one-step joint estimation framework for a sparse precision matrix and a latent variable partition. This allows graph estimation and partition recovery to reinforce each other, rather than clustering a separately estimated graph. The method treats the partition as an explicit estimation target and allows nonzero cross-cluster dependence, relying on a modularity criterion in which within-cluster connectivity is denser than between-cluster connectivity. Simulations and real-data applications show more stable and interpretable graph-and-cluster representations than two-stage alternatives.

The third part studies statistical inference with limited gold-standard labels and abundant black-box predictions. Because these predictions are not ground truth, valid use requires bias correction. We develop adaptive prediction-powered inference, which learns a score-side adjustment from labeled data to approximate the variance-optimal conditional score adjustment through Taylor-based and ensemble-based constructions. Simulations and real-data examples show that the method preserves coverage while producing smaller confidence regions than existing prediction-powered and surrogate-adjustment methods.