Single-cell spatial transcriptomics (ST) enables the measurement of gene expression of individual cells while simultaneously capturing the spatial positions of these cells within a tissue sample. To utilize these spatial positions effectively, careful model selection is required to ensure conclusions reflect spatial dependencies in the underlying biology. In this dissertation, we contribute three novel methodologies that merge deep learning with statistical inference for ST data.

First, we attempt to better predict gene expression by leveraging the spatial context included in spatial transcriptomics data. Comparing predictions from a spatial model to those from a baseline regressor without cell neighborhood information offers insights into how expression changes because of cell-cell communication (CCC) signals. However, to trust conclusions reached from such a paired modeling framework, the baseline version of a model needs to be a valid non-spatial reference point. To this end, we develop a graph convolutional network (GCN) that uses graphs defined by cellular positions to predict gene expression and compare against a counterpart model without spatial context.

Second, we study a clustering task for ST data through a Bayesian framework. A central challenge in spatial transcriptomics is to identify distinct cell communities that not only reflect transcriptional heterogeneity but also preserve spatial coherence across tissue. These clusters often represent biological components such as cortical layers, tissue microenvironments, or pathological regions, whose spatial organization is critical for interpreting tissue structure and function. Existing exact Bayesian methods often rely on hard assignments, limiting flexibility. To address this limitation, we introduce a stochastic variational inference (SVI) method designed to learn posterior spot cluster distributions that are both spatially coherent and biologically interpretable. This approach is more computationally efficient than methods that rely on posterior sampling techniques, such as Markov Chain Monte Carlo (MCMC), which can be expensive to retrain.

Third, we leverage normalizing flows as the approximate posterior distributions for variational inference on ST data. Normalizing flows transform simple base distributions into more expressive ones by stacking invertible transformations based on the change-of-variables formula. This allows us to model flexible, multi-modal posteriors over soft cluster assignments beyond the capacity of standard variational families.