Biostatistics Dept. Seminar: Graph Semi-Supervised Learning for Point Classification on Data Manifolds
Biostatistics Department Seminar
Title: Graph Semi-Supervised Learning for Point Classification on Data Manifolds
Abstract: Many modern classification problems involve data that live in high-dimensional spaces but exhibit strong low-dimensional structure. Motivated by the manifold hypothesis, this talk presents a graph-based semi-supervised learning framework that explicitly exploits this geometric structure to improve generalization. We model data as samples from an unknown low-dimensional manifold embedded in a high-dimensional ambient space. The manifold is first approximated in an unsupervised manner using a variational autoencoder, whose latent representations provide data-dependent coordinates. From these embeddings, we construct a geometric graph using Gaussian-weighted edges based on pairwise distances, turning the original classification problem into a semi-supervised node classification task on a graph, which we solve using a graph neural network. The main contribution of this work is a theoretical analysis of the statistical generalization behavior of this data–manifold–graph pipeline. Under uniform sampling assumptions, we show that the generalization gap of the semi-supervised learning task decreases as the graph size grows, up to the optimization error of the GNN. We further show that a simple training strategy that periodically resamples slightly larger graphs during training leads to asymptotically vanishing generalization error. We conclude with experimental results on image classification benchmarks, including MedMNIST, which support the theory and illustrate how leveraging learned geometric structure can improve both robustness and scalability in graph-based learning.
Speaker
Luana Ruiz is an Assistant Professor in the Department of Applied Mathematics and Statistics and a member of the Data Science and AI Institute at Johns Hopkins University, Whiting School of Engineering..
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2025-2026 Monday Seminar Series
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