Deep clustering with valid statistical testing for latent space clusters
Selective Inference for Deep Clustering in Latent Spaces
Machine Learning
Summary
Clustering helps find groups in complicated data, but checking if these groups are really meaningful is hard, especially when the data is first transformed by deep learning. The authors develop a way to properly test these groups statistically, correcting biases from reusing the same data for both finding and testing clusters. Their method works for clusters formed from deep neural network features, making the statistical results more trustworthy. They show with experiments and real data that their approach controls errors and can find significant group differences.
What this means in practice
- •For genomic data analysts: Test statistical differences between cellular clusters derived from deep-learning features while controlling false positive rates.
- •For machine learning engineers: Evaluate the statistical significance of clusters formed via deep embeddings to improve trust and model validation in high-dimensional data tasks.
Authors
Eina Mizui, Tomohiro Shiraishi, Shunichi Nishino, Ichiro Takeuchi
Abstract
Deep clustering is a powerful approach for discovering meaningful structures in high-dimensional data by learning a low-dimensional latent representation prior to clustering. Despite its empirical success, assessing the statistical reliability of the resulting clusters remains challenging. Testing discovered clusters on the same data induces selection bias and invalidates classical $p$-values. Selective inference (SI) provides a principled framework for correcting this bias, but existing methods focus on clustering performed directly on the observed features. In this work, we develop an SI framework for deep clustering with a fixed pretrained encoder. The key challenge is that cluster assignments are determined through a nonlinear transformation from the original data space to the latent space, resulting in a substantially more complex selection process than in conventional clustering. Our method provides a computationally tractable way to account for this process and enables valid statistical testing of differences between clusters identified in the latent space. Synthetic experiments demonstrate that the proposed method controls the Type I error rate while achieving higher power than valid but conservative baselines, and genomic applications show that it can identify significant cluster differences while appropriately accounting for selection bias. Our framework provides a principled approach to quantifying the statistical reliability of structures discovered by deep clustering.