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Global-Local Dirichlet Processes for Clustering Grouped Data in the Presence of Group-Specific Idiosyncratic Variables
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Proposes the global-local (GLocal) Dirichlet process for clustering grouped data with shared and group-specific variables, with truncation error bounds and a variational Bayes algorithm, applied to TCGA pan-GI cancer data.
Problem
Clustering grouped data where observations share some variables across groups but other variables are available only for certain groups, so existing HDP-type grouped clustering methods (which need a common variable set) cannot use the group-specific variables.
Approach
A Bayesian nonparametric prior in which each group's random measure is a DP with base measure U_j ⊗ V, where V is a shared DP-distributed global measure and U_j is a group-specific local measure; local clusters are nested within global clusters, so group-specific variables refine shared clusters.
Key results
- In simulations, GLocal DP achieves higher global-level ARI than HDP and higher local-level ARI than per-group GMM, with the advantage growing as local-variable separation increases.
- Truncation error bounds decay exponentially in both truncation levels T and K, and the posterior approximation error is O of the same bound.
- On TCGA GI cancers, the VI algorithm runs in under 9 minutes on a laptop, and local clusters (e.g., by smoking history or lymph node count) show distinct survival curves.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GLocal DP instead of HDP | Global-level clustering · Simulations | ARI | Helped |
| Use GLocal DP instead of GMM | Local-level clustering · Simulations | ARI | Helped |
| Increase separation in the local variables | GLocal DP · Simulations | ARI | Helped |
| Use GLocal DP instead of vHDPMM under less-separated conditions | Global and local clustering · Simulations | clustering accuracy | Helped |
| Use GLocal DP instead of vHDPMM with well-separated clusters | Global and local clustering · Simulations | clustering accuracy | No clear effect |
| Use variational inference instead of MCMC | GLocal DP · Simulations | clustering accuracy | No clear effect |
Surprising findings
- GLocal DP outperforms vHDPMM even when vHDPMM is the true generative model under less separated conditions.
Limitations
- Variational inference only finds local optima and depends on initialization, requiring multiple restarts.
- Assumes Gaussian likelihood for global and local variables in the presented algorithm.
- Global variables are reduced to top ten principal components for the real data application.
Experimental setup
Datasets: TCGA pan-gastrointestinal cancer gene expression and clinical data simulated grouped data
Benchmarks: simulated grouped data TCGA pan-GI cancer dataset
Metrics: adjusted Rand index Kaplan-Meier survival curves
Baselines: HDP Gaussian mixture model vHDPMM nested DP
Builds on: hierarchical Dirichlet process nested Dirichlet process Blei & Jordan variational inference versatile hierarchical Dirichlet process mixture model
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