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A Unified Framework for Variable Selection in Model-Based Clustering with Missing Not at Random
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Extends SelvarClust-style SRUW variable selection for model-based clustering to MNARz missingness (class-dependent missingness) using a spectral-Laplacian adaptive penalty for ranking plus BIC-based role assignment, with theory and experiments on simulated and Arabidopsis transcriptome data.
Problem
Variable selection for Gaussian model-based clustering when data are high-dimensional and missing not at random, which existing methods handle only in isolation.
Approach
Combines a data-driven spectral (graph-Laplacian) penalty matrix in penalized GMM ranking with an MNARz missingness mechanism tied to latent class inside the SRUW role-assignment EM, yielding a unified two-stage procedure with identifiability and consistency results.
Key results
- On simulations at 50% MNAR, SelvarMNARz achieves mean ARI 0.511 vs 0.363 (Clustvarsel), 0.348 (Selvar), 0.344 (VarSelLCM), with p<0.001.
- SelvarMNARz gives highest ARI and lowest WNRMSE across all missingness levels in both simulated scenarios (20 replications).
- On the Arabidopsis data the method partitions genes into 18 clusters and reclassifies P6 and P7 as redundant.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SelvarMNARz instead of Clustvarsel | Clustvarsel · Simulated data, MNAR 50% missingness | ARI: 0.363 -> 0.511 | Helped |
| Use SelvarMNARz instead of Selvar | Selvar · Simulated data, MNAR 50% missingness | ARI: 0.348 -> 0.511 | Helped |
| Use SelvarMNARz instead of VarSelLCM | VarSelLCM · Simulated data, MNAR 50% missingness | ARI: 0.344 -> 0.511 | Helped |
Surprising findings
- Under the proposed method, P6 and P7, previously found informative, are reclassified as redundant variables explained by P1-P4 on the transcriptome data.
Limitations
- Restricted to continuous data via Gaussian mixture models; categorical or mixed-type data not handled.
- Theoretical guarantees rely on regularity conditions and known model specification (K, m, r, l).
Experimental setup
Datasets: simulated Gaussian mixture datasets (7 and 14 variables) Arabidopsis thaliana transcriptome (1,267 genes)
Benchmarks: simulated datasets with MAR/MNAR missingness Arabidopsis transcriptome
Metrics: ARI WNRMSE proportion of correct relevant variable selection Welch t-test p-value
Baselines: Clustvarsel Selvar VarSelLCM
Builds on: SRUW model (Maugis et al.) SelvarClustMV MNARz (Sportisse et al.) penalized GMM for clustering (Celeux et al.) adaptive lasso
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