Multi-modal VAE
Compresses a patient's full molecular profile into a biological fingerprint
z_prolif correlation with proliferation markers
Statistical orthogonality: z_ctx_clean to proliferation
Recovered z_meth variance. Enables detection of resistance mechanisms invisible to standard models.
Combined NB + MSE + BCE likelihood
Overview
A neural network that compresses a patient's full molecular profile — thousands of gene expression values, mutations, copy number changes, and methylation patterns — into a compact mathematical fingerprint of 328 numbers that capture the essential biology. Similar tumors end up nearby in this space, different tumors far apart. The model handles missing data gracefully: if only gene expression is available, it still produces a reliable fingerprint with wider uncertainty.
Latent Space Structure
z_prolifProliferation rate latent. Supervised on MKI67/PCNA/TOP2A/BUB1/PLK1. Target r > 0.90.
z_pathway50 MSigDB Hallmark pathways × 4 dimensions each. Biologically interpretable pathway activities.
z_ctx_cleanProliferation-free biological context. Residualized post-hoc with guaranteed zero prolif leakage.
z_residualCaptures variation not in curated pathways. Non-pathway-specific biological signal.
z_methEpigenetic patterns from methylation encoder. Correlates with differentiation state.
z_cnv_spatialChromosomal instability patterns from 1D CNN on copy number data.
Inputs
4 inputsRNA-seq2,579 genesLog1p-transformed TME Boost gene list + proliferation markers
CNV1,886 genesContinuous copy number values, z-score standardized
DNA Mutations500 genesBinary mutation indicators with zero-inflated likelihood
Methylation1,000 probesBeta values [0,1], standardized
Outputs
2 outputsz_for_ode_v1328Canonical latent tensor for downstream integration
ReconstructionsPer-modalityReconstructed omics for validation
Mathematical Formulation
Evidence Lower Bound with β-annealing
Product-of-Experts for multi-modal fusion
Correlation supervision with proliferation markers
Key Features
- Product-of-Experts (PoE) fusion for graceful missing modality handling
- Additive decoder architecture for interpretable reconstruction
- Pathway-guided factorization using MSigDB Hallmark gene sets
- Supervised proliferation encoding with marker correlation loss
- Post-hoc residualization for clean context separation
Key Innovations
- 1Structured latent space with biological interpretability
- 2Statistical orthogonality (R² < 0.001) between subspaces
- 3Solved latent collapse: recovered epigenetic variance (0.607 vs ~0)
- 4Multi-modal fusion robust to 40%+ missing data
Hyperparameters
1e-3128Linear warmup 0→1 over 50 epochs0.5 per latent group1.0AdamW (weight_decay=1e-4)Training Details
Trained on 9,415 TCGA samples across 33 cancer types. Two-phase: Phase 1 freezes z_rna_private, Phase 2 unfreezes. GroupWiseKL + CrossReconstructionLoss for collapse prevention. Early stopping on validation ELBO.