Parameter Scaling

MaxFuse Parameter Scaling - Research Notes

Experiment Overview

Context

MaxFuse was originally configured for a 26-marker CODEX dataset with ~1,284 RNA cells and ~1.7M protein cells. When migrating to a 59-marker PhenoCycler dataset, the default parameters caused CCA overfitting because:

1. More protein features (59 vs 26) means more dimensions for CCA to fit
2. Same number of RNA cells (~1,284) means higher risk of fitting noise
3. CCA with too many components finds trivially perfect correlations by fitting noise

Critical Issue: CCA Overfitting

The most dangerous parameter is cca_components. With 25 CCA components and 59 protein features, CCA can find nearly perfect correlations that don't reflect real biological signal.

Rule of thumb: cca_components = min(n_shared - 1, sqrt(n_prot_active) + 1, hard_cap)

For 59 markers with 26 shared features:

• n_prot_active = 59 - 26 = 33
• sqrt(33) + 1 ≈ 7
• Use 7 CCA components, not 25

Verified Parameters

Parameter Scaling Table

Critical rule: All SVD components MUST be < n_features - 1.

Small Panel (<25 markers) Considerations

When protein_active == protein_shared (all markers are shared):

• The sqrt rule for CCA components breaks (n_prot_active = 0)
• Use simpler rule: cca_components = min(n_shared - 1, 10)
• Metacell size of 2 provides minimal benefit - use metacell_size=1 (disabled)

Implementation Code

# In notebook 2_integration.ipynb

# 1. Graph construction SVD
svd_comp1_graph = min(50, n_rna_features - 1)   # RNA: increased from 40
svd_comp2_graph = min(30, n_prot_features - 1)  # Protein: increased from 15

# 2. Initial pivots (shared features only - be conservative)
svd_shared1 = min(20, n_shared - 1)  # Reduced from 25
svd_shared2 = min(18, n_shared - 1)  # Reduced from 20

# 3. CCA components - CRITICAL
n_prot_active = n_prot_features - n_shared
cca_components = min(
    n_shared - 1,                     # Can't exceed shared features
    int(np.sqrt(n_prot_active)) + 1,  # sqrt rule for overfitting prevention
    12                                # Hard cap
)
cca_components = max(5, cca_components)  # At least 5

# 4. SVD before CCA
svd_cca_rna = min(50, n_rna_features - 1)
svd_cca_prot = min(35, n_prot_features - 1)  # NEW: was None (keep all)

# 5. Propagate - match CCA settings
fusor.propagate(
    svd_components1=min(50, n_rna_features - 1),
    svd_components2=min(35, n_prot_features - 1),
    wt1=0.7, wt2=0.7
)

Failed Attempts (Critical)

Key Insights

1. CCA components scale with sqrt, not linearly: Doubling protein features does NOT mean doubling CCA components. Use sqrt(n_active) + 1.

2. Protein SVD limits are essential: With more protein features, you MUST limit SVD before CCA to prevent overfitting. ~60% of features is a good target.

3. Graph SVD can be more generous: Graph construction is robust to dimensionality. Scale roughly with feature count.

4. Initial pivots need conservatism: The first matching uses only shared features (~26). Use fewer SVD components to avoid fitting noise.

5. Check canonical correlations: If the first few canonical correlations are all >0.95, you're overfitting. Reduce CCA components until you see meaningful decay.

Diagnostic Checks

After running with new parameters:

# Check 1: Canonical correlations should decay smoothly
# Good: [0.92, 0.85, 0.78, 0.65, 0.52, ...]
# Bad:  [0.99, 0.98, 0.97, 0.96, ...] (overfitting)

# Check 2: Distribution alignment
print(f"RNA: mean={rna.mean():.3f}, std={rna.std():.3f}")
print(f"Prot: mean={prot.mean():.3f}, std={prot.std():.3f}")
# Both should have similar scales (mean≈0, std≈1)

# Check 3: Matching quality
# Score distribution should be centered, not all near 1.0

References

• MaxFuse paper: Cross-modal data integration methods
• CCA overfitting: Rule of thumb is n_components < sqrt(min(n1, n2))
• Integration notebook: notebooks/2_integration.ipynb