Part 6: NNMM as Traditional Genomic Prediction

Overview

NNMM is a general framework that encompasses traditional genomic prediction models as special cases. By configuring the network architecture appropriately, you can use NNMM to perform standard single-trait BayesC (and other Bayesian alphabet methods).

This demonstrates that NNMM generalizes traditional genomic prediction rather than replacing it.

The Key Insight

Traditional genomic prediction models like BayesC can be expressed as a special case of NNMM by:

1. Using a completely missing middle layer - Latent nodes will be sampled based on genotype information
2. Using a linear activation function - This ensures the relationship between the latent layer and phenotype is linear

┌─────────────┐     ┌─────────────────┐     ┌─────────────┐
│  Genotypes  │ ──► │  Latent Nodes   │ ──► │ Phenotype   │
│   (SNPs)    │     │ (100% missing)  │     │    (y)      │
└─────────────┘     └─────────────────┘     └─────────────┘
                    Sampled via BayesC       Linear activation

This is mathematically equivalent to the traditional model:

\[y = X\beta + Z\alpha + e\]

where $\alpha$ are marker effects sampled using BayesC.

Example: Single-Trait BayesC via NNMM

using NNMM
using NNMM.Datasets
using DataFrames
using CSV
using Statistics
using Random

Random.seed!(42)

# Step 1: Load data (using simulated data with aligned individuals)
geno_path = Datasets.dataset("genotypes_1000snps.txt", dataset_name="simulated_omics_data")
pheno_path = Datasets.dataset("phenotypes_sim.txt", dataset_name="simulated_omics_data")
pheno_df = CSV.read(pheno_path, DataFrame)

# Step 2: Create middle layer with completely missing latent nodes
# Use at least 2 latent nodes for matrix operations in HMC
n_individuals = nrow(pheno_df)
latent_df = DataFrame(
    ID = pheno_df.ID,
    latent1 = fill(missing, n_individuals),
    latent2 = fill(missing, n_individuals)
)
latent_file = "latent_bayesc.csv"
CSV.write(latent_file, latent_df; missingstring="NA")

# Step 3: Create phenotype file
trait_df = pheno_df[:, [:ID, :trait1]]
trait_file = "trait_bayesc.csv"
CSV.write(trait_file, trait_df; missingstring="NA")

# Step 4: Define 3-layer network
layers = [
    Layer(layer_name = "geno", data_path = [geno_path]),
    Layer(layer_name = "latent", data_path = latent_file, missing_value = "NA"),
    Layer(layer_name = "phenotypes", data_path = trait_file, missing_value = "NA")
]

# Step 5: Define equations with LINEAR activation
equations = [
    # Genotypes → Latent (marker regression with BayesC)
    Equation(
        from_layer_name = "geno",
        to_layer_name = "latent",
        equation = "latent = intercept + geno",
        omics_name = ["latent1", "latent2"],
        method = "BayesC",
        estimatePi = true
    ),
    # Latent → Phenotype (LINEAR activation = standard regression)
    Equation(
        from_layer_name = "latent",
        to_layer_name = "phenotypes",
        equation = "phenotypes = intercept + latent",
        phenotype_name = ["trait1"],
        method = "BayesC",
        activation_function = "linear"  # Key: linear activation
    )
]

# Step 6: Run analysis
result = runNNMM(layers, equations;
    chain_length = 5000,
    burnin = 1000,
    output_folder = "nnmm_bayesc_results"
)

# Step 7: Get results
ebv = result["EBV_NonLinear"]
ebv.ID = string.(ebv.ID)
pheno_df.ID = string.(pheno_df.ID)

println("EBV mean: ", round(mean(Float64.(ebv.EBV)), digits=4))
println("EBV std:  ", round(std(Float64.(ebv.EBV)), digits=4))

# Check accuracy with true breeding values
merged = innerjoin(ebv, pheno_df[:, [:ID, :genetic_total]], on=:ID)
accuracy = cor(Float64.(merged.EBV), merged.genetic_total)
println("Accuracy: ", round(accuracy, digits=4))

# Cleanup
rm(latent_file, force=true)
rm(trait_file, force=true)

Current Limitations

Comparison: Direct BayesC vs NNMM as BayesC

Why Use NNMM for Traditional Analysis?

1. Unified framework: Same code structure for simple and complex models
2. Easy extension: Add observed omics data to the middle layer when available
3. Gradual complexity: Start with traditional model, add neural network components as needed
4. Future-proof: As more omics data becomes available, simply fill in the missing values

Other Bayesian Methods

You can use any Bayesian alphabet method by changing the method parameter:

# BayesA - marker-specific variances, all markers included
Equation(..., method="BayesA")

# BayesB - marker-specific variances, subset of markers included
Equation(..., method="BayesB", estimatePi=true)

# BayesC - common variance, subset of markers included (default)
Equation(..., method="BayesC", estimatePi=true)

# BayesL - Bayesian LASSO
Equation(..., method="BayesL")

# RR-BLUP - Ridge Regression BLUP (all markers, common variance)
Equation(..., method="RR-BLUP")

# GBLUP - Genomic BLUP (only for Layer 1→2)
# Note: GBLUP is only supported for the genotype→omics equation
Equation(..., method="GBLUP")  # Layer 1→2 only

Summary

NNMM provides a superset of traditional genomic prediction methods:

This design allows researchers to start with familiar methods and gradually incorporate more complex models as data and understanding grow.