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Mixed effect neural network: Genotypes -> Unobserved intemediate traits -> Phenotyes

Tips: please center the phenotypes to have zero mean.

Example(a): fully-connected neural networks, all intemediate traits are unobserved

  • nonlinear function (to define relationship between middle layer and phenotye): tanh (other supported activation functions: "sigmoid", "relu", "leakyrelu", "linear")
  • number of nodes in the middle layer: 3
  • Bayesian model: multiple independent single-trait BayesC (to sample marker effects on intemediate traits). Note, to use multi-trait Bayesian Alphabet models, please set mega_trait=false in runMCMC() function.
  • sample the unobserved intemediate traits in the middle layer: Hamiltonian Monte Carlo

# Step 1: Load packages
using JWAS,DataFrames,CSV,Statistics,JWAS.Datasets,Random
Random.seed!(123)

# Step 2: Read data 
phenofile  = dataset("phenotypes.csv") #get example data path
genofile   = dataset("genotypes.csv")  #get example data path

phenotypes = CSV.read(phenofile,DataFrame,delim = ',',header=true,missingstrings=["NA"]) #read phenotypes (output layer)
genotypes  = get_genotypes(genofile,separator=',',method="BayesC");                      #read genotypes  (input layer)


# Step 3: Build Model Equations 
model_equation  ="y1 = intercept + genotypes"  #name of phenotypes is "y1" in the phenotypes data
                                               #name of genotypes is "genotypes" (user-defined in the previous step)
                                               #the single-trait mixed model used between input and each node in middle layer is: middle node = intercept + genotypes
model = build_model(model_equation,
		    num_hidden_nodes=3,            #number of nodes in middle layer is 3
		    nonlinear_function="tanh");    #tanh function is used to approximate relationship between middle layer and phenotype


# Step 4: Run Analysis
out=runMCMC(model,phenotypes,chain_length=5000); 

# Step 5: Check Accuruacy
results    = innerjoin(out["EBV_NonLinear"], phenotypes, on = :ID) 
accuruacy  = cor(results[!,:EBV],results[!,:bv1])

Example output files

The i-th middle nodes will be named as "trait name"+"i". In our example, the observed trait is named "y1", and there are 3 middle nodes, so the middle nodes are named as "y11", "y12", and "y13", respectively.

Below is a list of files containing estimates and standard deviations for variables of interest.

file name description
EBV_NonLinear.txt estimated breeding values for observed trait
EBV_y11.txt estimated breeding values for middle node 1
EBV_y12.txt estimated breeding values for middle node 2
EBV_y13.txt estimated breeding values for middle node 3
genetic_variance.txt estimated genetic variance-covariance of all middle nodes
heritability.txt estimated heritability of all middle nodes
location_parameters.txt estimated bias of all middle nodes
neural_networks_bias_and_weights.txt. estimated bias of phenotypes and weights between middle nodes and phenotypes
pi_genotypes.txt estimated pi of all middle nodes
marker_effects_genotypes.txt estimated marker effects of all middle nodes
residual_variance.txt estimated residual variance-covariance for all middle nodes

Below is a list of files containing MCMC samples for variables of interest.

file name description
MCMC_samples_EBV_NonLinear.txt MCMC samples from the posterior distribution of breeding values for phenotypes
MCMC_samples_EBV_y11.txt MCMC samples from the posterior distribution of breeding values for middle node 1
MCMC_samples_EBV_y12.txt MCMC samples from the posterior distribution of breeding values for middle node 2
MCMC_samples_EBV_y13.txt MCMC samples from the posterior distribution of breeding values for middle node 3
MCMC_samples_genetic_variance.txt MCMC samples from the posterior distribution of genetic variance-covariance for all middle nodes
MCMC_samples_heritability.txt MCMC samples from the posterior distribution of heritability for all middle nodes
MCMC_samples_marker_effects_genotypes_y11 MCMC samples from the posterior distribution of marker effects for middle node 1
MCMC_samples_marker_effects_genotypes_y12 MCMC samples from the posterior distribution of marker effects for middle node 2
MCMC_samples_marker_effects_genotypes_y13 MCMC samples from the posterior distribution of marker effects for middle node 3
MCMC_samples_marker_effects_variances_genotypes.txt MCMC samples from the posterior distribution of marker effect variance for all middle nodes
MCMC_samples_neural_networks_bias_and_weights.txt. MCMC samples from the posterior distribution of bias of observed trait and weights between middle nodes and phenotypes
MCMC_samples_pi_genotypes.txt MCMC samples from the posterior distribution of pi for all middle nodes
MCMC_samples_residual_variance.txt MCMC samples from the posterior distribution of residual variance-covariance for all middle nodes