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Getting Started with missoNet

Yixiao Zeng, Celia M. T. Greenwood

2025-09-02

1 Introduction

The missoNet package implements a powerful framework for multitask learning with missing responses, simultaneously estimating:

1.1 The Model

The conditional Gaussian model is: \[ \mathbf{Y} = \mathbf{1}\mu^T + \mathbf{X}\mathbf{B} + \mathbf{E}, \quad \mathbf{E} \sim \mathrm{MVN}(0, \Theta^{-1}) \] where:

For theoretical details, see Zeng et al. (2025).

1.2 Installation

# Install from CRAN (when available)
install.packages("missoNet")

# Or install development version from GitHub
devtools::install_github("yixiao-zeng/missoNet")
# Load the package
library(missoNet)

2 Quick Start

2.1 Generate Example Data

The package includes a flexible data generator for testing:

# Generate synthetic data
sim <- generateData(
  n = 200,                # Sample size
  p = 50,                 # Number of predictors
  q = 10,                 # Number of responses
  rho = 0.1,              # Missing rate (10%)
  missing.type = "MCAR"   # Missing completely at random
)

# Examine the data structure
str(sim, max.level = 1)
#> List of 7
#>  $ X           : num [1:200, 1:50] -0.424 0.84 -2.546 1.825 1.217 ...
#>  $ Y           : num [1:200, 1:10] -0.0884 -0.3687 2.7607 -2.1025 3.2892 ...
#>  $ Z           : num [1:200, 1:10] -0.0884 -0.3687 2.7607 -2.1025 3.2892 ...
#>  $ Beta        : num [1:50, 1:10] 0 0 0 0 0 0 0 0 0 0 ...
#>  $ Theta       : num [1:10, 1:10] 1 0 0 0 0 0 0 0 0 0 ...
#>  $ rho         : num [1:10] 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
#>  $ missing.type: chr "MCAR"
#>  - attr(*, "class")= chr "missoNet.sim"
# Check dimensions
cat("Predictors (X):", dim(sim$X), "\n")
#> Predictors (X): 200 50
cat("Complete responses (Y):", dim(sim$Y), "\n")
#> Complete responses (Y): 200 10
cat("Observed responses (Z):", dim(sim$Z), "\n")
#> Observed responses (Z): 200 10
cat("Missing rate:", sprintf("%.1f%%", mean(is.na(sim$Z)) * 100), "\n")
#> Missing rate: 10.0%

2.2 Basic Model Fitting

# Fit missoNet with automatic parameter selection
fit <- missoNet(
  X = sim$X,
  Y = sim$Z,  # Use observed responses with missing values
  GoF = "BIC" # Goodness-of-fit criterion
)
#> 
#> =============================================================
#>                           missoNet
#> =============================================================
#> 
#> > Initializing model...
#> 
#> --- Model Configuration -------------------------------------
#>   Data dimensions:      n =   200, p =   50, q =   10
#>   Missing rate (avg):    10.0%
#>   Selection criterion:  BIC
#>   Lambda grid:          standard (dense)
#>   Lambda grid size:     50 x 50 = 2500 models
#> -------------------------------------------------------------
#> 
#> --- Optimization Progress -----------------------------------
#>   Stage 1: Initializing warm starts
#>   Stage 2: Grid search (sequential)
#> -------------------------------------------------------------
#> 
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#> 
#> -------------------------------------------------------------
#> 
#> > Refitting optimal model ...
#> 
#> 
#> --- Optimization Results ------------------------------------
#>   Optimal lambda.beta:   5.8376e-01
#>   Optimal lambda.theta:  1.2260e-01
#>   BIC value:              4305.2563
#>   Active predictors:     31 / 50 (62.0%)
#>   Network edges:         3 / 45 (6.7%)
#> -------------------------------------------------------------
#> 
#> =============================================================

# Extract optimal estimates
Beta.hat <- fit$est.min$Beta
Theta.hat <- fit$est.min$Theta
mu.hat <- fit$est.min$mu
# Model summary
cat("Selected lambda.beta:", fit$est.min$lambda.beta, "\n")
#> Selected lambda.beta: 0.5837619
cat("Selected lambda.theta:", fit$est.min$lambda.theta, "\n")
#> Selected lambda.theta: 0.1225953
cat("Active predictors:", sum(rowSums(abs(Beta.hat)) > 1e-8), "/", nrow(Beta.hat), "\n")
#> Active predictors: 31 / 50
cat("Network edges:", sum(abs(Theta.hat[upper.tri(Theta.hat)]) > 1e-8), 
    "/", ncol(Theta.hat) * (ncol(Theta.hat)-1) / 2, "\n")
#> Network edges: 3 / 45

2.3 Visualization

# Visualize the regularization path
plot(fit, type = "heatmap")

# Visualize the regularization path in a scatter plot
plot(fit, type = "scatter")

2.4 Making Predictions

# Split data for demonstration
train_idx <- 1:150
test_idx <- 151:200

# Refit on training data
fit_train <- missoNet(
  X = sim$X[train_idx, ],
  Y = sim$Z[train_idx, ],
  GoF = "BIC",
  verbose = 0  # Suppress output
)

# Predict on test data
Y_pred <- predict(fit_train, newx = sim$X[test_idx, ])

# Evaluate predictions (using complete data for comparison)
mse <- mean((Y_pred - sim$Y[test_idx, ])^2)
cat("Test set MSE:", round(mse, 4), "\n")
#> Test set MSE: 1.2326

3 Understanding Missing Data Mechanisms

missoNet handles three types of missing data:

# Generate data with different missing mechanisms
n <- 300; p <- 30; q <- 8; rho <- 0.15

sim_mcar <- generateData(n, p, q, rho, missing.type = "MCAR")
sim_mar <- generateData(n, p, q, rho, missing.type = "MAR")
sim_mnar <- generateData(n, p, q, rho, missing.type = "MNAR")

# Visualize missing patterns
par(mfrow = c(1, 3), mar = c(4, 4, 3, 1))

# MCAR pattern
image(1:q, 1:n, t(is.na(sim_mcar$Z)), 
      col = c("white", "darkred"),
      xlab = "Response", ylab = "Observation",
      main = "MCAR: Random Pattern")

# MAR pattern
image(1:q, 1:n, t(is.na(sim_mar$Z)), 
      col = c("white", "darkred"),
      xlab = "Response", ylab = "Observation",
      main = "MAR: Depends on X")

# MNAR pattern
image(1:q, 1:n, t(is.na(sim_mnar$Z)), 
      col = c("white", "darkred"),
      xlab = "Response", ylab = "Observation",
      main = "MNAR: Depends on Y")

4 Model Selection Strategies

4.1 Comparing Selection Criteria

# Fit with different criteria
criteria <- c("AIC", "BIC", "eBIC")
results <- list()

for (crit in criteria) {
  results[[crit]] <- missoNet(
    X = sim$X,
    Y = sim$Z,
    GoF = crit,
    verbose = 0
  )
}

# Compare selected models
comparison <- data.frame(
  Criterion = criteria,
  Lambda.Beta = sapply(results, function(x) x$est.min$lambda.beta),
  Lambda.Theta = sapply(results, function(x) x$est.min$lambda.theta),
  Active.Predictors = sapply(results, function(x) 
    sum(rowSums(abs(x$est.min$Beta)) > 1e-8)),
  Network.Edges = sapply(results, function(x) 
    sum(abs(x$est.min$Theta[upper.tri(x$est.min$Theta)]) > 1e-8)),
  GoF.Value = sapply(results, function(x) x$est.min$gof)
)

print(comparison, digits = 4)
#>      Criterion Lambda.Beta Lambda.Theta Active.Predictors Network.Edges GoF.Value
#> AIC        AIC      0.3770     0.007715                42            34      4021
#> BIC        BIC      0.5838     0.122595                31             3      4305
#> eBIC      eBIC      0.5838     0.122595                31             3      4483

4.2 Custom Lambda Grids

# Define custom regularization paths
lambda.beta <- 10^seq(0, -2, length.out = 15)
lambda.theta <- 10^seq(0, -2, length.out = 15)

# Fit with custom grid
fit_custom <- missoNet(
  X = sim$X,
  Y = sim$Z,
  lambda.beta = lambda.beta,
  lambda.theta = lambda.theta,
  verbose = 0
)
# Grid coverage summary
cat("  Beta range: [", 
    sprintf("%.4f", min(fit_custom$param_set$gof.grid.beta)), ", ",
    sprintf("%.4f", max(fit_custom$param_set$gof.grid.beta)), "]\n", sep = "")
#>   Beta range: [0.0100, 1.0000]
cat("  Theta range: [", 
    sprintf("%.4f", min(fit_custom$param_set$gof.grid.theta)), ", ",
    sprintf("%.4f", max(fit_custom$param_set$gof.grid.theta)), "]\n", sep = "")
#>   Theta range: [0.0100, 1.0000]
cat("  Total models evaluated:", length(fit_custom$param_set$gof), "\n")
#>   Total models evaluated: 225

5 Working with Real Data Patterns

5.1 Handling Variable Missing Rates

# Create data with variable missing rates across responses
n <- 300; p <- 30; q <- 8; rho <- 0.15
rho_vec <- seq(0.05, 0.30, length.out = q)

sim_var <- generateData(
  n = 300,
  p = 30,
  q = 8,
  rho = rho_vec,  # Different missing rate for each response
  missing.type = "MAR"
)

# Examine missing patterns
miss_summary <- data.frame(
  Response = paste0("Y", 1:q),
  Target = rho_vec,
  Actual = colMeans(is.na(sim_var$Z))
)

print(miss_summary, digits = 3)
#>   Response Target Actual
#> 1       Y1 0.0500 0.0367
#> 2       Y2 0.0857 0.0500
#> 3       Y3 0.1214 0.1167
#> 4       Y4 0.1571 0.1633
#> 5       Y5 0.1929 0.2000
#> 6       Y6 0.2286 0.2267
#> 7       Y7 0.2643 0.2367
#> 8       Y8 0.3000 0.3033

# Fit model accounting for variable missingness
fit_var <- missoNet(
  X = sim_var$X,
  Y = sim_var$Z,
  adaptive.search = TRUE, # Fast adaptive search
  verbose = 0
)

# Visualize
plot(fit_var)

5.2 Incorporating Prior Knowledge

# Use penalty factors to incorporate prior information
p <- ncol(sim$X)
q <- ncol(sim$Z)

# Example: We know predictors 1-10 are important
beta.pen.factor <- matrix(1, p, q)
beta.pen.factor[1:10, ] <- 0.1  # Lighter penalty for known important predictors

# Example: We expect certain response pairs to be connected
theta.pen.factor <- matrix(1, q, q)
theta.pen.factor[1, 2] <- theta.pen.factor[2, 1] <- 0.1
theta.pen.factor[3, 4] <- theta.pen.factor[4, 3] <- 0.1

# Fit with prior information
fit_prior <- missoNet(
  X = sim$X,
  Y = sim$Z,
  beta.pen.factor = beta.pen.factor,
  theta.pen.factor = theta.pen.factor
)

6 Tips for Optimal Performance

6.1 Standardization

# Standardization is recommended (default: TRUE)
# for numerical stability and comparable penalties
fit_std <- missoNet(X = sim$X, Y = sim$Z, 
                    standardize = TRUE, 
                    standardize.response = TRUE)

# Without standardization (for pre-scaled data)
fit_no_std <- missoNet(X = scale(sim$X), Y = scale(sim$Z), 
                       standardize = FALSE,
                       standardize.response = FALSE)

6.2 Convergence Settings

# Adjust convergence settings based on problem difficulty and time constraints
fit_tight <- missoNet(
  X = sim$X,
  Y = sim$Z,
  beta.tol = 1e-6,      # Tighter tolerance
  theta.tol = 1e-6,
  beta.max.iter = 10000,  # More iterations allowed
  theta.max.iter = 10000
)

# For quick exploration, use looser settings
fit_quick <- missoNet(
  X = sim$X,
  Y = sim$Z,
  beta.tol = 1e-3,      # Looser tolerance
  theta.tol = 1e-3,
  beta.max.iter = 1000,   # Fewer iterations
  theta.max.iter = 1000,
  adaptive.search = TRUE # Fast adaptive search
)

7 Summary

Key features of missoNet:
  ✓ Handles missing responses naturally through unbiased estimating equations
  ✓ Joint estimation of regression and network structures
  ✓ Flexible regularization with separate penalties for coefficients and network
  ✓ Multiple selection criteria (AIC/BIC/eBIC, cross-validation)
  ✓ Efficient algorithms with warm starts and adaptive search
  ✓ Comprehensive visualization tools
For advanced features including cross-validation, see the companion vignettes.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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