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Getting Started with missoNet
In missoNet: Joint Sparse Regression & Network Learning with Missing Data
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.width = 7,
fig.height = 5,
fig.align = "center",
out.width = "90%",
dpi = 90,
message = FALSE,
warning = FALSE
)
options(width = 100)
Introduction
The missoNet package implements a powerful framework for multitask learning with missing responses, simultaneously estimating:
-
Regression coefficients ($\mathbf{B}$): Relationships between predictors and multiple responses
-
Conditional network ($\Theta$): Dependencies among responses after accounting for predictors
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:
-
$\mathbf{Y} \in \mathbb{R}^{n \times q}$: Response matrix (may contain missing values)
-
$\mathbf{X} \in \mathbb{R}^{n \times p}$: Predictor matrix (complete)
-
$\mathbf{B} \in \mathbb{R}^{p \times q}$: Coefficient matrix
-
$\Theta \in \mathbb{R}^{q \times q}$: Precision matrix (inverse covariance)
-
$\mu \in \mathbb{R}^q$: Intercept vector
For theoretical details, see Zeng et al. (2025).
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)
Quick Start
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)
# Check dimensions
cat("Predictors (X):", dim(sim$X), "\n")
cat("Complete responses (Y):", dim(sim$Y), "\n")
cat("Observed responses (Z):", dim(sim$Z), "\n")
cat("Missing rate:", sprintf("%.1f%%", mean(is.na(sim$Z)) * 100), "\n")
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
)
# 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")
cat("Selected lambda.theta:", fit$est.min$lambda.theta, "\n")
cat("Active predictors:", sum(rowSums(abs(Beta.hat)) > 1e-8), "/", nrow(Beta.hat), "\n")
cat("Network edges:", sum(abs(Theta.hat[upper.tri(Theta.hat)]) > 1e-8),
"/", ncol(Theta.hat) * (ncol(Theta.hat)-1) / 2, "\n")
Visualization
# Visualize the regularization path
plot(fit, type = "heatmap")
# Visualize the regularization path in a scatter plot
plot(fit, type = "scatter")
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")
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$Z)),
col = c("white", "darkred"),
xlab = "Response", ylab = "Observation",
main = "MNAR: Depends on Y")
Model Selection Strategies
Comparing Selection Criteria
# Fit with different criteria
criteria <- c("AIC", "BIC", "eBIC")
results <- list()
for (crit in criteria) {
results[[crit]] <- missoNet(
X = sim$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$gof)
)
print(comparison, digits = 4)
Custom Lambda Grids
# Define custom regularization paths
lambda.beta <- 10^seq(0, -2, length.out = 15)
lambda.theta <- 10^seq(0, -2, length.out = 15)
# Fit with custom grid
fit_custom <- missoNet(
X = sim$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$gof.grid.beta)), "]\n", sep = "")
cat(" Theta range: [",
sprintf("%.4f", min(fit_custom$param_set$gof.grid.theta)), ", ",
sprintf("%.4f", max(fit_custom$param_set$gof.grid.theta)), "]\n", sep = "")
cat(" Total models evaluated:", length(fit_custom$param_set$gof), "\n")
Working with Real Data Patterns
Handling Variable Missing Rates
# Create data with variable missing rates across responses
n <- 300; p <- 30; q <- 8; rho <- 0.15
rho_vec <- seq(0.05, 0.30, length.out = q)
sim_var <- generateData(
n = 300,
p = 30,
q = 8,
rho = rho_vec, # Different missing rate for each response
missing.type = "MAR"
)
# Examine missing patterns
miss_summary <- data.frame(
Response = paste0("Y", 1:q),
Target = rho_vec,
Actual = colMeans(is.na(sim_var$Z))
)
print(miss_summary, digits = 3)
# 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)
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
)
Tips for Optimal Performance
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)
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
)
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.
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missoNet documentation built on Sept. 9, 2025, 5:55 p.m.
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
knitr::opts_chunk$set( collapse = TRUE, comment = "#>", fig.width = 7, fig.height = 5, fig.align = "center", out.width = "90%", dpi = 90, message = FALSE, warning = FALSE ) options(width = 100)
Introduction
The missoNet package implements a powerful framework for multitask learning with missing responses, simultaneously estimating:
-
Regression coefficients ($\mathbf{B}$): Relationships between predictors and multiple responses
-
Conditional network ($\Theta$): Dependencies among responses after accounting for predictors
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:
-
$\mathbf{Y} \in \mathbb{R}^{n \times q}$: Response matrix (may contain missing values)
-
$\mathbf{X} \in \mathbb{R}^{n \times p}$: Predictor matrix (complete)
-
$\mathbf{B} \in \mathbb{R}^{p \times q}$: Coefficient matrix
-
$\Theta \in \mathbb{R}^{q \times q}$: Precision matrix (inverse covariance)
-
$\mu \in \mathbb{R}^q$: Intercept vector
For theoretical details, see Zeng et al. (2025).
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)
Quick Start
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)
# Check dimensions cat("Predictors (X):", dim(sim$X), "\n") cat("Complete responses (Y):", dim(sim$Y), "\n") cat("Observed responses (Z):", dim(sim$Z), "\n") cat("Missing rate:", sprintf("%.1f%%", mean(is.na(sim$Z)) * 100), "\n")
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 ) # 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") cat("Selected lambda.theta:", fit$est.min$lambda.theta, "\n") cat("Active predictors:", sum(rowSums(abs(Beta.hat)) > 1e-8), "/", nrow(Beta.hat), "\n") cat("Network edges:", sum(abs(Theta.hat[upper.tri(Theta.hat)]) > 1e-8), "/", ncol(Theta.hat) * (ncol(Theta.hat)-1) / 2, "\n")
Visualization
# Visualize the regularization path plot(fit, type = "heatmap")
# Visualize the regularization path in a scatter plot plot(fit, type = "scatter")
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")
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$Z)), col = c("white", "darkred"), xlab = "Response", ylab = "Observation", main = "MNAR: Depends on Y")
Model Selection Strategies
Comparing Selection Criteria
# Fit with different criteria criteria <- c("AIC", "BIC", "eBIC") results <- list() for (crit in criteria) { results[[crit]] <- missoNet( X = sim$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$gof) ) print(comparison, digits = 4)
Custom Lambda Grids
# Define custom regularization paths lambda.beta <- 10^seq(0, -2, length.out = 15) lambda.theta <- 10^seq(0, -2, length.out = 15) # Fit with custom grid fit_custom <- missoNet( X = sim$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$gof.grid.beta)), "]\n", sep = "") cat(" Theta range: [", sprintf("%.4f", min(fit_custom$param_set$gof.grid.theta)), ", ", sprintf("%.4f", max(fit_custom$param_set$gof.grid.theta)), "]\n", sep = "") cat(" Total models evaluated:", length(fit_custom$param_set$gof), "\n")
Working with Real Data Patterns
Handling Variable Missing Rates
# Create data with variable missing rates across responses n <- 300; p <- 30; q <- 8; rho <- 0.15 rho_vec <- seq(0.05, 0.30, length.out = q) sim_var <- generateData( n = 300, p = 30, q = 8, rho = rho_vec, # Different missing rate for each response missing.type = "MAR" ) # Examine missing patterns miss_summary <- data.frame( Response = paste0("Y", 1:q), Target = rho_vec, Actual = colMeans(is.na(sim_var$Z)) ) print(miss_summary, digits = 3) # 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)
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 )
Tips for Optimal Performance
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)
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 )
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.
Try the missoNet package in your browser
Any scripts or data that you put into this service are public.
R Package Documentation
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We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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