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DOI CRAN/METACRAN CRAN/METACRAN

A multimodal high dimensionnal method accounting for missing data and measurement error heterogenity

AdapDiscom Package

The AdapDiscom package provides implementations of AdapDISCOM, a novel adaptive direct sparse regression method for high-dimensional multimodal data with block-wise missingness and measurement errors. Building on the DISCOM framework, AdapDISCOM introduces modality-specific weighting schemes to account for heterogeneity in data structures and error magnitudes across modalities. Unlike existing methods that are limited to a fixed number of blocks, AdapDISCOM supports any number of blocks K, making it highly flexible for diverse multimodal data applications. The package includes robust variants (AdapDISCOM-Huber) and computationally efficient versions (Fast-AdapDISCOM) to handle heavy-tailed distributions and large-scale datasets. AdapDISCOM has been shown to consistently outperform existing methods such as DISCOM, SCOM, and imputation based, particularly under heterogeneous contamination scenarios, providing a scalable framework for realistic multimodal data analysis with missing data and measurement errors.

Installation

# Install from local source
devtools::install_local("https://github.com/AODiakite/AdapDiscom")

# Load the package
library(AdapDiscom)

Main Functions

The package provides four main estimation functions:

  1. adapdiscom()
  2. discom()
  3. fast_adapdiscom()
  4. fast_discom()

Different Covariance Structures

The package handles different covariance structures:

# Number of variables
p <-  10
# Load the package
library(AdapDiscom)
# AR(1) structure
Sigma_ar1 <- generate.cov(p, example = 1)

# Block diagonal structure
Sigma_block <- generate.cov(p, example = 2)

# Kronecker product structure
Sigma_kron <- generate.cov(p, example = 3)

Basic Usage Example

Data Simulation

This simulation scenario represents a simple replication of scenario 2 from the AdapDISCOM’s paper. It is case study with 300 variables distributed across 3 equal blocks (100 variables each), where each block follows a different covariance structure: the first block uses an AR(1) structure, the second a block-diagonal structure, and the third a Kronecker product structure. The training data (n=440) exhibits a structured missing data pattern where each quarter of the sample is completely missing one of the three variable blocks, creating heterogeneity in data availability that reflects real-world situations where different subgroups of subjects may have access to different sets of measurements. The true coefficient vector β follows a sparse pattern with only 5% of variables having non-zero effects (β = 0.5), allowing evaluation of the method’s ability to correctly identify relevant variables in a high-dimensional context with heterogeneous missing data.

library(AdapDiscom)
library(MASS)
set.seed(123)
# Set parameters
p <- 300
n <- 440
n.tuning <- 200
n.test <- 400
p1 <- p%/%3
p2 <- p%/%3
p3 <- p - p1 - p2
pp <- c(p1, p2, p3)  # Block sizes
sigma <- 1
# Generate different covariance matrices for each block
cov.mat1 <- generate.cov(p1, 1)  # AR(1) structure for block 1
cov.mat2 <- generate.cov(p2, 2)  # Block diagonal for block 2
cov.mat3 <- generate.cov(p3, 3)  # Kronecker product for block 3
# Generate true beta coefficients
beta1 <- rep(c(rep(0.5, 5), rep(0, 95)), p/100)
beta.true <- beta1

# Generate complete data for all samples
pre.x1 <- mvrnorm(n + n.tuning + n.test, rep(0, p%/%3), cov.mat1)
pre.x2 <- mvrnorm(n + n.tuning + n.test, rep(0, p%/%3), cov.mat2)
pre.x3 <- mvrnorm(n + n.tuning + n.test, rep(0, p%/%3), cov.mat3)
pre.x <- cbind(pre.x1, pre.x2, pre.x3)
pre.ep <- rnorm(n + n.tuning + n.test, 0, sigma)

# Training data
n.com <- n/4
n1 <- n2 <- n3 <- n4 <- n.com
X.train <- pre.x[1:n, ]
ep <- pre.ep[1:n]
y.train <- X.train %*% beta1 + ep 
colnames(X.train) <- paste0("X", 1:p)

# Introduce missing data pattern
X.train[(n1 + 1):(n1 + n2), (p1 + p2 + 1):(p1 + p2 + p3)] <- NA
X.train[(n1 + n2 + 1):(n1 + n2 + n3), (p1 + 1):(p1 + p2)] <- NA
X.train[(n1 + n2 + n3 + 1):(n1 + n2 + n3 + n4), (1:p1)] <- NA

# Tuning data
X.tuning <- pre.x[(n + 1):(n + n.tuning), ]
ep.tuning <- pre.ep[(n + 1):(n + n.tuning)]
y.tuning <- X.tuning %*% beta1 + ep.tuning
colnames(X.tuning) <- paste0("X", 1:p)

# Test data
X.test <- pre.x[(n + n.tuning + 1):(n + n.tuning + n.test), ]
ep.test <- pre.ep[(n + n.tuning + 1):(n + n.tuning + n.test)]
y.test <- X.test %*% beta1 + ep.test
colnames(X.test) <- paste0("X", 1:p)

Running AdapDiscom

# Run AdapDiscom with default parameters
result <- adapdiscom(
  beta = beta.true,      # True coefficients (optional, for evaluation)
  x = X.train,          # Training data
  y = y.train,          # Training response
  x.tuning = X.tuning,  # Tuning data
  y.tuning = y.tuning,  # Tuning response
  x.test = X.test,      # Test data
  y.test = y.test,      # Test response
  nlambda = 20,         # Number of lambda values
  nalpha = 10,          # Number of alpha values
  pp = pp,              # Block sizes
  robust = 0,           # Classical estimation
  standardize = TRUE,   # Standardize data
  itcp = TRUE          # Include intercept
)

# View results
print(result$R2)
          [,1]
[1,] 0.8089201

Examining Results

The functions return a list with the following components:

# Optimal parameters
cat("Optimal lambda:", result$lambda, "\n")
Optimal lambda: 0.2823072 

cat("Optimal alpha:", result$alpha, "\n")
Optimal alpha: 0.4641589 0.2154435 0.4641589 0.4641589 

# Performance metrics
cat("Training error:", result$train.error, "\n")
Training error: 1.178665 

cat("Test error:", result$test.error, "\n")
Test error: 1.526394 

cat("R-squared:", result$R2, "\n")
R-squared: 0.8089201 

# Model selection
cat("Number of selected variables:", result$select, "\n")
Number of selected variables: 27 

# If true beta provided, evaluation metrics
if (!is.null(beta.true)) {
  cat("Estimation error:", result$est.error, "\n")
  cat("False Positive Rate:", result$fpr, "\n")
  cat("False Negative Rate:", result$fnr, "\n")
}
Estimation error: 0.7911645 
False Positive Rate: 0.04210526 
False Negative Rate: 0 

# Estimated coefficients
head(result$a1)  # First 6 coefficients
[1] 0.36421275 0.57343638 0.70592242 0.56074589 0.42810130 0.09403387

Comparing Methods

# Compare different methods
methods <- c("adapdiscom", "discom", "fast_adapdiscom", "fast_discom")
results <- list()

# AdapDiscom
results$adapdiscom <- result # Already computed above

# DISCOM
results$discom <- discom(
  beta = beta.true, x = X.train, y = y.train,
  x.tuning = X.tuning, y.tuning = y.tuning,
  x.test = X.test, y.test = y.test,
  nlambda = 20,  pp = pp
)

# Fast AdapDiscom
results$fast_adapdiscom <- fast_adapdiscom(
  beta = beta.true, x = X.train, y = y.train,
  x.tuning = X.tuning, y.tuning = y.tuning,
  x.test = X.test, y.test = y.test,
  nlambda = 20,  pp = pp
)

# Fast DISCOM
results$fast_discom <- fast_discom(
  beta = beta.true, x = X.train, y = y.train,
  x.tuning = X.tuning, y.tuning = y.tuning,
  x.test = X.test, y.test = y.test,
  nlambda = 20, pp = pp
)

# Compare performance
comparison <- data.frame(
  Method = names(results),
  Test_Error = sapply(results, function(x) x$test.error),
  R_Squared = sapply(results, function(x) x$R2),
  Selected_Vars = sapply(results, function(x) x$select),
  Est_Error = sapply(results, function(x) x$est.error),
  FPR = sapply(results, function(x) x$fpr),
  FNR = sapply(results, function(x) x$fnr),
  Time = sapply(results, function(x) x$time)
)

print(comparison)
                         Method Test_Error R_Squared Selected_Vars Est_Error
adapdiscom           adapdiscom   1.526394 0.8089201            27 0.7911645
discom                   discom   1.698120 0.7851645            27 0.8079454
fast_adapdiscom fast_adapdiscom   1.471665 0.8173831            33 0.7132907
fast_discom         fast_discom   1.471665 0.8173831            33 0.7132907
                       FPR FNR    Time
adapdiscom      0.04210526   0 465.022
discom          0.04210526   0   5.422
fast_adapdiscom 0.06315789   0   1.825
fast_discom     0.06315789   0   0.897

Note

When the missing blocks are of equal size within each modality and are disjoint across modalities (i.e., no observations have missing data in multiple modalities simultaneously), Fast-AdapDISCOM reduces to Fast-DISCOM since the adaptive weighting scheme becomes uniform across all modalities.

Robust Estimation

The package supports robust estimation using Huber’s M-estimator:

# Run with robust estimation
result_robust <- adapdiscom(
  beta = beta.true,
  x = X.train, y = y.train,
  x.tuning = X.tuning, y.tuning = y.tuning,
  x.test = X.test, y.test = y.test,
  nlambda = 20, nalpha = 10, pp = pp,
  robust = 1,        # Enable robust estimation
  k.value = 1.5      # Huber tuning parameter
)

Advanced Parameters

# Advanced usage with custom parameters
result_advanced <- adapdiscom(
  beta = beta.true,
  x = X.train, y = y.train,
  x.tuning = X.tuning, y.tuning = y.tuning,
  x.test = X.test, y.test = y.test,
  nlambda = 30,              # More lambda values
  nalpha = 15,               # More alpha values
  pp = pp,
  robust = 0,
  standardize = TRUE,
  itcp = TRUE,
  lambda.min.ratio = 0.001,  # Custom lambda range
  k.value = 1.5
)

Block Structure Requirements

  • AdapDiscom: Supports any number of blocks (specified by pp vector)
  • DISCOM: Supports 2, 3, or 4 blocks only
  • Fast variants: Optimized versions with reduced computational complexity

Tips for Usage

  1. Block sizes: Ensure sum(pp) == p (total number of variables)
  2. Sample sizes: Use adequate tuning and test sample sizes for reliable parameter selection
  3. Standardization: Generally recommended (standardize = TRUE)
  4. Robust estimation: Use when data contains outliers (robust = 1)
  5. Lambda range: Adjust lambda.min.ratio if needed for better regularization path

References

For more details on the methodology, please refer to the original papers on A multimodal high dimensionnal method accounting for missing data and measurement error heterogenity.

About

Provides adaptive direct sparse regression for high-dimensional multimodal data with heterogeneous missing patterns and measurement errors. 'AdapDISCOM' extends the 'DISCOM' framework with modality-specific adaptive weighting to handle varying data structures and error magnitudes across blocks.

https://doi.org/10.48550/arXiv.2508.00120

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machine-learning statistics methodology

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Adaptive Sparse Regression for High-Dimensional Multimodal Data Latest
Aug 3, 2025

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