| Type: | Package |
| Title: | Adaptive Sparse Regression for Block Missing Multimodal Data |
| Version: | 1.0.0 |
| Date: | 2025-08-18 |
| Description: | 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. The method supports flexible block configurations (any K blocks) and includes robust variants for heavy-tailed distributions ('AdapDISCOM'-Huber) and fast implementations for large-scale applications (Fast-'AdapDISCOM'). Designed for realistic multimodal scenarios where different data sources exhibit distinct missing data patterns and contamination levels. Diakité et al. (2025) <doi:10.48550/arXiv.2508.00120>. |
| License: | GPL-3 |
| URL: | https://doi.org/10.48550/arXiv.2508.00120 |
| BugReports: | https://github.com/AODiakite/AdapDiscom/issues |
| Depends: | R (≥ 3.5.0) |
| Imports: | softImpute, Matrix, scout, robustbase |
| RoxygenNote: | 7.3.2 |
| Encoding: | UTF-8 |
| Suggests: | knitr, rmarkdown, MASS |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2025-08-22 03:44:24 UTC; abdoul |
| Author: | Diakite Abdoul Oudouss [aut, cre, cph], Barry Amadou [aut] |
| Maintainer: | Diakite Abdoul Oudouss <abdouloudoussdiakite@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2025-08-27 16:30:27 UTC |
AdapDiscom: An Adaptive Sparse Regression Method for High-Dimensional Multimodal Data With Block-Wise Missingness and Measurement Errors
Description
AdapDiscom: An Adaptive Sparse Regression Method for High-Dimensional Multimodal Data With Block-Wise Missingness and Measurement Errors
Usage
adapdiscom(
beta,
x,
y,
x.tuning,
y.tuning,
x.test,
y.test,
nlambda,
nalpha,
pp,
robust = 0,
standardize = TRUE,
itcp = TRUE,
lambda.min.ratio = NULL,
k.value = 1.5
)
Arguments
beta |
Vector, true beta coefficients (optional) |
x |
Matrix, training data |
y |
Vector, training response |
x.tuning |
Matrix, tuning data |
y.tuning |
Vector, tuning response |
x.test |
Matrix, test data |
y.test |
Vector, test response |
nlambda |
Integer, number of lambda values |
nalpha |
Integer, number of alpha values |
pp |
Vector, block sizes |
robust |
Integer, 0 for classical, 1 for robust estimation of covariance |
standardize |
Logical, whether to standardize covariates. When TRUE, uses training data mean and standard deviation to standardize tuning and test sets. When robust=1, uses Huber-robust standard deviation estimates |
itcp |
Logical, whether to include intercept |
lambda.min.ratio |
Numeric, 'lambda.min.ratio' sets the smallest lambda value in the grid, expressed as a fraction of 'lambda.max'—the smallest lambda for which all coefficients are zero. By default, it is '0.0001' when the number of observations ('nobs') exceeds the number of variables ('nvars'), and '0.01' when 'nobs < nvars'. Using a very small value in the latter case can lead to overfitting. |
k.value |
Numeric, tuning parameter for robust estimation |
Value
List with estimation results
Value
The function returns a list containing the following components:
- err
A multi-dimensional array storing the mean squared error (MSE) for all combinations of tuning parameters alpha and lambda.
- est.error
The estimation error, calculated as the Euclidean distance between the estimated beta coefficients and the true beta (if provided).
- lambda
The optimal lambda value chosen via cross-validation on the tuning set.
- alpha
A vector of the optimal alpha values, also selected on the tuning set.
- train.error
The mean squared error on the tuning set for the optimal parameter combination.
- test.error
The mean squared error on the test set for the final, optimal model.
- y.pred
The predicted values for the observations in the test set.
- R2
The R-squared value, which measures the proportion of variance explained by the model on the test set.
- a0
The intercept of the final model.
- a1
The vector of estimated beta coefficients for the final model.
- select
The number of non-zero coefficients, representing the number of selected variables.
- xtx
The final regularized covariance matrix used to fit the optimal model.
- fpr
The False Positive Rate (FPR) if the true beta is provided. It measures the proportion of irrelevant variables incorrectly selected.
- fnr
The False Negative Rate (FNR) if the true beta is provided. It measures the proportion of relevant variables incorrectly excluded.
- lambda.all
The complete vector of all lambda values tested during cross-validation.
- beta.cov.lambda.max
The estimated beta coefficients using the maximum lambda value.
- time
The total execution time of the function in seconds.
Examples
# Simple example with synthetic data
n <- 100
p <- 20
# Generate synthetic data with 2 blocks
set.seed(123)
x_train <- matrix(rnorm(n * p), n, p)
x_tuning <- matrix(rnorm(50 * p), 50, p)
x_test <- matrix(rnorm(30 * p), 30, p)
# True coefficients
beta_true <- c(rep(2, 5), rep(0, 15))
# Response variables
y_train <- x_train %*% beta_true + rnorm(n)
y_tuning <- x_tuning %*% beta_true + rnorm(50)
y_test <- x_test %*% beta_true + rnorm(30)
# Block sizes (2 blocks of 10 variables each)
pp <- c(10, 10)
# Run AdapDiscom
result <- 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)
# View results
print(paste("Test R-squared:", round(result$R2, 3)))
print(paste("Selected variables:", result$select))
Compute X'X Matrix
Description
Compute X'X Matrix
Usage
compute.xtx(x, robust = 0, k_value = 1.5)
Arguments
x |
Matrix, input data matrix |
robust |
Integer, 0 for classical estimate, 1 for Huber robust estimate |
k_value |
Numeric, tuning parameter for Huber function |
Value
Covariance matrix
Examples
# Create sample data with missing values
set.seed(123)
x <- matrix(rnorm(100), 20, 5)
x[sample(100, 10)] <- NA # Introduce missing values
# Classical covariance estimation
xtx_classical <- compute.xtx(x, robust = 0)
print(round(xtx_classical, 3))
# Robust covariance estimation
xtx_robust <- compute.xtx(x, robust = 1, k_value = 1.5)
print(round(xtx_robust, 3))
Compute X'y Vector
Description
Compute X'y Vector
Usage
compute.xty(x, y, robust = 0, k_value = 1.5)
Arguments
x |
Matrix, input data matrix |
y |
Vector, response vector |
robust |
Integer, 0 for classical estimate, 1 for Huber robust estimate |
k_value |
Numeric, tuning parameter for Huber function |
Value
Covariance vector
Examples
# Create sample data
set.seed(123)
x <- matrix(rnorm(100), 20, 5)
y <- rnorm(20)
x[sample(100, 8)] <- NA # Missing values in x
# Classical cross-covariance
xty_classical <- compute.xty(x, y, robust = 0)
print(round(xty_classical, 3))
# Robust cross-covariance
xty_robust <- compute.xty(x, y, robust = 1)
print(round(xty_robust, 3))
DISCOM: Optimal Sparse Linear Prediction for Block-missing Multi-modality Data Without Imputation
Description
DISCOM: Optimal Sparse Linear Prediction for Block-missing Multi-modality Data Without Imputation
Usage
discom(
beta,
x,
y,
x.tuning,
y.tuning,
x.test,
y.test,
nlambda,
nalpha,
pp,
robust = 0,
standardize = TRUE,
itcp = TRUE,
lambda.min.ratio = NULL,
k.value = 1.5
)
Arguments
beta |
Vector, true beta coefficients (optional) |
x |
Matrix, training data |
y |
Vector, training response |
x.tuning |
Matrix, tuning data |
y.tuning |
Vector, tuning response |
x.test |
Matrix, test data |
y.test |
Vector, test response |
nlambda |
Integer, number of lambda values |
nalpha |
Integer, number of alpha values |
pp |
Vector, block sizes. Discom supports 2, 3, or 4 blocks. |
robust |
Integer, 0 for classical, 1 for robust estimation |
standardize |
Logical, whether to standardize covariates. When TRUE, uses training data mean and standard deviation to standardize tuning and test sets. When robust=1, uses Huber-robust standard deviation estimates |
itcp |
Logical, whether to include intercept |
lambda.min.ratio |
Numeric, 'lambda.min.ratio' sets the smallest lambda value in the grid, expressed as a fraction of 'lambda.max'—the smallest lambda for which all coefficients are zero. By default, it is '0.0001' when the number of observations ('nobs') exceeds the number of variables ('nvars'), and '0.01' when 'nobs < nvars'. Using a very small value in the latter case can lead to overfitting. |
k.value |
Numeric, tuning parameter for robust estimation |
Value
List with estimation results
Value
The function returns a list containing the following components:
- err
A multi-dimensional array storing the mean squared error (MSE) for all combinations of tuning parameters alpha and lambda.
- est.error
The estimation error, calculated as the Euclidean distance between the estimated beta coefficients and the true beta (if provided).
- lambda
The optimal lambda value chosen via cross-validation on the tuning set.
- alpha
A vector of the optimal alpha values, also selected on the tuning set.
- train.error
The mean squared error on the tuning set for the optimal parameter combination.
- test.error
The mean squared error on the test set for the final, optimal model.
- y.pred
The predicted values for the observations in the test set.
- R2
The R-squared value, which measures the proportion of variance explained by the model on the test set.
- a0
The intercept of the final model.
- a1
The vector of estimated beta coefficients for the final model.
- select
The number of non-zero coefficients, representing the number of selected variables.
- xtx
The final regularized covariance matrix used to fit the optimal model.
- fpr
The False Positive Rate (FPR) if the true beta is provided. It measures the proportion of irrelevant variables incorrectly selected.
- fnr
The False Negative Rate (FNR) if the true beta is provided. It measures the proportion of relevant variables incorrectly excluded.
- lambda.all
The complete vector of all lambda values tested during cross-validation.
- beta.cov.lambda.max
The estimated beta coefficients using the maximum lambda value.
- time
The total execution time of the function in seconds.
Examples
# Simple example with synthetic multimodal data
n <- 100
p <- 24
# Generate synthetic data with 3 blocks
set.seed(456)
x_train <- matrix(rnorm(n * p), n, p)
x_tuning <- matrix(rnorm(50 * p), 50, p)
x_test <- matrix(rnorm(30 * p), 30, p)
# True coefficients with sparse structure
beta_true <- c(rep(1.5, 4), rep(0, 4), rep(-1, 4), rep(0, 12))
# Response variables
y_train <- x_train %*% beta_true + rnorm(n, sd = 0.5)
y_tuning <- x_tuning %*% beta_true + rnorm(50, sd = 0.5)
y_test <- x_test %*% beta_true + rnorm(30, sd = 0.5)
# Block sizes (3 blocks of 8 variables each)
pp <- c(8, 8, 8)
# Run DISCOM
result <- 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 = 25, nalpha = 15, pp = pp)
# View results
print(paste("Test error:", round(result$test.error, 4)))
print(paste("R-squared:", round(result$R2, 3)))
print(paste("Variables selected:", result$select))
Fast AdapDiscom
Description
Fast AdapDiscom
Usage
fast_adapdiscom(
beta,
x,
y,
x.tuning,
y.tuning,
x.test,
y.test,
nlambda,
pp,
robust = 0,
n.l = 30,
standardize = TRUE,
itcp = TRUE,
lambda.min.ratio = NULL,
k.value = 1.5
)
Arguments
beta |
Vector, true beta coefficients (optional) |
x |
Matrix, training data |
y |
Vector, training response |
x.tuning |
Matrix, tuning data |
y.tuning |
Vector, tuning response |
x.test |
Matrix, test data |
y.test |
Vector, test response |
nlambda |
Integer, number of lambda values |
pp |
Vector, block sizes |
robust |
Integer, 0 for classical, 1 for robust estimation |
n.l |
Integer, number of tuning parameter ('l') values for fast variants (number of alpha values) |
standardize |
Logical, whether to standardize covariates. When TRUE, uses training data mean and standard deviation to standardize tuning and test sets. When robust=1, uses Huber-robust standard deviation estimates |
itcp |
Logical, whether to include intercept |
lambda.min.ratio |
Numeric, 'lambda.min.ratio' sets the smallest lambda value in the grid, expressed as a fraction of 'lambda.max'—the smallest lambda for which all coefficients are zero. By default, it is '0.0001' when the number of observations ('nobs') exceeds the number of variables ('nvars'), and '0.01' when 'nobs < nvars'. Using a very small value in the latter case can lead to overfitting. |
k.value |
Numeric, tuning parameter for robust estimation |
Value
List with estimation results
Value
The function returns a list containing the following components:
- err
A multi-dimensional array storing the mean squared error (MSE) for all combinations of tuning parameters alpha and lambda.
- est.error
The estimation error, calculated as the Euclidean distance between the estimated beta coefficients and the true beta (if provided).
- lambda
The optimal lambda value chosen via cross-validation on the tuning set.
- alpha
A vector of the optimal alpha values, also selected on the tuning set.
- train.error
The mean squared error on the tuning set for the optimal parameter combination.
- test.error
The mean squared error on the test set for the final, optimal model.
- y.pred
The predicted values for the observations in the test set.
- R2
The R-squared value, which measures the proportion of variance explained by the model on the test set.
- a0
The intercept of the final model.
- a1
The vector of estimated beta coefficients for the final model.
- select
The number of non-zero coefficients, representing the number of selected variables.
- xtx
The final regularized covariance matrix used to fit the optimal model.
- fpr
The False Positive Rate (FPR) if the true beta is provided. It measures the proportion of irrelevant variables incorrectly selected.
- fnr
The False Negative Rate (FNR) if the true beta is provided. It measures the proportion of relevant variables incorrectly excluded.
- lambda.all
The complete vector of all lambda values tested during cross-validation.
- beta.cov.lambda.max
The estimated beta coefficients using the maximum lambda value.
- time
The total execution time of the function in seconds.
Examples
# Fast computation example with synthetic data
n <- 80
p <- 16
# Generate synthetic data with 2 blocks
set.seed(789)
x_train <- matrix(rnorm(n * p), n, p)
x_tuning <- matrix(rnorm(40 * p), 40, p)
x_test <- matrix(rnorm(25 * p), 25, p)
# True coefficients
beta_true <- c(rep(1.2, 3), rep(0, 5), rep(-0.8, 2), rep(0, 6))
# Response variables
y_train <- x_train %*% beta_true + rnorm(n, sd = 0.3)
y_tuning <- x_tuning %*% beta_true + rnorm(40, sd = 0.3)
y_test <- x_test %*% beta_true + rnorm(25, sd = 0.3)
# Block sizes (2 blocks of 8 variables each)
pp <- c(8, 8)
# Run fast AdapDiscom (faster with fewer tuning parameters)
result <- 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 = 15, pp = pp, n.l = 20)
# View results
print(paste("Test R-squared:", round(result$R2, 3)))
print(paste("Computation time:", round(result$time[3], 2), "seconds"))
Fast DISCOM
Description
Fast DISCOM
Usage
fast_discom(
beta,
x,
y,
x.tuning,
y.tuning,
x.test,
y.test,
nlambda,
pp,
robust = 0,
n.l = 30,
standardize = TRUE,
itcp = TRUE,
lambda.min.ratio = NULL,
k.value = 1.5
)
Arguments
beta |
Vector, true beta coefficients (optional) |
x |
Matrix, training data |
y |
Vector, training response |
x.tuning |
Matrix, tuning data |
y.tuning |
Vector, tuning response |
x.test |
Matrix, test data |
y.test |
Vector, test response |
nlambda |
Integer, number of lambda values |
pp |
Vector, block sizes |
robust |
Integer, 0 for classical, 1 for robust estimation |
n.l |
Integer, number of tuning parameter ('l') values for fast variants |
standardize |
Logical, whether to standardize covariates. When TRUE, uses training data mean and standard deviation to standardize tuning and test sets. When robust=1, uses Huber-robust standard deviation estimates |
itcp |
Logical, whether to include intercept |
lambda.min.ratio |
Numeric, 'lambda.min.ratio' sets the smallest lambda value in the grid, expressed as a fraction of 'lambda.max'—the smallest lambda for which all coefficients are zero. By default, it is '0.0001' when the number of observations ('nobs') exceeds the number of variables ('nvars'), and '0.01' when 'nobs < nvars'. Using a very small value in the latter case can lead to overfitting. |
k.value |
Numeric, tuning parameter for robust estimation |
Value
List with estimation results
Value
The function returns a list containing the following components:
- err
A multi-dimensional array storing the mean squared error (MSE) for all combinations of tuning parameters alpha and lambda.
- est.error
The estimation error, calculated as the Euclidean distance between the estimated beta coefficients and the true beta (if provided).
- lambda
The optimal lambda value chosen via cross-validation on the tuning set.
- alpha
A vector of the optimal alpha values, also selected on the tuning set.
- train.error
The mean squared error on the tuning set for the optimal parameter combination.
- test.error
The mean squared error on the test set for the final, optimal model.
- y.pred
The predicted values for the observations in the test set.
- R2
The R-squared value, which measures the proportion of variance explained by the model on the test set.
- a0
The intercept of the final model.
- a1
The vector of estimated beta coefficients for the final model.
- select
The number of non-zero coefficients, representing the number of selected variables.
- xtx
The final regularized covariance matrix used to fit the optimal model.
- fpr
The False Positive Rate (FPR) if the true beta is provided. It measures the proportion of irrelevant variables incorrectly selected.
- fnr
The False Negative Rate (FNR) if the true beta is provided. It measures the proportion of relevant variables incorrectly excluded.
- lambda.all
The complete vector of all lambda values tested during cross-validation.
- beta.cov.lambda.max
The estimated beta coefficients using the maximum lambda value.
- time
The total execution time of the function in seconds.
Examples
# Fast DISCOM example with synthetic multimodal data
n <- 70
p <- 18
# Generate synthetic data with 3 blocks
set.seed(321)
x_train <- matrix(rnorm(n * p), n, p)
x_tuning <- matrix(rnorm(35 * p), 35, p)
x_test <- matrix(rnorm(20 * p), 20, p)
# True coefficients with block structure
beta_true <- c(rep(1.0, 3), rep(0, 3), rep(-1.2, 3), rep(0, 3), rep(0.8, 3), rep(0, 3))
# Response variables
y_train <- x_train %*% beta_true + rnorm(n, sd = 0.4)
y_tuning <- x_tuning %*% beta_true + rnorm(35, sd = 0.4)
y_test <- x_test %*% beta_true + rnorm(20, sd = 0.4)
# Block sizes (3 blocks of 6 variables each)
pp <- c(6, 6, 6)
# Run fast DISCOM (efficient for large datasets)
result <- 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, n.l = 25)
# View results
print(paste("Test error:", round(result$test.error, 4)))
print(paste("R-squared:", round(result$R2, 3)))
print(paste("Runtime:", round(result$time, 2), "seconds"))
Generate Covariance Matrix
Description
Generate Covariance Matrix
Usage
generate.cov(p, example)
Arguments
p |
Integer, dimension of the covariance matrix |
example |
Integer, type of covariance structure (1=AR(1), 2=Block diagonal, 3=Kronecker product) |
Value
A p x p covariance matrix
Examples
# AR(1) covariance structure
Sigma1 <- generate.cov(p = 20, example = 1)
print(Sigma1[1:3, 1:3])
# Block diagonal structure (p must be multiple of 5)
Sigma2 <- generate.cov(p = 25, example = 2)
print(Sigma2[1:5, 1:5])
# Kronecker product structure (p must be multiple of 10)
Sigma3 <- generate.cov(p = 100, example = 3)
print(dim(Sigma3))
Get Block Indices
Description
Get Block Indices
Usage
get_block_indices(pp)
Arguments
pp |
Vector, block sizes |
Value
List with start and end indices for each block
Examples
# Define block sizes
pp <- c(10, 15, 20)
indices <- get_block_indices(pp)
print(indices)
# Shows: $starts = c(1, 11, 26) and $ends = c(10, 25, 45)
# For two blocks
pp2 <- c(25, 25)
indices2 <- get_block_indices(pp2)
print(indices2)
Compute Lambda Max for L1 Regularization using KKT Conditions
Description
Compute Lambda Max for L1 Regularization using KKT Conditions
Usage
lambda_max(X, y, Methode = "lasso", robust = 0)
Arguments
X |
Matrix, design matrix |
y |
Vector, response vector |
Methode |
Character, method for computation |
robust |
Integer, 0 for classical, 1 for robust |
Value
Maximum lambda value
Examples
# Generate sample data
set.seed(123)
n <- 50; p <- 20
X <- matrix(rnorm(n*p), n, p)
y <- rnorm(n)
# Different methods for lambda_max computation
lmax_lasso <- lambda_max(X, y, Methode = "lasso")
lmax_discom <- lambda_max(X, y, Methode = "discom")
print(paste("Lambda max (lasso):", round(lmax_lasso, 4)))
print(paste("Lambda max (discom):", round(lmax_discom, 4)))