# DISCOM: Optimal Sparse Linear Prediction for Block-missing Multi-modality Data Without Imputation ```r 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 ## Returns 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 ```r # 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)) ```

discom function