objective_function_SL: Objective Function for Structural Learning (SL)

In covalchemy: Constructing Joint Distributions with Control Over Statistical Properties

Objective Function for Structural Learning (SL)

Description

This function calculates the objective function for a structural learning task. It computes multiple components such as the total variation (TV) distance between original and generated datasets (X vs. X_prime, Y vs. Y_prime), the changes in regression coefficients (beta0 and beta1), the R² differences for each category in Z, and the inter-cluster centroid distances. The loss function combines these components using penalty parameters (lambda1, lambda2, lambda3, lambda4).

Usage

objective_function_SL(
  X_prime,
  Y_prime,
  X,
  Y,
  Z,
  p,
  beta0_orig,
  beta1_orig,
  lambda1,
  lambda2,
  lambda3,
  lambda4,
  R2_orig,
  printc = FALSE
)

Arguments

X_prime	A numeric vector representing the generated values of X.
Y_prime	A numeric vector representing the generated values of Y.
X	A numeric vector representing the original values of X.
Y	A numeric vector representing the original values of Y.
Z	A categorical vector representing the categories for each observation.
p	A numeric vector representing the target correlation values for each category in Z.
beta0_orig	The original intercept value for the regression model.
beta1_orig	The original slope value for the regression model.
lambda1	Penalty parameters to control the importance of different loss components.
lambda2	Penalty parameters to control the importance of different loss components.
lambda3	Penalty parameters to control the importance of different loss components.
lambda4	Penalty parameters to control the importance of different loss components.
R2_orig	The original R² value for the model (not used directly in the calculation but might be for reference).
printc	A boolean flag to control printing of intermediate values for debugging.

Value

A numeric value representing the total loss calculated by the objective function.

Examples

# Test Case 1: Simple random data with normal distribution
set.seed(123)
X <- rnorm(100)
Y <- rnorm(100)
Z <- sample(1:3, 100, replace = TRUE)
X_prime <- rnorm(100)
Y_prime <- rnorm(100)
p <- c(0.5, 0.7, 0.9)
beta0_orig <- 0
beta1_orig <- 1
lambda1 <- lambda2 <- lambda3 <- lambda4 <- 1
R2_orig <- 0.9
loss <- objective_function_SL(X, Y, Z, X_prime, Y_prime, p, beta0_orig, beta1_orig,
                               lambda1, lambda2, lambda3, lambda4, R2_orig)
print(loss)

# Test Case 2: Skewed data with different categories and a larger lambda for penalty
X <- rexp(100)
Y <- rpois(100, lambda = 2)
Z <- sample(1:4, 100, replace = TRUE)
X_prime <- rnorm(100)
Y_prime <- rnorm(100)
p <- c(0.3, 0.5, 0.8, 0.6)
beta0_orig <- 0.5
beta1_orig <- 1.5
lambda1 <- lambda2 <- lambda3 <- 0.5
lambda4 <- 2
R2_orig <- 0.85
loss <- objective_function_SL(X, Y, Z, X_prime, Y_prime, p, beta0_orig, beta1_orig,
                               lambda1, lambda2, lambda3, lambda4, R2_orig)
print(loss)

covalchemy documentation built on April 12, 2025, 2:15 a.m.