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# Robust Regression Implementation
# This program implements a regression algorithm that can be evolved to better handle outliers
robust_regression <- function(X, y) {
# EVOLVE-BLOCK-START
# Simple least squares regression as initial implementation
# This can be evolved to use more robust methods like:
# - Huber regression
# - RANSAC
# - Theil-Sen estimator
# - Iteratively reweighted least squares
# Add intercept column
X_with_intercept <- cbind(1, X)
# Calculate coefficients using normal equation
# beta = (X'X)^(-1) X'y
XtX <- t(X_with_intercept) %*% X_with_intercept
Xty <- t(X_with_intercept) %*% y
# Solve for coefficients
coefficients <- solve(XtX, Xty)
# Calculate predictions
predictions <- X_with_intercept %*% coefficients
# Calculate residuals
residuals <- y - predictions
# Return results
return(list(
coefficients = coefficients,
predictions = predictions,
residuals = residuals
))
# EVOLVE-BLOCK-END
}
# Function to calculate model performance metrics
calculate_metrics <- function(y_true, y_pred, residuals) {
n <- length(y_true)
# Mean Squared Error
mse <- mean(residuals^2)
# Mean Absolute Error
mae <- mean(abs(residuals))
# R-squared
ss_res <- sum(residuals^2)
ss_tot <- sum((y_true - mean(y_true))^2)
r_squared <- 1 - (ss_res / ss_tot)
# Robust metrics
# Median Absolute Error
medae <- median(abs(residuals))
# Percentage of outliers (residuals > 2 standard deviations)
outlier_threshold <- 2 * sd(residuals)
outlier_percentage <- sum(abs(residuals) > outlier_threshold) / n
return(list(
mse = mse,
mae = mae,
r_squared = r_squared,
medae = medae,
outlier_robustness = 1 - outlier_percentage
))
}
# Main execution function
main <- function() {
# This will be called by the evaluator with test data
# The evaluator will provide X and y through the environment
# Perform robust regression
result <- robust_regression(X, y)
# Calculate metrics
metrics <- calculate_metrics(y, result$predictions, result$residuals)
return(metrics)
} |