splines and GP disagreeing

spline_GP_nonuniform_x.R

# Created by chat GPT

# Load necessary libraries
library(splines)
library(GPfit)

# Set seed for reproducibility
set.seed(123)

# Generate non-uniform data
x <- c(rnorm(50, mean = -1, sd = 0.3), rnorm(50, mean = 1, sd = 0.3))  # Two modes
x <- sort(x)  # Sort x for visualization
y <- sin(2 * pi * x) + rnorm(length(x), mean = 0, sd = 0.2)  # Sinusoidal curve with constant scatter

# Normalize x for GP fitting
x_scaled <- (x - min(x)) / (max(x) - min(x))

# Fit a natural spline
spline_fit <- lm(y ~ ns(x, df = 5))

# Fit a Gaussian Process
gp_model <- GP_fit(X = matrix(x_scaled, ncol = 1), Y = y)

# Generate predictions
x_pred <- seq(min(x), max(x), length.out = 500)  # Dense grid for smooth lines
x_pred_scaled <- (x_pred - min(x)) / (max(x) - min(x))  # Normalize x_pred

# Spline predictions
spline_pred <- predict(spline_fit, newdata = data.frame(x = x_pred))

# Gaussian Process predictions
gp_pred <- predict(gp_model, matrix(x_pred_scaled, ncol = 1))

# Plot the data
plot(x, y, pch = 16, col = "blue", main = "Spline and Gaussian Process Fit (Non-Uniform Data)",
     xlab = "x", ylab = "y", ylim = c(-2, 2))

# Add spline fit
lines(x_pred, spline_pred, col = "red", lwd = 2, lty = 2)

# Add Gaussian Process fit
lines(x_pred, gp_pred$Y_hat, col = "green", lwd = 2)

# Add legend
legend("topright", legend = c("Scatter", "Spline Fit", "GP Fit"),
       col = c("blue", "red", "green"), pch = c(16, NA, NA),
       lty = c(NA, 2, 1), lwd = c(NA, 2, 2), bty = "n")