Today, give a try to Techtonique web app, a tool designed to help you make informed, data-driven decisions using Mathematics, Statistics, Machine Learning, and Data Visualization. Here is a tutorial with audio, video, code, and slides: https://moudiki2.gumroad.com/l/nrhgb
matern32 was inspired in 2019 (still work in progress) by Journal of Statistical Software’s paper Kernel-Based Regularized Least Squares in R (KRLS) and Stata (krls), but uses Matérn 3/2 kernels instead of Gaussian kernels. In 2025, conformal prediction allows to obtain prediction intervals/predictive simulations, making Kernel Ridge Regression comparable to Gaussian Processes, but in a frequentist and non-Gaussian way. In matern32, there are ways to deal with scalability by using clustering. To finish, matern32’s models could be used as surrogates for other models’ interpretability. The package is available on the CRAN-like repository located at: https://r-packages.techtonique.net.
Install package
options(repos = c(
techtonique = "https://r-packages.techtonique.net",
CRAN = "https://cloud.r-project.org"
))
install.packages("matern32")
Data set
X <- as.matrix(MASS::Boston[,-14])
y <- MASS::Boston[,14]
set.seed(123)
idx_train <- sample.int(dim(X)[1], size=floor(0.8*dim(X)[1]))
Fitting a model
fit_obj <- matern32::fit_matern32(x = X[idx_train,], y = y[idx_train], lambda = 0.01)
print(sqrt(mean((predict(fit_obj, X[-idx_train,]) - y[-idx_train])**2)))
Prediction intervals
fit_obj <- matern32::fit_matern32(x = X[idx_train,], y = y[idx_train], lambda = 0.01, method = "conformal")
preds_splitconformal <- predict(fit_obj, X[-idx_train,], level=95, method = "splitconformal")
preds_kdeconformal <- predict(fit_obj, X[-idx_train,], level=95, method = "kde")
preds_bootstrapconformal <- predict(fit_obj, X[-idx_train,], level=95, method = "bootstrap")
preds_surrogateconformal <- predict(fit_obj, X[-idx_train,], level=95, method = "surrogate")
# coverage
(coverage_splitconformal <- mean((y[-idx_train] >= preds_splitconformal$lower) & (y[-idx_train] <= preds_splitconformal$upper)))
(coverage_kdeconformal <- mean((y[-idx_train] >= preds_kdeconformal$lower) & (y[-idx_train] <= preds_kdeconformal$upper)))
(coverage_bootstrapconformal <- mean((y[-idx_train] >= preds_bootstrapconformal$lower) & (y[-idx_train] <= preds_bootstrapconformal$upper)))
(coverage_surrogateconformal <- mean((y[-idx_train] >= preds_surrogateconformal$lower) & (y[-idx_train] <= preds_surrogateconformal$upper)))
## [1] 0.9705882
## [1] 0.9803922
## [1] 0.9509804
## [1] 0.9705882
# Extract predictions and true values
x_test <- 1:length(y[-idx_train])
y_test <- y[-idx_train]
# Define a helper function to plot prediction intervals
plot_intervals <- function(x, y, lower, upper, method_name) {
plot(x, y, type = "p", pch = 16, col = "blue", xlab = "Observation", ylab = "Value",
main = paste("Prediction Intervals -", method_name))
polygon(c(x, rev(x)), c(lower, rev(upper)), col = rgb(0.1, 0.1, 0.8, 0.2), border = NA)
predicted_mean <- (lower + upper) / 2
lines(x, predicted_mean, col = "red", lwd = 2)
}
par(mfrow = c(2, 2))
# Plot for Split Conformal
plot_intervals(x_test, y_test, preds_splitconformal$lower, preds_splitconformal$upper, "Split Conformal")
# Plot for KDE Conformal
plot_intervals(x_test, y_test, preds_kdeconformal$lower, preds_kdeconformal$upper, "KDE Conformal")
# Plot for Bootstrap Conformal
plot_intervals(x_test, y_test, preds_bootstrapconformal$lower, preds_bootstrapconformal$upper, "Bootstrap Conformal")
# Plot for Surrogate Conformal
plot_intervals(x_test, y_test, preds_surrogateconformal$lower, preds_surrogateconformal$upper, "Surrogate Conformal")
Summary of the fit object
set.seed(123)
idx_train <- sample.int(dim(X)[1], size=floor(0.8*dim(X)[1]))
fit_obj <- matern32::fit_matern32(x = X[idx_train,], y = y[idx_train], lambda = 10**seq(-10, 10, by=1))
summary_fit_obj <- summary(fit_obj)
print(summary_fit_obj$coefficients)
print(summary_fit_obj$distro_effects)
## Response:
## Min. 1st Qu. Median 3rd Qu. Max.
## 5.000 17.075 21.200 25.000 50.000
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -3.03267235 -0.25327394 0.01728901 0.25152124 3.96242412
##
## 1st order effects:
## Est Std. Error t value Pr(>|t|)
## crim -0.015533728 0.003412618 -4.5518504 7.110262e-06 ***
## zn 0.012918168 0.005120576 2.5227961 1.203844e-02 *
## indus -0.093436725 0.005342518 -17.4892686 5.209706e-51 ***
## chas -0.027694166 0.003298692 -8.3955003 8.620455e-16 ***
## nox -0.077653921 0.005197358 -14.9410371 2.982994e-40 ***
## rm 0.002787912 0.006121455 0.4554329 6.490506e-01
## age 0.043679670 0.006295629 6.9380951 1.656900e-11 ***
## dis 0.062018965 0.005839813 10.6200260 2.561189e-23 ***
## rad -0.013714025 0.005353229 -2.5618228 1.078648e-02 *
## tax -0.020752114 0.005214672 -3.9795627 8.229496e-05 ***
## ptratio -0.051585681 0.007020797 -7.3475530 1.187631e-12 ***
## black -0.012671878 0.003726811 -3.4001933 7.427270e-04 ***
## lstat 0.022905821 0.006081373 3.7665545 1.909751e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Distribution of marginal effects:
## crim zn indus
## Min. :-33.71609 Min. :-26.25433 Min. :-36.15176
## 1st Qu.: -0.08774 1st Qu.: 0.00000 1st Qu.: -0.51142
## Median : -0.00071 Median : 0.00000 Median : 0.00000
## Mean : -0.01553 Mean : 0.01292 Mean : -0.09344
## 3rd Qu.: 0.05751 3rd Qu.: 0.00000 3rd Qu.: 0.35316
## Max. : 35.56141 Max. : 34.76033 Max. : 39.87066
## chas nox rm
## Min. :-33.02901 Min. :-30.19254 Min. :-39.47099
## 1st Qu.: 0.00000 1st Qu.: -0.53001 1st Qu.: -0.40596
## Median : 0.00000 Median : -0.01607 Median : 0.00379
## Mean : -0.02769 Mean : -0.07765 Mean : 0.00279
## 3rd Qu.: 0.00000 3rd Qu.: 0.38369 3rd Qu.: 0.47967
## Max. : 47.28859 Max. : 48.83468 Max. : 31.30072
## age dis rad
## Min. :-48.99448 Min. :-49.28409 Min. :-48.77398
## 1st Qu.: -0.48461 1st Qu.: -0.38916 1st Qu.: -0.24625
## Median : -0.00854 Median : 0.01820 Median : 0.00000
## Mean : 0.04368 Mean : 0.06202 Mean : -0.01371
## 3rd Qu.: 0.41998 3rd Qu.: 0.53055 3rd Qu.: 0.18253
## Max. : 37.23469 Max. : 45.85877 Max. : 28.94673
## tax ptratio black
## Min. :-28.77790 Min. :-41.98826 Min. :-56.24045
## 1st Qu.: -0.39855 1st Qu.: -0.41279 1st Qu.: -0.08059
## Median : 0.00000 Median : 0.00000 Median : 0.00000
## Mean : -0.02075 Mean : -0.05159 Mean : -0.01267
## 3rd Qu.: 0.31538 3rd Qu.: 0.41205 3rd Qu.: 0.09704
## Max. : 28.95582 Max. : 57.52405 Max. : 38.48930
## lstat
## Min. :-38.85329
## 1st Qu.: -0.49120
## Median : -0.00353
## Mean : 0.02291
## 3rd Qu.: 0.44015
## Max. : 58.95171
##
## Multiple R-squared: 0.9946523 Adjusted R-squared: 0.9944741
##
## Residuals Box test: 0.5072909 Residuals Shapiro test: 9.852929e-17
##
## LOOCV error: 3914.125 lambda: 0.01
## Est Std. Error t value Pr(>|t|)
## crim -0.015533728 0.003412618 -4.5518504 7.110262e-06 ***
## zn 0.012918168 0.005120576 2.5227961 1.203844e-02 *
## indus -0.093436725 0.005342518 -17.4892686 5.209706e-51 ***
## chas -0.027694166 0.003298692 -8.3955003 8.620455e-16 ***
## nox -0.077653921 0.005197358 -14.9410371 2.982994e-40 ***
## rm 0.002787912 0.006121455 0.4554329 6.490506e-01
## age 0.043679670 0.006295629 6.9380951 1.656900e-11 ***
## dis 0.062018965 0.005839813 10.6200260 2.561189e-23 ***
## rad -0.013714025 0.005353229 -2.5618228 1.078648e-02 *
## tax -0.020752114 0.005214672 -3.9795627 8.229496e-05 ***
## ptratio -0.051585681 0.007020797 -7.3475530 1.187631e-12 ***
## black -0.012671878 0.003726811 -3.4001933 7.427270e-04 ***
## lstat 0.022905821 0.006081373 3.7665545 1.909751e-04 ***
## crim zn indus
## Min. :-33.71609 Min. :-26.25433 Min. :-36.15176
## 1st Qu.: -0.08774 1st Qu.: 0.00000 1st Qu.: -0.51142
## Median : -0.00071 Median : 0.00000 Median : 0.00000
## Mean : -0.01553 Mean : 0.01292 Mean : -0.09344
## 3rd Qu.: 0.05751 3rd Qu.: 0.00000 3rd Qu.: 0.35316
## Max. : 35.56141 Max. : 34.76033 Max. : 39.87066
## chas nox rm
## Min. :-33.02901 Min. :-30.19254 Min. :-39.47099
## 1st Qu.: 0.00000 1st Qu.: -0.53001 1st Qu.: -0.40596
## Median : 0.00000 Median : -0.01607 Median : 0.00379
## Mean : -0.02769 Mean : -0.07765 Mean : 0.00279
## 3rd Qu.: 0.00000 3rd Qu.: 0.38369 3rd Qu.: 0.47967
## Max. : 47.28859 Max. : 48.83468 Max. : 31.30072
## age dis rad
## Min. :-48.99448 Min. :-49.28409 Min. :-48.77398
## 1st Qu.: -0.48461 1st Qu.: -0.38916 1st Qu.: -0.24625
## Median : -0.00854 Median : 0.01820 Median : 0.00000
## Mean : 0.04368 Mean : 0.06202 Mean : -0.01371
## 3rd Qu.: 0.41998 3rd Qu.: 0.53055 3rd Qu.: 0.18253
## Max. : 37.23469 Max. : 45.85877 Max. : 28.94673
## tax ptratio black
## Min. :-28.77790 Min. :-41.98826 Min. :-56.24045
## 1st Qu.: -0.39855 1st Qu.: -0.41279 1st Qu.: -0.08059
## Median : 0.00000 Median : 0.00000 Median : 0.00000
## Mean : -0.02075 Mean : -0.05159 Mean : -0.01267
## 3rd Qu.: 0.31538 3rd Qu.: 0.41205 3rd Qu.: 0.09704
## Max. : 28.95582 Max. : 57.52405 Max. : 38.48930
## lstat
## Min. :-38.85329
## 1st Qu.: -0.49120
## Median : -0.00353
## Mean : 0.02291
## 3rd Qu.: 0.44015
## Max. : 58.95171
par(mfrow=c(1, 2))
plot(fit_obj, choice = "coeffs")
plot(fit_obj, choice = "GCV")
plot(fit_obj, choice = "residuals")
Comments powered by Talkyard.