Sparse Nonparametric Regression for High-Dimensional Data

Estimation of sparse nonlinear functions in nonparametric regression using component selection and smoothing. Designed for the analysis of high-dimensional data, the models support various data types, including exponential family models and Cox proportional hazards models. The methodology is based on Lin and Zhang (2006) .

cossonet

Installation

We first load the library for cossonet and set a seed for reproducibility.

devtools::install_github("jiieunshin/cossonet")
library(cossonet)
set.seed(20250101)

Data generation

The function data_generation generates example datasets with continuous response. We generate a training set with $n=200$ and $p=20$, and a test set with $n=1000$ and $p=20$.

tr = data_generation(n = 200, p = 20, SNR = 9, response = "continuous")
te = data_generation(n = 1000, p = 20, SNR = 9, response = "continuous")

Model fitting

The function cossonet is the main function that fits the model. We have to input training set in this function. And Specific values are required to the arguments, such as family, lambda0, and lambda_theta`.

lambda0_seq = exp(seq(log(2^{-5}), log(2^{-1}), length.out = 20))
lambda_theta_seq = exp(seq(log(2^{-8}), log(2^{-5}), length.out = 20))

fit = cossonet(tr$x, tr$y, family = 'gaussian',
	       lambda0 = lambda0_seq,
	       lambda_theta = lambda_theta_seq
	       )

Prediction

The function cossonet.predict is used to predict new data based on the fitted model. The output includes predicted values $\hat{f}$ (from f.new) and $\hat{\mu}$ (from mu.new) for the new data. The predicted value and predictive accuracy for the test set using our fitted model can be obtained by

pred = cossonet.predict(fit, te$x)
mean((te$f - pred$f.new)^2)