cossonet

Introduction

The package is an function that estimates sparse nonlinear components using the COSSO penalty. This package is available from the Comprehensive R Archive Network. This script describes a example of how to use the package.

Installation

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

install.packages("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)

References

• Lin, Y., & Zhang, H. (2006). Component selection and smoothing in multivariate nonparametric regression.
  Annals of Statistics, 34(5), 2272–2297. doi:10.1214/009053606000000722.