mlbench.friedman3: Benchmark Problem Friedman 3

In mlbench: Machine Learning Benchmark Problems

Benchmark Problem Friedman 3

Description

The regression problem Friedman 3 as described in Friedman (1991) and Breiman (1996). Inputs are 4 independent variables uniformly distrtibuted over the ranges

0 \le x1 \le 100

40 \pi \le x2 \le 560 \pi

0 \le x3 \le 1

1 \le x4 \le 11

The outputs are created according to the formula

y = \mbox{atan}((x2 x3 - (1/(x2 x4)))/x1) + e

where e is N(0,sd).

Usage

mlbench.friedman3(n, sd=0.1)

Arguments

n	number of patterns to create
sd	Standard deviation of noise. The default value of 0.1 gives a signal to noise ratio (i.e., the ratio of the standard deviations) of 3:1. Thus, the variance of the function itself (without noise) accounts for 90% of the total variance.

Value

Returns a list with components

x	input values (independent variables)
y	output values (dependent variable)

References

Breiman, Leo (1996) Bagging predictors. Machine Learning 24, pages 123-140.

Friedman, Jerome H. (1991) Multivariate adaptive regression splines. The Annals of Statistics 19 (1), pages 1-67.

mlbench documentation built on May 31, 2023, 6:18 p.m.