sim_Friedman2

The regression problem Friedman 2 as described in Friedman (1991) and
Breiman (1996). Inputs are 4 independent variables uniformly
distributed 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
$$y = (x1^2 + (x2 x3 - (1/(x2 x4)))^2)^{0.5} + e$$
where e is $N(0,sd^2)$.

Bayesian Additive Regression Kernels (BARK) provides
an implementation for non-parametric function estimation using Levy
Random Field priors for functions that may be represented as a
sum of additive multivariate kernels. Kernels are located at
every data point as in Support Vector Machines, however, coefficients
may be heavily shrunk to zero under the Cauchy process prior, or even,
set to zero. The number of active features is controlled by priors on
precision parameters within the kernels, permitting feature selection. For
more details see Ouyang, Z (2008) "Bayesian Additive Regression Kernels",
Duke University. PhD dissertation, Chapter 3 and Wolpert, R. L, Clyde, M.A,
and Tu, C. (2011) "Stochastic Expansions with Continuous Dictionaries Levy
Adaptive Regression Kernels, Annals of Statistics Vol (39) pages 1916-1962
<doi:10.1214/11-AOS889>.

Merlise Clyde

bark

Bayesian Additive Regression Kernels

Zhi Ouyang

Robert Wolpert

sim_Friedman2 function

<dl><dt>n</dt>
<dd>number of data points to create</dd>
<dt>sd</dt>
<dd>Standard deviation of noise. The default value of 125 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.</dd></dl>

Arguments

Simulated Regression Problem Friedman 2 — sim_Friedman2

<dl>

<dt>n</dt>
<dd>number of data points to create</dd>


<dt>sd</dt>
<dd>Standard deviation of noise. The default value of 125 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.</dd>

</dl>

sim_Friedman2: Simulated Regression Problem Friedman 2

Description

Usage

Value

Arguments

References

See Also

Examples