bases

Basis Expansions for Regression Modeling

https://github.com/corymccartan/bases

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Basis Expansions for Regression Modeling

README.Rmd

---
output: github_document
---



```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
)
set.seed(16802)
```

# **bases** 


[![R-CMD-check](https://github.com/CoryMcCartan/bases/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/CoryMcCartan/bases/actions/workflows/R-CMD-check.yaml)
[![CRAN status](https://www.r-pkg.org/badges/version/bases)](https://CRAN.R-project.org/package=bases)


**bases** provides various basis expansions for flexible regression modeling,
including random Fourier features (`?b_rff`), exact kernel / Gaussian process
feature maps (`?b_ker`), Bayesian Additive Regression Trees prior features
(`?b_bart`), and a helpful interface for n-way interactions (`?b_inter`). The
provided functions may be used within any modeling formula, allowing the use of
kernel methods and other basis expansions in modeling functions that do not
otherwise support them.  

Along with the basis expansions, a number of kernel functions (`?kernels`)
are also provided, which support kernel arithmetic to form new kernels. Basic 
ridge regression functionality (`?ridge`) is included as well.

Finally, the package provides a
[recipes](https://recipes.tidymodels.org/)-friendly interface, so that these
basis expansions can be combined with other transformations and used within the
[tidymodels](https://www.tidymodels.org/) framework.

## Installation

You can install **bases** from CRAN:

``` r
install.packages("bases")
```

You can install the development version with 

```r
remotes::install_github("CoryMcCartan/bases")
```

## Example: random Fourier features

The basis functions in **bases** all start with `b_` and are designed to work in
the same way as built-in basis expansions like `bs()` or `poly()`: simply
include the function in a model formula.

So fitting an approximate kernel regression with random Fourier features is as simple as wrapping the relevant variables in a call to the corresponding basis function, `b_rff()`.
The default kernel is a Gaussian/RBF kernel with length scale 1 which is applied to predictors after rescaling them to have unit variance.

```{r}
library(bases)

# Box & Jenkins (1976) sales data
x = 1:150
y = as.numeric(BJsales) 

lm(y ~ b_rff(x, p = 5)) # 5 random features
```

You can provide a different `kernel = ` argument to switch kernels.
Many common kernels are provided with the package; see `?kernels`.

```r
b_rff(x, kernel = k_matern(scale = 0.1, nu = 5/2))
b_rff(x, kernel = k_rq(scale = 2, alpha = 2))
```

In practice, RFF are usually fit with penalization, such as via ridge regression.
Below, we visualize several RFF ridge regression fits versus a simple linear model, using the `ridge()` function provided in the package.
```{r rbf-plot}
k = k_rbf(scale = 0.2)
plot(x, y, xlab = "Month", ylab = "Sales")
lines(x, fitted(lm(y ~ x)), lty = "dashed", lwd = 1.5)
for (i in 1:20) {
    m_rff = ridge(y ~ b_rff(x, kernel = k))
    lines(x, fitted(m_rff), col = "#4584")
}
```

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