Expand feature matrix using basis splines

Performs a basis expansion for many features at once, returning output that is compatible for use with the grpreg() function. Returns an expanded matrix along with a vector that describes its grouping.

Usage

expand_spline(x, df = 3, degree = 3, type = c("ns", "bs"))

Arguments

x: Features to be expanded (numeric matrix).
df: Degrees of freedom (numeric; default = 3).
degree: Degree of the piecewise polynomial (integer; default = 3 (cubic splines)).
type: Type of spline, either B-spline ("bs") or natural cubic spline ("ns"; default).

Value

An object of class expandedMatrix consisting of:

X: A matrix of dimension nrow(x) by df*ncol(x)
group: A vector of length df*ncol(x) that describes the grouping structure
Additional metadata on the splines, such as knot locations, required in order to evaluate spline at new feature values (e.g., for prediction)

Details

expand_spline() uses the function splines::bs() or splines::ns() to generate a basis matrix for each column of x. These matrices represent the spline basis for piecewise polynomials with specified degree evaluated separately for each original column of x. These matrices are then column-bound to form a single grouped matrix of derived features. A vector that describes the grouping present in the resulting matrix is also generated. The resulting object can be passed to grpreg().

This methodology was originally proposed by Ravikumar et al. (2009), who named it SPAM (SParse Additive Modeling).

References

Ravikumar P, Lafferty J, Liu H and Wasserman L (2009). Sparse additive models. Journal of the Royal Statistical Society Series B, 71: 1009-1030.

Examples

Data <- gen_nonlinear_data(n=1000)
X <- expand_spline(Data$X)
fit <- grpreg(X, Data$y)
plot_spline(fit, "V02", lambda = 0.03)