basis_of_degree {hal9001}

Compute Degree of Basis Functions

Description

Find the full list of basis functions up to a particular degree

Usage

basis_of_degree(
  x,
  degree,
  smoothness_orders,
  include_zero_order,
  include_lower_order
)

Arguments

x

An input matrix containing observations and covariates following standard conventions in problems of statistical learning.

degree

The highest order of interaction terms for which the basis functions ought to be generated. The default (NULL) corresponds to generating basis functions for the full dimensionality of the input matrix.

smoothness_orders

An integer vector of length ncol(x) specifying the desired smoothness of the function in each covariate. k = 0 is no smoothness (indicator basis), k = 1 is first order smoothness, and so on. For an additive model, the component function for each covariate will have the degree of smoothness as specified by smoothness_orders. For non-additive components (tensor products of univariate basis functions), the univariate basis functions in each tensor product have smoothness degree as specified by smoothness_orders.

include_zero_order

A logical, indicating whether the zeroth order basis functions are included for each covariate (if TRUE), in addition to the smooth basis functions given by smoothness_orders. This allows the algorithm to data-adaptively choose the appropriate degree of smoothness.

include_lower_order

A logical, like include_zero_order, except including all basis functions of lower smoothness degrees than specified via smoothness_orders.

Value

A list containing basis functions and cutoffs generated from a set of input columns up to a particular pre-specified degree.