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Generate locally spiky smooth (LSS) response data.

generate_y_lss.Rd

Generate LSS response data with a specified error distribution given the observed data matrices.

Usage

generate_y_lss(
  X,
  k,
  s,
  thresholds = 1,
  signs = 1,
  betas = 1,
  intercept = 0,
  overlap = FALSE,
  err = NULL,
  return_support = FALSE,
  ...
)

Arguments

X

Data matrix or data frame.

k

Order of the interactions.

s

Number of interactions in the LSS model or a matrix of the support indices with each interaction taking a row in this matrix and ncol = k.

thresholds

A scalar or a s x k matrix of the thresholds for each term in the LSS model.

signs

A scalar or a s x k matrix of the sign of each interaction (1 means > while -1 means <).

betas

Scalar, vector, or function to generate coefficients corresponding to interaction terms. See \codegenerate_coef().

intercept

Scalar intercept term.

overlap

If TRUE, simulate support indices with replacement; if FALSE, simulate support indices without replacement (so no overlap)

err

Function from which to generate simulated error vector. Default is NULL which adds no error to the DGP.

return_support

Logical specifying whether or not to return a vector of the support column names. If X has no column names, then the indices of the support are used.

...

Other arguments to pass to err() to generate the error vector.

Value

If return_support = TRUE, returns a list of three:

y

A response vector of length nrow(X).

support

A vector of feature indices indicating all features used in the true support of the DGP.

int_support

A vector of signed feature indices in the true (interaction) support of the DGP. For example, "1+_2-" means that the interaction between high values of feature 1 and low values of feature 2 appears in the underlying DGP.

If return_support = FALSE, returns only the response vector y.

Details

Here, data is generated from the following LSS model: $$E(Y|X) = intercept + sum_{i = 1}^{s} beta_i prod_{j = 1}^{k}1(X_{S_j} lessgtr thresholds_ij)$$

For more details on the LSS model, see Behr, Merle, et al. "Provable Boolean Interaction Recovery from Tree Ensemble obtained via Random Forests." arXiv preprint arXiv:2102.11800 (2021).

Examples

X <- generate_X_gaussian(.n = 100, .p = 10)

# generate data from: y = 1(X_1 > 0, X_2 > 0) + 1(X_3 > 0, X_4 > 0)
y <- generate_y_lss(X = X, k = 2, s = matrix(1:4, nrow = 2, byrow = TRUE),
                    thresholds = 0, signs = 1, betas = 1)

# generate data from: y = 3 * 1(X_1 < 0) - 1(X_2 > 1) + N(0, 1)
y <- generate_y_lss(X = X, k = 1, 
                    s = matrix(1:2, nrow = 2),
                    thresholds = matrix(0:1, nrow = 2), 
                    signs = matrix(c(-1, 1), nrow = 2),
                    betas = c(3, -1),
                    err = rnorm)