Maximum Entropy Covariance estimator

Computes a maximum-entropy motivated covariance estimator for SDR.

Usage

cov_mec(
  X,
  y,
  nslices = 6,
  response_type = c("continuous", "categorical", "survival"),
  delta = NULL,
  alpha = NULL,
  eps = 1e-06,
  ...
)

Arguments

X

Numeric matrix or data frame.

y

Numeric response vector.

nslices

Number of response slices.

response_type

Response type. One of "continuous", "categorical", or "survival".

delta

Optional event indicator for survival data.

alpha

Convex weight assigned to the entropy-maximising slice covariance. If NULL, alpha is chosen adaptively from the condition number of the pooled covariance.

eps

Small positive eigenvalue floor used for log-determinant stability.

...

Additional arguments passed to internal methods.

Value

A covariance matrix with attributes containing the shrinkage weight and entropy diagnostics.

Details

The estimator uses response slicing to obtain slice-specific covariance matrices, selects the covariance matrix with maximum log-determinant entropy, and combines it with the pooled covariance matrix through convex shrinkage.

For censored survival responses, the function accepts delta and applies a survival-aware response construction before slicing.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])
Sigma <- cov_mec(X, y = mtcars$mpg, nslices = 4)
attr(Sigma, "alpha")
#> [1] 0.95
attr(Sigma, "entropy_slice")
#> [1] 1