jpt.base.correlation.xi

Chatterjee’s xi correlation coefficient.

A rank-based measure of functional dependence introduced by Chatterjee (JASA, 2021). The coefficient equals 0 iff X and Y are independent and 1 iff Y is a measurable function of X.

Functions

xi_correlation(→ float)	Compute Chatterjee's xi correlation.
xi_correlation_matrix(→ numpy.ndarray)	Compute xi for all feature-target pairs.

Module Contents

jpt.base.correlation.xi.xi_correlation(x: numpy.ndarray, y: numpy.ndarray) → float

Compute Chatterjee’s xi correlation.

Measures the degree to which y is a measurable function of x. Requires only two sorts and a linear pass, giving O(n log n) complexity.

Parameters:

• x – feature values, shape (n,)

• y – target values, shape (n,)

Returns:

xi coefficient in [-0.5, 1]

jpt.base.correlation.xi.xi_correlation_matrix(data: numpy.ndarray, feature_indices: numpy.ndarray, target_indices: numpy.ndarray, row_indices: numpy.ndarray | None = None) → numpy.ndarray

Compute xi for all feature-target pairs.

Returns a matrix M where M[i, j] = xi(data[:, feature_indices[i]],

data[:, target_indices[j]]).

Parameters:

• data – array (n x d)

• feature_indices – feature column indices

• target_indices – target column indices

• row_indices – optional row subset

Returns:

xi matrix (nf x nt)