Turner Least Squares

turner.py

# Based off of Mumford et al. (2011)
# Derived from a figure, as there was no actual math presented :\
# 
# It's a sort of minimal-assumption regression regularization method

import numpy as np
 
def turnerLeastSquares(designMatrix, samples):
    nuisance = np.sum(designMatrix, axis=1).reshape((designMatrix.shape[0], 1))
 
    fitted = np.zeros((designMatrix.shape[1], samples.shape[1]))
 
    for j in range(designMatrix.shape[1]):
        column = designMatrix[:, [j]]

        # Create a design matrix with the current column and the rest
        # of the matrix collapsed into a single column
        turnerMatrix = np.hstack((column, nuisance - column))
        fits = np.linalg.lstsq(turnerMatrix, samples)[0]

        # Keep only the parameters of interest
        fitted[j, :] = fits[0, :]
 
    return fitted