Quadratic feature basis for the logistic ratio estimator

[1, z, vech(z z')] for z = (theta, x). The basis is chosen so the estimator is exact for a linear-Gaussian simulator: there \(\log p(x \mid \theta)\) is a quadratic form in \((\theta, x)\), so the log ratio's parameter dependence lies inside this span and the fit is limited only by estimation error (see fit_logistic_ratio() for why the evidence term does not spoil that). It is the regression oracle for nre() that "linear_gaussian" is for npe() and nle().

Usage

nre_features(theta, x)

Details

It costs 1 + d + d(d+1)/2 columns for d = dim_theta + dim_x, so it is a baseline for small models, not a substitute for a neural classifier on wide data.