Density

With density=True, the default, a fitted model is also a density model of its input.

logp = model.score_samples(X)   # (n,) log density of each row
mean_logp = model.score(X)      # the mean of score_samples

How the density is built

The change of variables formula gives the density of an input from the density of its latent vector and the Jacobian of the flow. The latent density has two parts. One is a density over positions of the layout. The other is a Gaussian over the residual whose mean and variance depend on the position, preceded by a few extra coupling layers that leave the layout coordinates unchanged.

Training includes a likelihood term, so the whole map is shaped as a density model while it learns the layout. The position-dependent part is fitted after training, at the first call that needs it, which is why the first density call after fit takes longer than the ones after it.

Units and comparisons

score_samples returns the natural logarithm of the density of the whitened input, which differs from the density of the raw input by a constant for a given training set. Values compare between points of one model, and between models fitted to the same data. They do not compare between models fitted to different data.

For padded inputs the density includes the padding columns, set to zero for the evaluated points. See Choosing the input.

Model selection

score is the mean log density, so scikit-learn model selection uses held-out likelihood when no other scorer is given.

from sklearn.model_selection import GridSearchCV

search = GridSearchCV(FloDR(max_iter=1600), {"w": [1.0, 2.0, 3.0]}, cv=3).fit(X)
search.best_params_

Each candidate is fitted once per fold, so a search costs as many fits as candidates times folds.

Without the density

FloDR(density=False) skips the likelihood term and the conditional fit. score_samples and score are then absent, and hasattr(model, "score") is False. conditional_spread, atypicality and spread_calibration raise a ValueError. hidden_contrast still works.