Flexible discriminant analysis on the flattened representation

One discriminant per response, over every bin-by-channel column of the representation, fitted as mda's fda(method = mars) fits it and as biomod2 fits FDA. Optimal scoring gives presence and absence one score each and regresses the scored response on a MARS basis of the columns; the fitted score is the one canonical variate, and a unit's prediction is its posterior probability of presence under two normal classes around the class centroids on that variate, with the classes' shares among the fitting units as priors.

Usage

discriminant(
  data = NULL,
  degree = 1L,
  penalty = NULL,
  max_terms = NULL,
  min_gain = 0.001,
  prune = TRUE,
  calibrate = TRUE,
  threads = 1L
)

Arguments

data

A representation the learner is pinned to, or NULL to run across every representation of the run.

degree

The most hinges a term of the basis multiplies.

penalty

The generalised cross-validation's charge per term beyond its own degree of freedom, taken at half. NULL is mda's, 2 at degree one and 3 above.

max_terms

The most terms the forward pass reaches, the intercept included. NULL is max(21, 2 p + 1) for p columns; an even number is taken one lower.

min_gain

The least share of the residuals a forward step is kept for.

prune

Whether the pruning pass runs. Without it every term of the forward pass is kept.

calibrate

Whether the posterior is recalibrated by a probit regression, as biomod2 does.

threads

Responses fitted at once, or, with one response to fit, columns searched at once. The model is the same on any number.

Value

A learner().

Details

The basis is mda's own MARS, which biomod2 reaches through fda() and which differs from earth's that mars() reproduces. Each forward step adds a column linearly or a pair of hinges on it, max(0, x - t) and max(0, t - x), choosing by Friedman's running updates, and the pass stops when a step lowers the residuals by less than min_gain of them, when they fall to min_gain of the null model's, when the generalised cross-validation passes ten times the null model's, or at max_terms terms. The pruning pass drops the term of least t statistic, one at a time, and keeps the subset of least generalised cross-validation, which counts each term beyond the intercept as 1 + penalty / 2 degrees of freedom. The defaults are mda's, which biomod2 passes unchanged under its default option set and under "bigboss": degree one, penalty = 2, min_gain = 0.001 and max_terms = max(21, 2 p + 1) for p columns.

The case weights are the response head's, positive_weights() under presence-absence. They set the classes' scores and the variate, as fda() reads them, and not the basis: mda's forward pass sets them to one. Under the shipped presence-absence head those weights are on, so a default discriminant() is mda's specification fitted under them; a head registered without weights fits it unweighted.

biomod2 always recalibrates an FDA posterior by a probit regression of the response on it, under the case weights, and predicts through that regression. calibrate = TRUE does the same, on the units the discriminant was fitted on; FALSE predicts the posterior itself. biomod2 rounds the posterior to three decimals before recalibrating it, which is not reproduced.

The forward pass, the pruning, the scoring and the recalibration live in the core the Python package calls, pinned against mda and R's glm() in the fixtures, so the two languages keep the same terms and predict the same probabilities. A response holding one value is predicted its mean, and so is one whose scored response the basis does not reach; both are named in unfitted. The learner needs a presence-absence response, and a head whose loss is not the binary cross-entropy is refused.

Examples

discriminant()
discriminant(data = grain("season"), calibrate = FALSE)