Exactness

ExplainPolySVM by default does not approximate the model it explains. This page states when that holds and when it stops holding.

The transformation is exact

transform_svm() produces a linear model with full fidelity to the original SVM. For every observation,

es.decision_function(x)          # ExplainPolySVM
svm_model.decision_function(x)   # scikit-learn

agree to numerical precision. The package’s test suite asserts this exactly, for both SVC and SVR models, with a tolerance of \(10^{-10}\). No truncation, no Taylor expansion and no restriction on the degree of the kernel is involved: the polynomial kernel is expanded in full, and the redundancy between permutation-equivalent interactions is what makes that affordable.

Differences at the level of \(10^{-12}\) or so between the two decision functions are ordinary floating-point accumulation, not a modelling error.

Degree contributions are also exact

degree_contributions() evaluates the polynomial kernel expansion in closed form rather than by summing interactions, but it computes the same quantity: each column matches the sum of the weighted interactions of that degree, and the columns plus the intercept sum to the decision function. The test suite asserts both, again at \(10^{-10}\). Since the calculation never builds the expansion, it is exact for models that are far too large to transform.

Masking makes the model deliberately approximate

Masking suppresses interactions, so a masked model no longer reproduces the original decision function. This is also the point of the masked model. The question a mask answers is how much of the model do I lose by keeping only these interactions, at the cost that the exactness above no longer holds.

There are two distinct ways to mask, and they differ in whether the loss is recoverable:

• decision_function(x, mask=True) applies the mask to that evaluation only. The full linear model is retained, so you can compare masked and unmasked predictions freely.

• transform_svm(mask=True) shrinks the stored linear model permanently. The linear_model_is_masked flag records this, and every subsequent call works on the reduced model. Recovering the discarded interactions requires transforming again from the support vectors.

For evaluating a feature selection, the first form is usually what you want.

Zero-weight interactions are not always zero contributions

With coef0=0, scikit-learn’s default, every interaction below the kernel degree has an exactly zero weight, as described in Interpreting the explanations. Those interactions still appear in get_interactions() and in the linear model; they simply contribute nothing. A mask built from weight magnitudes will rank them last.