Method overview

Understand prototypes, target-rival contrasts, and FPDE variants

FPDE is a post-hoc feature attribution method for classification. It explains one input by contrasting that input with a prototype for a target class and a prototype for a rival class.

The result is one attribution value per feature. Positive values support the target class. Negative values support the rival class.

When to use FPDE

Use FPDE when you have:

• A feature matrix where each column has a consistent meaning
• Class labels for training samples
• A classifier that exposes predict_proba and classes_
• A need to explain target-versus-rival evidence at the feature level

FPDE does not retrain or modify the classifier. It uses training data to build prototypes, then uses those prototypes to explain individual inputs.

Core terms

Term	Meaning
Prototype	A representative class feature vector. FPDE 0.1.0 builds one class-mean prototype per class.
Target class	The class being explained, often the classifier’s predicted class.
Rival class	The contrast class, often the second-highest-probability class.
Evidence	The scalar target-versus-rival contrast decomposed by FPDE.
Attribution	A per-feature contribution to the evidence value.
Anchor	A reference vector used by Cos-FPDE before computing cosine contrasts.
Baseline	A replacement vector used for deletion and insertion perturbation curves.

Prototype construction

class_mean_prototypes(X, y) computes one prototype per class by averaging all training rows with that class label. FPDEEngine.fit(X_train, y_train, model) builds the same prototype state and stores it for repeated explanations.

For repeated workflows, prefer FPDEEngine because it reuses:

• Class-mean prototypes
• Prototype labels
• Mean and zero anchors
• The baseline vector
• Label-to-prototype lookup state

Target and rival selection

When you use FPDEEngine with a model, FPDE chooses the local contrast from predict_proba.

1. Select the target class

   The target class is the highest-probability class.

2. Select the rival class

   The rival class is the second-highest-probability class.

3. Map labels to prototypes

   FPDE maps both labels to their fitted class-mean prototypes.

When you call lower-level functions directly, pass positive_label and negative_label. If you omit negative_label, FPDE selects a non-target prototype according to the selected mode.

Diff-FPDE

Diff-FPDE decomposes the difference in squared distances from the input to the rival and target prototypes.

E_diff = ||x - p_neg||^2 - ||x - p_pos||^2
phi_j  = (x_j - p_neg_j)^2 - (x_j - p_pos_j)^2

The attribution values sum to the Diff-FPDE evidence. A positive feature value means that feature supports the target class under this squared-distance contrast.

Cos-FPDE

Cos-FPDE decomposes a regularized cosine-similarity contrast.

E_cos = cos_eps(x - anchor, p_pos - anchor)
        - cos_eps(x - anchor, p_neg - anchor)

Cos-FPDE is an exact coordinate decomposition of the cosine contrast. It is not a leave-one-feature-out causal effect, because the cosine denominator depends on all coordinates.

Hyb-FPDE

Hyb-FPDE mixes Diff-FPDE and Cos-FPDE attribution vectors.

phi_hyb_j = lambda_hyb * phi_diff_j + (1 - lambda_hyb) * phi_cos_j

lambda_hyb must be in [0, 1].

• lambda_hyb=1.0 uses the Diff-FPDE endpoint.
• lambda_hyb=0.0 uses the Cos-FPDE endpoint.
• Intermediate values blend both attribution vectors.

By default, Hyb-FPDE uses L1-normalized component attribution vectors before mixing. Set normalize="none" when you want to mix the raw component scales.

Where to go next

• Use Explain one sample for a practical local explanation.
• Use Select lambda_hyb to choose a fixed mixture weight.
• Use Interpreting results to read signs and evidence values correctly.