delta-audit

Δ-Attribution Concepts

This page explains the core concepts behind Δ-Attribution and how Delta-Audit implements them.

What is Δ-Attribution?

Δ-Attribution (Delta-Attribution) is a framework for understanding how model explanations change when models are updated. When you train a new version of a model, not only do the predictions change, but also the explanations of those predictions.

Core Concepts

Model Pairs (A→B)

A model pair consists of two models:

• Model A: The baseline/original model
• Model B: The updated/new model

The goal is to understand how explanations change from A to B.

Attribution Methods

Delta-Audit uses occlusion-based attribution methods:

1. Occlusion: Replace a feature with a baseline value and measure the change in model output
2. Clamping: Same as occlusion, but emphasizes the feature replacement aspect
3. Common Class Anchor: Use class-specific baseline values

Baseline Computation

• Mean Baseline: Use the mean value of each feature across the training set
• Median Baseline: Use the median value of each feature
• Zero Baseline: Use zero as the baseline value

Key Metrics

Behavioral Alignment Coefficient (BAC)

BAC measures how well attribution changes correlate with output changes:

BAC = Corr(||Δφ||₁, |Δf|)

Where:

• Δφ = φ_B - φ_A (attribution differences)
• Δf = f_B - f_A (output differences)

• ·

  ₁ = L1 norm

Interpretation: Higher BAC values indicate that when the model output changes significantly, the attributions also change significantly.

Differential Conservation Error (DCE)

DCE measures how much the sum of attribution changes differs from the actual output change:

DCE = E[|ΣΔφ - Δf|]

Interpretation: Lower DCE values indicate better conservation - the sum of attribution changes closely matches the output change.

Δ Magnitude L1

Measures the overall magnitude of attribution changes:

Δ Magnitude L1 = E[||Δφ||₁]

Interpretation: Higher values indicate larger changes in feature importance between models.

Rank Overlap @K

Measures how much the top-K features overlap between models:

Rank Overlap @K = |TopK(φ_A) ∩ TopK(φ_B)| / |TopK(φ_A) ∪ TopK(φ_B)|

Interpretation: Higher values indicate that the most important features remain similar between models.

Jensen-Shannon Divergence (JSD)

Measures the distributional shift between attribution sets:

JSD = 0.5 * KL(φ_A || M) + 0.5 * KL(φ_B || M)

Where M = 0.5 * (φ_A + φ_B)

Interpretation: Higher values indicate larger distributional changes in feature importance.

Experimental Design

Algorithm Pairs

Each algorithm is tested with 3 different hyperparameter pairs:

1. Pair 1: Different regularization/strength parameters
2. Pair 2: Different structural parameters (e.g., kernel, penalty)
3. Pair 3: Different optimization parameters (e.g., solver, algorithm)

Datasets

• Breast Cancer: Binary classification with 30 features
• Wine: Multi-class classification with 13 features
• Digits: Multi-class classification with 64 features

Evaluation Protocol

1. Stratified train/test split (80/20)
2. StandardScaler applied to all features
3. Random state fixed to 42 for reproducibility
4. Mean baseline computed from training data
5. Metrics computed on test set

Interpretation Guidelines

High BAC, Low DCE

• Good behavioral alignment
• Attribution changes correlate well with output changes
• Model updates are well-explained

Low BAC, High DCE

• Poor behavioral alignment
• Attribution changes don’t correlate with output changes
• Model updates are poorly explained

High Δ Magnitude

• Large changes in feature importance
• Model behavior has changed significantly

Low Rank Overlap

• Different features are important in the new model
• Model has learned different patterns

High JSD

• Large distributional shift in attributions
• Model explanations have changed substantially

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