Training Data Attribution

A classic statistical method that estimates the impact of removing a single training point on model parameters. By calculating the gradient of the loss with respect to a data point, influence functions answer the counterfactual question: 'How would the model change if this example was deleted?' This approach is model-agnostic but computationally expensive for deep neural networks, requiring the inversion of the Hessian matrix. Modern approximations like LiSSA and TracIn make this feasible for large-scale models.

A scalable influence estimator designed specifically for deep learning. TracIn attributes a test prediction to training examples by tracking the inner product of loss gradients at each checkpoint during the training process. The core idea: a training point is influential if its gradient direction aligns with the gradient of the test point across multiple training steps. This avoids the prohibitive Hessian computation of classic influence functions.

A decomposition technique that expresses a model's prediction as a weighted sum of the training data points. This method leverages the representer theorem from kernel methods, showing that the prediction for a test input can be decomposed into a linear combination of the model's similarity to each training example. It provides a direct, interpretable score for every training point's contribution to a single prediction.

A technique that measures attribution by computing the cosine similarity between the gradient vectors of the test loss and the training loss. The underlying assumption is that training examples with gradients highly similar to the test example's gradient were most responsible for shaping the model's decision boundary in that region. This method is particularly effective for identifying proponents (same class) and opponents (different class) in the training set.

A game-theoretic approach adapted from cooperative game theory to assign a fair contribution score to each training data point. The Data Shapley value computes the average marginal improvement a training point brings when added to all possible subsets of the training data. While theoretically robust and equitable, exact computation is exponential in cost, requiring Monte Carlo approximations like TMC-Shapley for practical use.

The most direct but computationally intensive method: systematically retrain the model multiple times with specific data subsets removed. By measuring the drop in performance or change in prediction after excluding a candidate set, this approach provides ground-truth attribution. While impractical for large models, it serves as the gold-standard baseline for validating the accuracy of all approximate attribution techniques.

A causal explanation method that identifies the minimal change to an input feature required to alter a model's prediction. While distinct from Training Data Attribution, counterfactuals are a complementary transparency technique that answers 'what if' questions about individual decisions, helping auditors understand the decision boundary shaped by the training data.

• Actionable Recourse: Provides a path for individuals to change an adverse outcome.
• Sparse Changes: Seeks the smallest number of feature alterations.
• Contrastive Reasoning: Explains a decision by presenting its closest alternative world.