Representer Point Selection via Local Jacobian Expansion for Post-hoc Classifier Explanation of Deep Neural Networks and Ensemble Models

Explaining the influence of training data on machine learning model predictions is a critical tool for debugging models through data curation. A recent appealing and efficient approach for this task was provided via the concept of Representer Point Selection (RPS), i.e. a method the leverages the dual form of l(2) regularized optimization in the last layer of the neural network to identify the contribution of training points to the prediction. However, two key drawbacks of RPS-l(2) are that they (i) lead to disagreement between the originally trained network and the RPS-l(2) regularized network modification and (ii) often yield a static ranking of training data for test points in the same class, independent of the test point being classified. Inspired by the RPS-l(2) approach, we propose an alternative method based on a local Jacobian Taylor expansion (LJE). We empirically compared RPS-LJE with the original RPS-l(2) on image classification (with ResNet), text classification recurrent neural networks (with Bi-LSTM), and tabular classification (with XGBoost) tasks. Quantitatively, we show that RPS-LJE slightly outperforms RPS-l(2) and other state-of-the-art data explanation methods by up to 3% on a data debugging task. More critically, we qualitatively observe that RPS-LJE provides stable and individualized explanations that are more coherent to each test data point. Overall, RPS-LJE represents a novel approach to RPS-l(2) that provides a powerful tool for sample-based model explanation and debugging.