Optimal Piecewise Local-Linear Approximations
This work addresses the need for global interpretability in machine learning models, which is crucial for building trust, but it is incremental as it extends existing local-linear methods to a global context.
The authors tackled the problem of explaining global model behavior in black-box models by developing a dynamic programming framework for optimal piecewise local-linear approximations, providing provable fidelity guarantees and demonstrating utility on synthetic and real datasets.
Existing works on "black-box" model interpretation use local-linear approximations to explain the predictions made for each data instance in terms of the importance assigned to the different features for arriving at the prediction. These works provide instancewise explanations and thus give a local view of the model. To be able to trust the model it is important to understand the global model behavior and there are relatively fewer works which do the same. Piecewise local-linear models provide a natural way to extend local-linear models to explain the global behavior of the model. In this work, we provide a dynamic programming based framework to obtain piecewise approximations of the black-box model. We also provide provable fidelity, i.e., how well the explanations reflect the black-box model, guarantees. We carry out simulations on synthetic and real datasets to show the utility of the proposed approach. At the end, we show that the ideas developed for our framework can also be used to address the problem of clustering for one-dimensional data. We give a polynomial time algorithm and prove that it achieves optimal clustering.