Provable concept learning for interpretable predictions using variational inference

In safety critical applications, practitioners are reluctant to trust neural networks when no interpretable explanations are available. Many attempts to provide such explanations revolve around pixel level attributions or use previously known concepts. In this paper we aim to provide explanations by provably identifying \emph{high-level, previously unknown concepts}. To this end, we propose a probabilistic modeling framework to derive (C)oncept (L)earning and (P)rediction (CLAP) -- a VAE-based classifier that uses visually interpretable concepts as linear predictors. Assuming that the data generating mechanism involves predictive concepts, we prove that our method is able to identify them while attaining optimal classification accuracy. We use synthetic experiments for validation, and also show that on real-world (PlantVillage and ChestXRay) datasets, CLAP effectively discovers interpretable factors for classifying diseases.

Fast rates for noisy interpolation require rethinking the effects of inductive bias

Good generalization performance on high-dimensional data crucially hinges on a simple structure of the ground truth and a corresponding strong inductive bias of the estimator. Even though this intuition is valid for regularized models, in this paper we caution against a strong inductive bias for interpolation in the presence of noise: Our results suggest that, while a stronger inductive bias encourages a simpler structure that is more aligned with the ground truth, it also increases the detrimental effect of noise. Specifically, for both linear regression and classification with a sparse ground truth, we prove that minimum $\ell_p$-norm and maximum $\ell_p$-margin interpolators achieve fast polynomial rates up to order $1/n$ for $p > 1$ compared to a logarithmic rate for $p = 1$. Finally, we provide experimental evidence that this trade-off may also play a crucial role in understanding non-linear interpolating models used in practice.