William Stafford Noble

Winston Chen, William Stafford Noble, Yang Young Lu · uw

The complexity of deep neural networks (DNNs) makes them powerful but also makes them challenging to interpret, hindering their applicability in error-intolerant domains. Existing methods attempt to reason about the internal mechanism of DNNs by identifying feature interactions that influence prediction outcomes. However, such methods typically lack a systematic strategy to prioritize interactions while controlling confidence levels, making them difficult to apply in practice for scientific discovery and hypothesis validation. In this paper, we introduce a method, called DeepROCK, to address this limitation by using knockoffs, which are dummy variables that are designed to mimic the dependence structure of a given set of features while being conditionally independent of the response. Together with a novel DNN architecture involving a pairwise-coupling layer, DeepROCK jointly controls the false discovery rate (FDR) and maximizes statistical power. In addition, we identify a challenge in correctly controlling FDR using off-the-shelf feature interaction importance measures. DeepROCK overcomes this challenge by proposing a calibration procedure applied to existing interaction importance measures to make the FDR under control at a target level. Finally, we validate the effectiveness of DeepROCK through extensive experiments on simulated and real datasets.

Winston Chen, Yifan Jiang, William Stafford Noble et al.

Machine learning (ML) models are powerful tools for detecting complex patterns within data, yet their "black box" nature limits their interpretability, hindering their use in critical domains like healthcare and finance. To address this challenge, interpretable ML methods have been developed to explain how features influence model predictions. However, these methods often focus on univariate feature importance, overlooking the complex interactions between features that ML models are capable of capturing. Recognizing this limitation, recent efforts have aimed to extend these methods to discover feature interactions, but existing approaches struggle with robustness and error control, especially under data perturbations. In this study, we introduce Diamond, a novel method for trustworthy feature interaction discovery. Diamond uniquely integrates the model-X knockoffs framework to control the false discovery rate (FDR), ensuring that the proportion of falsely discovered interactions remains low. A key innovation in Diamond is its non-additivity distillation procedure, which refines existing interaction importance measures to distill non-additive interaction effects, ensuring that FDR control is maintained. This approach addresses the limitations of off-the-shelf interaction measures, which, when used naively, can lead to inaccurate discoveries. Diamond's applicability spans a wide range of ML models, including deep neural networks, transformer models, tree-based models, and factorization-based models. Our empirical evaluations on both simulated and real datasets across various biomedical studies demonstrate Diamond's utility in enabling more reliable data-driven scientific discoveries. This method represents a significant step forward in the deployment of ML models for scientific innovation and hypothesis generation.

Jacob Schreiber, Jeffrey Bilmes, William Stafford Noble

We present apricot, an open source Python package for selecting representative subsets from large data sets using submodular optimization. The package implements an efficient greedy selection algorithm that offers strong theoretical guarantees on the quality of the selected set. Two submodular set functions are implemented in apricot: facility location, which is broadly applicable but requires memory quadratic in the number of examples in the data set, and a feature-based function that is less broadly applicable but can scale to millions of examples. Apricot is extremely efficient, using both algorithmic speedups such as the lazy greedy algorithm and code optimizers such as numba. We demonstrate the use of subset selection by training machine learning models to comparable accuracy using either the full data set or a representative subset thereof. This paper presents an explanation of submodular selection, an overview of the features in apricot, and an application to several data sets. The code and tutorial Jupyter notebooks are available at https://github.com/jmschrei/apricot

Yang Lu, Wenbo Guo, Xinyu Xing et al.

Saliency methods can make deep neural network predictions more interpretable by identifying a set of critical features in an input sample, such as pixels that contribute most strongly to a prediction made by an image classifier. Unfortunately, recent evidence suggests that many saliency methods poorly perform, especially in situations where gradients are saturated, inputs contain adversarial perturbations, or predictions rely upon inter-feature dependence. To address these issues, we propose a framework that improves the robustness of saliency methods by following a two-step procedure. First, we introduce a perturbation mechanism that subtly varies the input sample without changing its intermediate representations. Using this approach, we can gather a corpus of perturbed data samples while ensuring that the perturbed and original input samples follow the same distribution. Second, we compute saliency maps for the perturbed samples and propose a new method to aggregate saliency maps. With this design, we offset the gradient saturation influence upon interpretation. From a theoretical perspective, we show the aggregated saliency map could not only capture inter-feature dependence but, more importantly, robustify interpretation against previously described adversarial perturbation methods. Following our theoretical analysis, we present experimental results suggesting that, both qualitatively and quantitatively, our saliency method outperforms existing methods.

Yang Young Lu, Yingying Fan, Jinchi Lv et al.

Deep learning has become increasingly popular in both supervised and unsupervised machine learning thanks to its outstanding empirical performance. However, because of their intrinsic complexity, most deep learning methods are largely treated as black box tools with little interpretability. Even though recent attempts have been made to facilitate the interpretability of deep neural networks (DNNs), existing methods are susceptible to noise and lack of robustness. Therefore, scientists are justifiably cautious about the reproducibility of the discoveries, which is often related to the interpretability of the underlying statistical models. In this paper, we describe a method to increase the interpretability and reproducibility of DNNs by incorporating the idea of feature selection with controlled error rate. By designing a new DNN architecture and integrating it with the recently proposed knockoffs framework, we perform feature selection with a controlled error rate, while maintaining high power. This new method, DeepPINK (Deep feature selection using Paired-Input Nonlinear Knockoffs), is applied to both simulated and real data sets to demonstrate its empirical utility.