Enhancing Out-of-Distribution Detection with Multitesting-based Layer-wise Feature Fusion

Deploying machine learning in open environments presents the challenge of encountering diverse test inputs that differ significantly from the training data. These out-of-distribution samples may exhibit shifts in local or global features compared to the training distribution. The machine learning (ML) community has responded with a number of methods aimed at distinguishing anomalous inputs from original training data. However, the majority of previous studies have primarily focused on the output layer or penultimate layer of pre-trained deep neural networks. In this paper, we propose a novel framework, Multitesting-based Layer-wise Out-of-Distribution (OOD) Detection (MLOD), to identify distributional shifts in test samples at different levels of features through rigorous multiple testing procedure. Our approach distinguishes itself from existing methods as it does not require modifying the structure or fine-tuning of the pre-trained classifier. Through extensive experiments, we demonstrate that our proposed framework can seamlessly integrate with any existing distance-based inspection method while efficiently utilizing feature extractors of varying depths. Our scheme effectively enhances the performance of out-of-distribution detection when compared to baseline methods. In particular, MLOD-Fisher achieves superior performance in general. When trained using KNN on CIFAR10, MLOD-Fisher significantly lowers the false positive rate (FPR) from 24.09% to 7.47% on average compared to merely utilizing the features of the last layer.

Sketched Ridgeless Linear Regression: The Role of Downsampling

Overparametrization often helps improve the generalization performance. This paper proposes a dual view of overparametrization suggesting that downsampling may also help generalize. Motivated by this dual view, we characterize two out-of-sample prediction risks of the sketched ridgeless least square estimator in the proportional regime $m\asymp n \asymp p$, where $m$ is the sketching size, $n$ the sample size, and $p$ the feature dimensionality. Our results reveal the statistical role of downsampling. Specifically, downsampling does not always hurt the generalization performance, and may actually help improve it in some cases. We identify the optimal sketching sizes that minimize the out-of-sample prediction risks, and find that the optimally sketched estimator has stabler risk curves that eliminates the peaks of those for the full-sample estimator. We then propose a practical procedure to empirically identify the optimal sketching size. Finally, we extend our results to cover central limit theorems and misspecified models. Numerical studies strongly support our theory.