[Paper Review] Statistical Testing for Efficient Out of Distribution Detection in Deep Neural Networks.

Matan Haroush, Tzivel Frostig+2 more|arXiv (Cornell University)|Feb 25, 2021

Adversarial Robustness in Machine Learning36 references4 citations

TL;DR

This paper proposes a statistical hypothesis testing framework for Out-of-Distribution (OOD) detection in deep neural networks, treating OOD detection as a formal statistical test to guarantee a controlled false positive rate. By leveraging low-order statistics of network activations, the method achieves state-of-the-art OOD detection performance without retraining, at minimal computational cost.

ABSTRACT

Commonly, Deep Neural Networks (DNNs) generalize well on samples drawn from a distribution similar to that of the training set. However, DNNs' predictions are brittle and unreliable when the test samples are drawn from a dissimilar distribution. This presents a major concern for deployment in real-world applications, where such behavior may come at a great cost -- as in the case of autonomous vehicles or healthcare applications. This paper frames the Out Of Distribution (OOD) detection problem in DNN as a statistical hypothesis testing problem. Unlike previous OOD detection heuristics, our framework is guaranteed to maintain the false positive rate (detecting OOD as in-distribution) for test data. We build on this framework to suggest a novel OOD procedure based on low-order statistics. Our method achieves comparable or better than state-of-the-art results on well-accepted OOD benchmarks without retraining the network parameters -- and at a fraction of the computational cost.

Motivation & Objective

• To address the critical challenge of unreliable DNN predictions on out-of-distribution (OOD) data, especially in safety-critical applications like autonomous vehicles and healthcare.
• To overcome the limitations of heuristic-based OOD detection methods that lack statistical guarantees on false positive rates.
• To develop a method that maintains a controlled false positive rate while achieving high OOD detection performance.
• To design a computationally efficient OOD detection procedure that does not require retraining the network.

Proposed method

• The method frames OOD detection as a statistical hypothesis test, where the null hypothesis assumes the input is in-distribution.
• It uses low-order statistics—specifically, the mean and variance of final-layer features—as test statistics for the hypothesis test.
• The test statistic is compared against a threshold derived from the empirical distribution of in-distribution samples during a calibration phase.
• The method leverages the central limit theorem to approximate the sampling distribution of the test statistic under the null hypothesis.
• A significance level is set in advance to control the false positive rate, ensuring statistical reliability.
• The approach operates without fine-tuning or retraining the DNN, relying only on inference-time statistics from the pre-trained network.

Experimental results

Research questions

• RQ1 Can OOD detection be formalized as a statistical hypothesis test to guarantee a controlled false positive rate?
• RQ2 Can low-order statistics of deep network activations provide effective and efficient OOD detection without retraining?
• RQ3 How does the proposed method compare to state-of-the-art OOD detection techniques in terms of performance and computational cost?
• RQ4 Does the method maintain robustness across diverse data distributions and network architectures?

Key findings

• The proposed method achieves comparable or better OOD detection performance than state-of-the-art methods on standard benchmarks such as CIFAR-10 vs. SVHN and Tiny ImageNet.
• The method maintains a guaranteed false positive rate, as controlled by the significance level, across all evaluated datasets and network architectures.
• The computational cost of the method is significantly lower than existing approaches, requiring only inference-time statistics from the pre-trained model.
• The method does not require retraining or fine-tuning of the DNN, preserving the original model's performance and deployment efficiency.