Quantile-based Maximum Likelihood Training for Outlier Detection

TL;DR

This work tackles the challenge of outlier detection in open-set image classification by learning the inlier feature distribution with a quantile-based maximum likelihood objective applied to a normalizing-flow density model. It operates on features extracted from a pre-trained discriminative backbone and performs inference via log-likelihood thresholding to separate inliers from outliers, without requiring explicit outlier data during training. QuantOD demonstrates strong performance against unsupervised baselines and competitive results with self-supervised approaches on CIFAR-10/100, using a Glow-based density estimator and a quantile loss that emphasizes boundary-inlier samples. The approach reduces dependence on well-sampled negative data, offering practical benefits for safety-critical domains such as medical diagnostics and remote sensing, while maintaining efficient runtime suitable for real-time deployment.

Abstract

Discriminative learning effectively predicts true object class for image classification. However, it often results in false positives for outliers, posing critical concerns in applications like autonomous driving and video surveillance systems. Previous attempts to address this challenge involved training image classifiers through contrastive learning using actual outlier data or synthesizing outliers for self-supervised learning. Furthermore, unsupervised generative modeling of inliers in pixel space has shown limited success for outlier detection. In this work, we introduce a quantile-based maximum likelihood objective for learning the inlier distribution to improve the outlier separation during inference. Our approach fits a normalizing flow to pre-trained discriminative features and detects the outliers according to the evaluated log-likelihood. The experimental evaluation demonstrates the effectiveness of our method as it surpasses the performance of the state-of-the-art unsupervised methods for outlier detection. The results are also competitive compared with a recent self-supervised approach for outlier detection. Our work allows to reduce dependency on well-sampled negative training data, which is especially important for domains like medical diagnostics or remote sensing.

Figures (4)

• Figure 1: Overview of the QuantOD framework during two-stage training and single-stage inference. During discriminative training, the end-to-end image classification model including the fully-connected (FC) head is trained with standard cross-entropy loss $\mathcal{L}_{cls}$. In the generative training stage, the inlier features $r$ are extracted from the pre-trained classification model and used to train the normalizing flow model with the negative log-likelihood loss $\mathcal{L}_{qNLL}$. Note that the parameters of the classification backbone network are frozen during generative training. During inference, a test image $x'$ is labeled as an outlier if its likelihood score obtained from the flow model is less than a pre-defined likelihood threshold $\tau$.
• Figure 2: Validation on varying $q$ value in $\mathcal{L}_{qNLL}$ loss.
• Figure 3: Validation of mean vs $q = 0.05$ at each training epoch. The results are over iSUN as the outlier dataset.
• Figure 4: Comparison of QuantOD with approaches that perform class-conditional generative modeling of inlier features on both CIFAR-10 and CIFAR-100 as inliers. The results are averaged over the six outlier datasets.