ADAPTIVE ROBUST EVIDENTIAL OPTIMIZATION FOR OPEN SET DETECTION FROM IMBALANCED DATA

Abstract

Open set detection (OSD) aims at identifying data samples of an unknown class (i.e., open set) from those of known classes (i.e., closed set) based on a model trained from closed set samples. However, a closed set may involve a highly imbalanced class distribution. Accurately differentiating open set samples and those from a minority class in the closed set poses a fundamental challenge as the model may be equally uncertain when recognizing samples from the minority class. In this paper, we propose Adaptive Robust Evidential Optimization (AREO) that offers a principled way to quantify sample uncertainty through evidential learning while optimally balancing the model training over all classes in the closed set through adaptive distributively robust optimization (DRO). To avoid the model to primarily focus on the most difficult samples by following the standard DRO, adaptive DRO training is performed, which is governed by a novel multi-scheduler learning mechanism to ensure an optimal model training behavior that gives sufficient attention to the difficult samples and the minority class while capable of learning common patterns from the majority classes. Our experimental results on multiple real-world datasets demonstrate that the proposed model outputs uncertainty scores that can clearly separate samples from closed and open sets, respectively, and the detection results outperform the competitive baselines.

1. INTRODUCTION

In many practical scenarios (e.g., drug discovery, anomaly detection etc.), it is likely to encounter unknown samples and it is desirable that the model can properly detect these samples as unknown. Various approaches have been proposed to tackle the unknown sample detection problem (Bendale & Boult, 2016; Sun et al., 2020) , using techniques such as Weibull-Calibration SVM (W-SVM) (Scheirer et al., 2013 ), reconstruction error (Zhang & Patel, 2017 ), nearest neighbor (Júnior et al., 2016) , and quasi-linear function (Cevikalp & Yavuz, 2017 ). As a representative example, the Openmax framework removes softmax from the last layer of a neural network and includes an additional layer to produce the probability of a sample being unknown. This essentially redistributes the probability mass to (K + 1) classes (with unknown being a new class). Multiple efforts follow this direction (Sun et al., 2020; Neal et al., 2018) . While this technique is viable to detect open-set samples, the additional layer is included during the testing phase. As a result, the training still follows the closed set assumption. Recent advances in uncertainty quantification provide a more systematic way to break the closed set limitation by explicitly modeling the uncertainty mass that corresponds to the unknown class. One representative work is the evidential deep learning (EDL) model (Sensoy et al., 2018) , which treats the predicted multi-class probability as a multinomial opinion according to subjective logic (Jøsang, 2016) . Similar to EDL, Prior Networks (PNs) (Malinin & Gales, 2018) explicitly considers the distributional uncertainty that quantifies the distributional mismatch (Malinin & Gales, 2018) . The Posterior Networks further improves PNs by leveraging normalizing flows for density estimation in the latent space to predict a posterior distribution, which can be used to identify out-of-distribution (OOD) samples from in-distribution ones (Charpentier et al., 2020) . Despite the promising progress in OSD that focuses on differentiating samples from the closed and open sets, respectively, limited attention has been devoted to the situation where the closed set involves highly imbalanced classes, which may be quite common in many practical settings. For

