# A Self-Paced Multiple Instance Learning Framework for Weakly Supervised Video Anomaly Detection
## 1 Introduction  
As monitoring systems become more widespread, timely and accurate detection of abnormal behaviors or emergencies in surveillance videos is crucial for building smart cities and maintaining public safety. An abnormal event in a video typically refers to an unusual appearance or motion property, or to a normal appearance or motion property occurring at an anomalous time or in an anomalous space. The task of video anomaly detection involves identifying temporal or spatial anomalies within the video. In general, based on the granularity of available labels, the video anomaly detection methods can be typically classified into supervised learning [1], unsupervised learning [2, 3], and weakly supervised learning [4, 5]. Since manual frame-by-frame labeling of abnormal events in videos is extremely labor-intensive, supervised learning-based video anomaly detection methods are prohibitively costly. In contrast, unsupervised video anomaly detection methods rely on the similarities among samples to perform clustering, or modeling the distribution of normal samples. During testing, video frames that deviate significantly from the learned normal pattern are identified as anomalies. However, due to the absence of prior knowledge of anomalies, the effectiveness of unsupervised methods is generally limited [6]. Consequently, this paper primarily focuses on weak supervision-based videoanomaly detection methods, which rely solely on video-level labels (normal and abnormal) during the training process. The WS-VAD task was initially proposed by [PERSON] et al. [7] and formulated as a multi-instance learning (MIL) problem. In particular, normal and abnormal videos are considered negative and positive bags, respectively, and a series of non-overlapping video clips of equal length are treated as instances within each bag. This refers to a scenario in which only video-level labels are provided during training, while frame-by-frame anomaly detection must be performed during testing. If at least one anomalous instance is detected in a video, the video is labeled anomalous (i.e., a positive bag); otherwise, it is classified as normal (i.e., a negative bag). The objective of the WS-VAD task is to train an instance-level anomaly classifier using only video-level labels. During training, the most representative instances from both positive and negative bags are initially identified, and these selected instances, along with their corresponding bag-level labels, are then used to train the anomaly detection classifier. The training process forcibly reduces the predicted abnormal score for each selected representative segment in a normal video, while increasing the score of one or more selected segments with the highest abnormal scores in an abnormal video. During testing, the classifier predicts the anomaly score for each video segment, with all frames within a segment being assigned the same score, thereby enabling frame-by-frame anomaly detection. Based on this MIL framework, numerous studies have been conducted, leading to significant advancements [8; 9]. However, as a result of this training approach, the classifier is typically sensitive only to the most representative segments of both normal and abnormal videos, while neglecting other segments within these videos. Consequently, classifiers trained in this manner often yield biased results [10], tending to recognize only the most conspicuous anomalies, while subtle anomalies are frequently overlooked. For example, the classifier was able to identify anomalies when a car was vandalized but missed subtle anomalous activity by the person prior to the vandalism. The moment the car is destroyed can be seen as an easy anomaly, while the subtle abnormal activity by a person prior to the destruction can be seen as a difficult anomaly. A biased classifier may generally recognize only the easy anomalies while failing to recognize the difficult ones. In contrast, an unbiased classifier should be able to identify both easy and difficult anomalies in most cases.