# A Self-Paced Multiple Instance Learning Framework for Weakly Supervised Video Anomaly Detection
## 1 Introduction
The root cause of biased predictions in MIL stems from its training scheme, which involves biased sample selection. A natural idea is to train the classifier to utilize a broader set of video clips rather than only the top-\(k\) segments with the highest anomaly scores. To this end, previous studies [1; 10; 11] have made significant progress toward this goal, often by training classifiers on the most confident or reliable video clips along with their respective pseudo-labels. For example, [PERSON] et al. [1], using the 10-crop method, performed data augmentation on each video segment and then selected the segment with the least variance among the ten scores as the most confident one for training. Similarly, [PERSON] et al. [11] employed Monte Carlo dropout for uncertainty estimation on each video segment, with each segment generating multiple distinct scores via dropout. A specific proportion of segments with the lowest variance is selected, and their corresponding average score is used to train the classifier. In addition, [PERSON] et al. [10] considered the video clips with the most stable historical scores as confident sets, while the remaining clips were categorized as ambiguous sets. They employed supervised learning for clips within the confident sets and unsupervised clustering for clips within the ambiguous sets to facilitate classifier training. Although the aforementioned methods have demonstrated some success, they typically pre-define the proportion or number of reliable and confident samples to be selected, which lacks flexibility in adapting to different datasets, potentially impacting the generalization performance of the classifier. To address this issue, we propose a general self-paced multiple-instance learning (SP-MIL) framework inspired from the idea of self-paced learning [12]. To illustrate our framework, the comparative flow diagram is shown in Figure 1. For the baseline model, when given a sequence of video segments, segment-level features are typically derived via feature extraction and temporal modeling, after which a randomly initialized classifier is used to predict the abnormal score of each segment. Subsequently, the top-\(k\) segments with the highest anomaly scores are selected and aggregated to form video-level features. The classifier is then trained using these video-level features along with corresponding video-level labels to obtain the baseline model. It is worth noting that \(k\) is usually a pre-set fixed value that does not change with the training epochs. This setting makes the trained classifier biased and inaccurate in judging the abnormal degree of other segments in the video. Different from the baseline model, the proposed SP-MIL framework seeks to enhance the classifier's prediction ability by progressively and adaptively incorporating more representative video segments into each epoch of the whole training process, advancing from easy to hard segments through a self-paced learning strategy. Specifically, in each training epoch, the difficulty degree of each video segment is initially calculated based on its current anomaly score and its corresponding pseudo-label. Subsequently, based on the calculated complexity, the easiest video segment at this epoch is selected for training. As time progresses, the number of selected segments gradually increases in a progression from easy to hard. Furthermore, more segments will be adaptively selected and integrated into the classifier's training process. This enables the classifier to progressively incorporate more video segments, thereby enhancing its ability to distinguish between anomalous and normal cases, resulting in unbiased predictions. The main contributions of this paper can be summarized as follows:  
* We propose a general self-paced multiple-instance learning (SP-MIL) framework for the task of WS-VAD, which can significantly enhance the performance of widely used models (e.g., DeepMIL, RTFM, UR-DMU). To the best of our knowledge, this is the first work in which self-paced learning is used for WS-VAD.