# Regularized Instance Embedding for Deep Multi-Instance Learning
###### Abstract  
In the era of Big Data, multi-instance learning, as a weakly supervised learning framework, has various applications since it is helpful to reduce the cost of the data-labeling process. Due to this weakly supervised setting, learning effective instance representation/embedding is challenging. To address this issue, we propose an instance-embedding regularizer that can boost the performance of both instance- and bag-embedding learning in a unified fashion. Specifically, the crux of the instance-embedding regularizer is to maximize correlation between instance-embedding and underlying instance-label similarities. The embedding-learning framework was implemented using a neural network and optimized in an end-to-end manner using stochastic gradient descent. In experiments, various applications were studied, and the results show that the proposed instance-embedding-regularization method is highly effective, having state-of-the-art performance. multi-instance learning; neural network; weakly supervised learning; cancer classification; text classification +
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Thanks to the good capacity of neural networks, instance embedding can be plugged into a neural network. Recently, the authors of [5] revisited multi-instance neural networks and showed state-of-the-art bag classification performance. In [6], the authors proposed a 3D subconcept layer that was combined with a deep network to perform multi-instance multi-label classification in various domains. In these works, instance probabilities were treated as latent variables and then aggregated into bag probability via a pooling function, e.g., max pooling. Since the bag-level ground truth is given, instance probabilities can be adjusted using back-propagation. Because the max-pooling procedure omits some instance-level information, it is unnecessary to require all instances to have correct labels. As pointed out by [PERSON] et al. [7], in positive bags, some false-negative and false-positive instances barely affect bag classification. However, learning instance embedding relies on instance probabilities. Noisy instance probabilities very likely degrade instance-embedding quality. Inspired by the classical MIL work proposed by [PERSON] et al. [8], in which instances from a bag are treated in a non-independent and identically distributed (i.i.d.) way that exploits relations among instances and a mi-Graph algorithm was proposed to obtain a better MIL performance, we aimed to use instance relations to promote instance-embedding quality. This is different from mi-Graph that directly compares bags without considering instance embedding, as we employed instance embedding as the MIL backbone and further distinguished positive and negative instances in a bag. Our usage of instance relations was to encourage instances from a same class to have higher similarity and instances from different classes to have less similarity, which is similar to the goal of metric learning [9]. In metric learning, the goal is to learn the similarity between a pair of objects/instances rather than classification or regression. As we had instance probabilities as hidden nodes in a neural network, we could use instance probabilities to determine instance classes. In practice, given a pair of instances in a bag or a training batch, the proposed regularizer encourages instances with similar labels to have close embedding; otherwise, their embedding should be dissimilar. In other words, the regularizer maximizes correlations between the embedding- and the label-similarity matrices of instances. In summary, this work emphasizes the importance of instance-embedding learning in MIL. We designed an instance-embedding regularizer for taking instance relations into consideration instead of treating instances as i.i.d. samples. The regularizer was integrated into a single multi-instance neural network and optimized end-to-end.