No Pairs Left Behind: Improving Metric Learning with Regularized Triplet Objective

We propose a novel formulation of the triplet objective function that improves metric learning without additional sample mining or overhead costs. Our approach aims to explicitly regularize the distance between the positive and negative samples in a triplet with respect to the anchor-negative distance. As an initial validation, we show that our method (called No Pairs Left Behind [NPLB]) improves upon the traditional and current state-of-the-art triplet objective formulations on standard benchmark datasets. To show the effectiveness and potentials of NPLB on real-world complex data, we evaluate our approach on a large-scale healthcare dataset (UK Biobank), demonstrating that the embeddings learned by our model significantly outperform all other current representations on tested downstream tasks. Additionally, we provide a new model-agnostic single-time health risk definition that, when used in tandem with the learned representations, achieves the most accurate prediction of subjects' future health complications. Our results indicate that NPLB is a simple, yet effective framework for improving existing deep metric learning models, showcasing the potential implications of metric learning in more complex applications, especially in the biological and healthcare domains. Metric learning is the task of encoding similarity-based embeddings where similar samples are mapped closer in space and dissimilar ones afar (Xing et al., 2002; Wang et al., 2019; Roth et al., 2020). Deep metric learning (DML) has shown success in many domains, including computer vision (Hermans et al., 2017; Vinyals et al., 2016; Wang et al., 2018b) and natural language processing (Reimers & Gurevych, 2019; Mueller & Thyagarajan, 2016; Benajiba et al., 2019). Many DML models utilize paired samples to learn useful embeddings based on distance comparisons. The most common architectures among these techniques are the Siamese (Bromley et al., 1993) and triplet networks (Hoffer & Ailon, 2015). The main components of these models are the: (1) Strategies for constructing training tuples and (2) objectives that the model must minimize. Though many studies have focused on improving sampling strategies (Wu et al., 2017; Ge, 2018; Shrivastava et al., 2016; Kalantidis et al., 2020; Zhu et al., 2021), modifying the objective function has attracted less attention.