  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.
