Optimal transport (OT) theory describes general principles to define and select, among many possible choices, the most efficient way to map a probability measure onto another. That theory has been mostly used to estimate, given a pair of source and target probability measures , a parameterized map that can efficiently map onto . In many applications, such as predicting cell responses to treatments, the data measures (features of untreated/treated cells) that define optimal transport problems do not arise in isolation but are associated with a context (the treatment). To account for and incorporate that context in OT estimation, we introduce CondOT, an approach to estimate OT maps conditioned on a context variable, using several pairs of measures tagged with a context label . Our goal is to learn a global map which is not only expected to fit all pairs in the dataset , i.e., , but should generalize to produce meaningful maps conditioned on unseen contexts . Our approach harnesses and provides a novel usage for partially input convex neural networks, for which we introduce a robust and efficient initialization strategy inspired by Gaussian approximations. We demonstrate the ability of CondOT to infer the effect of an arbitrary combination of genetic or therapeutic perturbations on single cells, using only observations of the effects of said perturbations separately.
The matching principles behind optimal transport (OT) play an increasingly important role in machine learning, a trend which can be observed when OT is used to disambiguate datasets in applications (e.g. single-cell genomics) or used to improve more complex methods (e.g. balanced attention in transformers or self-supervised learning). To scale to more challenging problems, there is a growing consensus that OT requires solvers that can operate on…
Heart rate variability (HRV) is a practical and noninvasive measure of autonomic nervous system activity, which plays an essential role in cardiovascular health. However, using HRV to assess physiology status is challenging. Even in clinical settings, HRV is sensitive to acute stressors such as physical activity, mental stress, hydration, alcohol, and sleep. Wearable devices provide convenient HRV measurements, but the irregularity of…