Reproduce “Active Timepoint Selection for Learning Measure-Valued Trajectories” on OpenResearch

About this paper

Nicolas Huynh, Mihaela van der Schaar

An active learning framework is introduced to efficiently infer continuous probability paths from sparse observations by integrating Linearized Optimal Transport, Multi-Output Gaussian Processes, and intrinsic time-warping. This method demonstrates enhanced reconstruction accuracy for evolving probability distributions, especially in non-stationary regimes and with limited data, across synthetic and real-world biological and economic datasets.

Key insights

• Linearizing the Wasserstein space via LOT allows the application of standard regression techniques (like GPs) to probabilistically model measure-valued trajectories.
• Quantifying epistemic uncertainty over the latent space of probability distributions enables an effective active learning policy to strategically select new, informative measurement time points.
• Incorporating intrinsic time-warping addresses non-stationary dynamics, allowing the model to adapt its effective length scale to capture varying rates of distributional change.

Summary by alphaXiv.