# Continuous-Time Learning of Probability Distributions: A Case Study in a Digital Trial of Young Children with Type 1 Diabetes

arXiv: https://arxiv.org/abs/2603.24427 · HTML: https://mlsanity.com/paper/2603.24427/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 57 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Builds on (most cited first, 3 of 3)

- [Large sample analysis of the median heuristic](https://mlsanity.com/paper/1707.07269/) (2017)
- [Uncertainty quantification in metric spaces](https://mlsanity.com/paper/2405.05110/) (2024)
- [Beyond fixed thresholds: optimizing summaries of wearable device data via piecewise linearization of quantile functions](https://mlsanity.com/paper/2501.11777/) (2025)

## Built on by (most cited first, 1 of 1)

- [Gaussian mixture models in Hilbert spaces via kernel methods](https://mlsanity.com/paper/2605.05996/) (2026)

## Abstract (arXiv)

Understanding how biomarker distributions evolve over time is a central challenge in digital health and chronic disease monitoring. In diabetes, changes in the distribution of glucose measurements can reveal patterns of disease progression and treatment response that conventional summary measures miss. Motivated by a 26-week clinical trial comparing the closed-loop insulin delivery system t:slim X2 with standard therapy in children with type 1 diabetes, we propose a probabilistic framework to model the continuous-time evolution of time-indexed distributions using continuous glucose monitoring data (CGM) collected every five minutes. We represent the glucose distribution as a Gaussian mixture, with time-varying mixture weights governed by a neural ODE. We estimate the model parameter using a distribution-matching criterion based on the maximum mean discrepancy. The resulting framework is interpretable, computationally efficient, and sensitive to subtle temporal distributional changes. Applied to CGM trial data, the method detects treatment-related improvements in glucose dynamics that are difficult to capture with traditional analytical approaches.