# Joint trajectory and network inference via reference fitting

arXiv: https://arxiv.org/abs/2409.06879 · HTML: https://mlsanity.com/paper/2409.06879/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 49 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 8 of 8)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Multi-marginal Schr"odinger Bridges with Iterative Reference Refinement](https://mlsanity.com/paper/2408.06277/) (2024)
- [Inverse optimal transport](https://mlsanity.com/paper/1905.03950/) (2019)
- [Ground Metric Learning on Graphs](https://mlsanity.com/paper/1911.03117/) (2019)
- [Graphical continuous Lyapunov models](https://mlsanity.com/paper/2005.10483/) (2020)
- [Stochastic force inference via density estimation](https://mlsanity.com/paper/2310.02366/) (2023)
- [Learning Directed Graphical Models from Gaussian Data](https://mlsanity.com/paper/1906.08050/) (2019)

## Built on by (most cited first, 6 of 6)

- [Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots](https://mlsanity.com/paper/2410.22729/) (2024)
- [Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-seq Data Analysis](https://mlsanity.com/paper/2503.11347/) (2025)
- [A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots](https://mlsanity.com/paper/2605.08550/) (2026)
- [Gradient-flow SDEs have unique transient population dynamics](https://mlsanity.com/paper/2505.21770/) (2025)
- [Learning non-equilibrium diffusions with Schr"odinger bridges: from exactly solvable to simulation-free](https://mlsanity.com/paper/2505.16644/) (2025)
- [Simulation-free Structure Learning for Stochastic Population Dynamics](https://mlsanity.com/paper/2510.16656/) (2025)

## Abstract (arXiv)

Network inference, the task of reconstructing interactions in a complex system from experimental observables, is a central yet extremely challenging problem in systems biology. While much progress has been made in the last two decades, network inference remains an open problem. For systems observed at steady state, limited insights are available since temporal information is unavailable and thus causal information is lost. Two common avenues for gaining causal insights into system behaviour are to leverage temporal dynamics in the form of trajectories, and to apply interventions such as knock-out perturbations. We propose an approach for leveraging both dynamical and perturbational single cell data to jointly learn cellular trajectories and power network inference. Our approach is motivated by min-entropy estimation for stochastic dynamics and can infer directed and signed networks from time-stamped single cell snapshots.