Summary of Efficient Trajectory Inference in Wasserstein Space Using Consecutive Averaging, by Amartya Banerjee et al.
Efficient Trajectory Inference in Wasserstein Space Using Consecutive Averaging
by Amartya Banerjee, Harlin Lee, Nir Sharon, Caroline Moosmüller
First submitted to arxiv on: 30 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA); Optimization and Control (math.OC)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This research proposes innovative methods for reconstructing continuous processes from cross-sectional measurements, a common challenge in fields like computational biology. The authors introduce B-spline approximation and interpolation techniques that utilize consecutive averaging within the Wasserstein space. By combining subdivision schemes with optimal transport-based geodesic, these methods enable trajectory inference at a chosen level of precision and smoothness. They can also handle scenarios where particles divide over time. The study proves linear convergence rates and evaluates performance on cell data featuring bifurcations, merges, and trajectory splitting scenarios like supercells, comparing it to state-of-the-art methods. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about finding a way to reconstruct a continuous process from some measurements that are taken at different times. This is important in fields like biology where we want to understand how cells move or grow over time. The researchers came up with new ways to do this using something called B-splines and the Wasserstein space. Their method can also handle situations where things get smaller or bigger over time. They tested their method on some cell data and showed that it works well. |
Keywords
* Artificial intelligence * Inference * Precision
