Relative Entropy Estimation in Function Space: Theory and Applications to Trajectory Inference

2026-04-22 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Life Sciences & Biology · Depth: Expert, quick

Summary

A new framework has been developed for estimating the Kullback-Leibler (KL) divergence between probability measures in function space, specifically addressing challenges in Trajectory Inference (TI) from snapshot data. This framework provides a tractable, data-driven estimator scalable to realistic datasets, such as those found in single-cell genomics where destructive measurements prevent direct observation of path-space laws. Validation on a benchmark suite demonstrates that the estimated functional KL accurately matches the analytic KL. When applied to synthetic and real scRNA-seq datasets, this method reveals inconsistencies in current TI evaluation metrics, offering a more coherent comparison of different TI approaches and highlighting discrepancies in inferred dynamics, particularly in data-sparse regions. This functional KL estimator serves as a principled criterion for evaluating trajectory inference under conditions of partial observability.

Key takeaway

For AI Scientists and Research Scientists working on Trajectory Inference, this functional KL divergence framework offers a robust evaluation metric that overcomes limitations of traditional marginal prediction. You should consider integrating this method to coherently compare different TI algorithms, especially when dealing with partially observed or sparse datasets, to ensure more accurate assessment of inferred dynamics and identify potential model discrepancies.

Key insights

A new functional KL divergence estimator provides a principled way to evaluate trajectory inference under partial observability.

Principles

• Path-space laws are non-identifiable from finite marginals.
• Functional KL divergence enables coherent TI method comparison.

Method

The framework estimates Kullback-Leibler divergence between probability measures on function space, yielding a tractable, data-driven estimator scalable to snapshot datasets for trajectory inference.

In practice

• Evaluate trajectory inference methods with functional KL.
• Identify discrepancies in inferred dynamics in sparse data.

Topics

• Relative Entropy Estimation
• Kullback-Leibler Divergence
• Function Space
• Trajectory Inference
• Single-cell RNA Sequencing (scRNA-seq)

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.