arXiv:2605.28075v1 Announce Type: new Abstract: Many learning problems require predicting how populations evolve under an unknown transformation. A natural representation for such populations is a probability measure, with point clouds as a key example. In this work, we study the measure-to-measure (M2M) regression problem, in which one seeks to learn a map between probability measures from a finite collection of observed input-output pairs. In contrast to classical regression, where individual samples are transformed independently, M2M regression treats entire distributions as the data points
This research builds on recent advances in transformer architectures and their application to complex data types, extending them to probability measures.
Learning transformations between entire distributions rather than individual samples opens new avenues for modeling complex systems in fields like AI, finance, and climate science.
Traditional regression models primarily handle individual data points; this introduces a method to learn relationships between entire probability distributions, enhancing predictive capabilities for population-level dynamics.
- · AI researchers
- · Data scientists
- · Industries with population-level, dynamic data (e.g., finance, epidemiology)
- · Traditional statistical modeling approaches for complex systems
- · Methods reliant solely on point-to-point transformations
Improved predictive models for systems where aggregate behavior is more critical than individual events.
Development of new AI applications that can forecast and manage population-level shifts across various domains.
Enhanced automation in fields requiring understanding and prediction of dynamic, uncertain population changes, potentially impacting white-collar workflows.
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Read at arXiv cs.LG