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[2410.07003] Mirror Bridges Between Probability Measures
Summary
The paper introduces a novel model called mirror bridges for conditional resampling from probability measures, addressing challenges in generating samples from complex distributions.
Why It Matters
This research is significant as it tackles a fundamental issue in machine learning and statistics: efficiently sampling from difficult-to-reach probability measures. The proposed method simplifies existing approaches and enhances control over sample variation, which can improve various applications in data science and AI.
Key Takeaways
- Introduces the mirror bridge model for conditional resampling.
- Solves the Schrödinger bridge problem to generate new samples.
- Offers significant algorithmic simplifications over existing methods.
- Provides control over in-distribution variations of samples.
- Demonstrates empirical benefits across multiple application domains.
Computer Science > Machine Learning arXiv:2410.07003 (cs) [Submitted on 9 Oct 2024 (v1), last revised 21 Feb 2026 (this version, v3)] Title:Mirror Bridges Between Probability Measures Authors:Leticia Mattos Da Silva, Silvia Sellán, Francisco Vargas, Justin Solomon View a PDF of the paper titled Mirror Bridges Between Probability Measures, by Leticia Mattos Da Silva and 3 other authors View PDF HTML (experimental) Abstract:Resampling from a target measure whose density is unknown is a fundamental problem in mathematical statistics and machine learning. A setting that dominates the machine learning literature consists of learning a map from an easy-to-sample prior, such as the Gaussian distribution, to a target measure. Under this model, samples from the prior are pushed forward to generate a new sample on the target measure, which is often difficult to sample from directly. A related problem of particular interest is that of generating a new sample proximate to or otherwise conditioned on a given input sample. In this paper, we propose a new model called the mirror bridge to solve this problem of conditional resampling. Our key observation is that solving the Schrödinger bridge problem between a distribution and itself provides a natural way to produce new samples, giving in-distribution variations of an input data point. We demonstrate how to efficiently estimate the solution of this largely overlooked version of the Schrödinger bridge problem. We show that our proposed me...