Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-dimensional Data-driven Priors for Inverse Problems
Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of machine learning, the use of data-driven population-level distr...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2025-01-01
|
| Series: | The Astrophysical Journal |
| Subjects: | |
| Online Access: | https://doi.org/10.3847/1538-4357/ad9b92 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825208900278812672 |
|---|---|
| author | Gabriel Missael Barco Alexandre Adam Connor Stone Yashar Hezaveh Laurence Perreault-Levasseur |
| author_facet | Gabriel Missael Barco Alexandre Adam Connor Stone Yashar Hezaveh Laurence Perreault-Levasseur |
| author_sort | Gabriel Missael Barco |
| collection | DOAJ |
| description | Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of machine learning, the use of data-driven population-level distributions (encoded, e.g., in a trained deep neural network) as priors is emerging as an appealing alternative to simple parametric priors in a variety of inverse problems. However, in many astrophysical applications it is often difficult or even impossible to acquire independent and identically distributed samples from the underlying data-generating process of interest to train these models. In these cases, corrupted data or a surrogate, e.g., a simulator, is often used to produce training samples, meaning that there is a risk of obtaining misspecified priors. This, in turn, can bias the inferred posteriors in ways that are difficult to quantify, which limits the potential applicability of these models in real-world scenarios. In this work, we propose addressing this issue by iteratively updating the population-level distributions by retraining the model with posterior samples from different sets of observations, and we showcase the potential of this method on the problem of background image reconstruction in strong gravitational lensing when score-based models are used as data-driven priors. We show that, starting from a misspecified prior distribution, the updated distribution becomes progressively closer to the underlying population-level distribution, and the resulting posterior samples exhibit reduced bias after several updates. |
| format | Article |
| id | doaj-art-e4ac00f6fcbb4820be794531682bc350 |
| institution | Kabale University |
| issn | 1538-4357 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | The Astrophysical Journal |
| spelling | doaj-art-e4ac00f6fcbb4820be794531682bc3502025-02-06T17:46:14ZengIOP PublishingThe Astrophysical Journal1538-43572025-01-01980110810.3847/1538-4357/ad9b92Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-dimensional Data-driven Priors for Inverse ProblemsGabriel Missael Barco0https://orcid.org/0009-0008-5839-5937Alexandre Adam1https://orcid.org/0000-0001-8806-7936Connor Stone2https://orcid.org/0000-0002-9086-6398Yashar Hezaveh3https://orcid.org/0000-0002-8669-5733Laurence Perreault-Levasseur4https://orcid.org/0000-0003-3544-3939Ciela Institute , Montréal, Canada ; [email protected]; Mila—Quebec Artificial Intelligence Institute , Montréal, Canada; Department of Physics , Université de Montréal, Montréal, CanadaCiela Institute , Montréal, Canada ; [email protected]; Mila—Quebec Artificial Intelligence Institute , Montréal, Canada; Department of Physics , Université de Montréal, Montréal, CanadaCiela Institute , Montréal, Canada ; [email protected]; Mila—Quebec Artificial Intelligence Institute , Montréal, Canada; Department of Physics , Université de Montréal, Montréal, CanadaCiela Institute , Montréal, Canada ; [email protected]; Mila—Quebec Artificial Intelligence Institute , Montréal, Canada; Department of Physics , Université de Montréal, Montréal, Canada; Center for Computational Astrophysics , Flatiron Institute, New York, USA; Perimeter Institute for Theoretical Physics , Waterloo, Canada; Trottier Space Institute , McGill University, Montréal, CanadaCiela Institute , Montréal, Canada ; [email protected]; Mila—Quebec Artificial Intelligence Institute , Montréal, Canada; Department of Physics , Université de Montréal, Montréal, Canada; Center for Computational Astrophysics , Flatiron Institute, New York, USA; Perimeter Institute for Theoretical Physics , Waterloo, Canada; Trottier Space Institute , McGill University, Montréal, CanadaBayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of machine learning, the use of data-driven population-level distributions (encoded, e.g., in a trained deep neural network) as priors is emerging as an appealing alternative to simple parametric priors in a variety of inverse problems. However, in many astrophysical applications it is often difficult or even impossible to acquire independent and identically distributed samples from the underlying data-generating process of interest to train these models. In these cases, corrupted data or a surrogate, e.g., a simulator, is often used to produce training samples, meaning that there is a risk of obtaining misspecified priors. This, in turn, can bias the inferred posteriors in ways that are difficult to quantify, which limits the potential applicability of these models in real-world scenarios. In this work, we propose addressing this issue by iteratively updating the population-level distributions by retraining the model with posterior samples from different sets of observations, and we showcase the potential of this method on the problem of background image reconstruction in strong gravitational lensing when score-based models are used as data-driven priors. We show that, starting from a misspecified prior distribution, the updated distribution becomes progressively closer to the underlying population-level distribution, and the resulting posterior samples exhibit reduced bias after several updates.https://doi.org/10.3847/1538-4357/ad9b92Strong gravitational lensingBayesian statisticsHierarchical modelsPrior distributionPosterior distributionSky surveys |
| spellingShingle | Gabriel Missael Barco Alexandre Adam Connor Stone Yashar Hezaveh Laurence Perreault-Levasseur Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-dimensional Data-driven Priors for Inverse Problems The Astrophysical Journal Strong gravitational lensing Bayesian statistics Hierarchical models Prior distribution Posterior distribution Sky surveys |
| title | Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-dimensional Data-driven Priors for Inverse Problems |
| title_full | Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-dimensional Data-driven Priors for Inverse Problems |
| title_fullStr | Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-dimensional Data-driven Priors for Inverse Problems |
| title_full_unstemmed | Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-dimensional Data-driven Priors for Inverse Problems |
| title_short | Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-dimensional Data-driven Priors for Inverse Problems |
| title_sort | tackling the problem of distributional shifts correcting misspecified high dimensional data driven priors for inverse problems |
| topic | Strong gravitational lensing Bayesian statistics Hierarchical models Prior distribution Posterior distribution Sky surveys |
| url | https://doi.org/10.3847/1538-4357/ad9b92 |
| work_keys_str_mv | AT gabrielmissaelbarco tacklingtheproblemofdistributionalshiftscorrectingmisspecifiedhighdimensionaldatadrivenpriorsforinverseproblems AT alexandreadam tacklingtheproblemofdistributionalshiftscorrectingmisspecifiedhighdimensionaldatadrivenpriorsforinverseproblems AT connorstone tacklingtheproblemofdistributionalshiftscorrectingmisspecifiedhighdimensionaldatadrivenpriorsforinverseproblems AT yasharhezaveh tacklingtheproblemofdistributionalshiftscorrectingmisspecifiedhighdimensionaldatadrivenpriorsforinverseproblems AT laurenceperreaultlevasseur tacklingtheproblemofdistributionalshiftscorrectingmisspecifiedhighdimensionaldatadrivenpriorsforinverseproblems |