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The NFLikelihood: an unsupervised DNNLikelihood from Normalizing Flows
by Humberto Reyes-Gonzalez, Riccardo Torre
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Humberto Reyes-González |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2309.09743v2 (pdf) |
| Code repository: | https://github.com/NF4HEP/NFLikelihoods |
| Data repository: | https://zenodo.org/record/8349144 |
| Date submitted: | 2024-04-10 13:48 |
| Submitted by: | Reyes-González, Humberto |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Experimental, Computational, Phenomenological |
Abstract
We propose the NFLikelihood, an unsupervised version, based on Normalizing Flows, of the DNNLikelihood proposed in Ref.[1]. We show, through realistic examples, how Autoregressive Flows, based on affine and rational quadratic spline bijectors, are able to learn complicated high-dimensional Likelihoods arising in High Energy Physics (HEP) analyses. We focus on a toy LHC analysis example already considered in the literature and on two Effective Field Theory fits of flavor and electroweak observables, whose samples have been obtained throught the HEPFit code. We discuss advantages and disadvantages of the unsupervised approach with respect to the supervised one and discuss possible interplays of the two.
List of changes
- Minor corrections and changes with respect to v1.
-Minor changes to tables.
-Updated results (marginal differences) including uncertainty estimation .
-Added reference to the Soft-clip bijector.
-Clarification about the naming conventions used for each Normalizing Flow architecture.
Current status:
Reports on this Submission
Strengths
- towards ML implementation of LHC likelihoods: very much needed and method looks very promising
- chosen examples are high-dimensional and seem realistic
- much improved presentation compared to v1
Weaknesses
-
Report
The authors have addressed almost all points to my satisfaction. I have only 3 minor comments that can be addressed without showing me again:
- When evaluating the SWD 100 times, are the 2D directions sampled anew in each of these 100 evaluations? Or is the same set of 2D directions used 100 times? Please add this info.
- In order to improve the performance on the not-so-well fitted parameters, the authors write these "be likely fixed after further fine-tunning the hyper-parameters or adding more training points". I suggest adding "or adding more bijectors to the flow" as another option to increase expressivity.
- There is one typo remaining that I had already pointed out: On p7, in section 4.2, "table 3" should be "table 6" in the text.
Requested changes
see report
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Author: Humberto Reyes-González on 2024-05-23 [id 4507]
(in reply to Report 1 on 2024-04-24)We thank again the Referee for their careful reading and constructive suggestions. Below we reply separately to each of their comments.
Referee - When evaluating the SWD 100 times, are the 2D directions sampled anew in each of these 100 evaluations? Or is the same set of 2D directions used 100 times? Please add this info.
Response The 2D directions are randomly drawn each time independently. We clarify this in the manuscript.
Referee - In order to improve the performance on the not-so-well fitted parameters, the authors write these "be likely fixed after further fine-tunning the hyper-parameters or adding more training points". I suggest adding "or adding more bijectors to the flow" as another option to increase expressivity.
Response
Thank you for the suggestion. In previous studies with generic multi-modal distributions, we found that, at least for A-RQS, using more than 2 bijectors didn't make much difference as compared to enlarging the NNs and the number of knots. Of course, is hard to generalise this statement for all possible cases. To keep it general we now write: 'be likely fixed after further fine-tunning the hyper-parameters, increasing the number of trainable parameters or adding more training points.'
Referee - There is one typo remaining that I had already pointed out: On p7, in section 4.2, "table 3" should be "table 6" in the text.
Response Apologies for overlooking this. The typo has been corrected now.