Machine Learning for Likelihood-Free Inference, Lecture notes of Particle Physics

Download Machine Learning for Likelihood-Free Inference and more Lecture notes Particle Physics in PDF only on Docsity!

Machine Learning for

Likelihood-Free Inference

Luc Le Pottier

University of Michigan, CERN ATLAS Group

J. Brehmer et al. ; adapted by APS/Alan Stonebraker

Outline

• Project Intro
• Project Work
• Future Work
• Project Lessons
• Cultural Experiences

Project Intro

• Likelihood function allows for EFT parameter calculation  Describes the compatibility of data with model parameters  must be approximated: difficult to do precisely in high-dim parameter/observable spaces
• Current methods:  Matrix Element Method, Optimal observables, naïve Parameter scans, Neural Network classification  All trained on event/parameters sample pairs – no extra use of particle physics structures
• New method: training deep neural networks to approximate the likelihood function, using the joint likelihood ratio and joint score in loss functions. ALICE Method Cross-Entropy Estimator-based loss function

Finished Work

• Using the MadMiner machine learning toolkit (1, 2, 3) , with an implementation of the ALICE algorithm, claimed to be one of the more ‘sample-efficient’ algorithms (good for testing and debugging). (2)
• Problem Introduction (January)  Wrote a python module for testing ML algorithms on arbitrary-dimensional ‘toy’ processes  Validated precision results of various algorithms using the tractable likelihoods of these toy processes  Made clear that ALICES is a good algorithm to prototype new processes with w

Slight Problems

• ttH CP parity parameterization is limited to the range [0, 1], with simulation benchmarks at the boundary points
• Results in strange predicted likelihood functions / 17
• Assuming a gaussian likelihood function, extrapolated variances of log-likelihood are terrible
• Determined after hundreds of different deep neural net configurations and sample augmentations that a new statistical approach is needed
• Will likely receive attention from stats PHD in the near future

Finished Work

• Authored a python module and linux CLI utility
• Provides a wrapper for

 Complex environment setup for

madminer/madgraph

 Process backend setup

 Generation and storage of a wide array of

samples, models, and evaluations

• Allows for near-instant prototyping of the madminer framework with arbitrarily complex processes

 Helps a lot with finding a suitable set of ML

parameters for a given process

/ 17

Progress thus far / 17 Good sample augmentation Poor sample augmentation

Future Work

• Update module to work with recently-released madminer version
• Finish (majority) of documentation
• Add 4-5 more ‘sample processes’ to demonstrate applicability of the program to arbitrary processes with minimal effort
• Perform and write up a short study on how to quickly find optimal ML parameters for a new problem (lots of research wrt this, but not much written down) Luckily, I have until May 10 th to do these things! / 17

Vallee blanche in Chamonix Culture! Zz in cully (^) Hiking in the jura

Questions?