An official website of the United States government
Abstract High-fidelity simulators that connect theoretical models with observations are indispensable tools in many sciences. If the likelihood is known, inference can proceed using standard techniques. However, when the likelihood is intractable or unknown, a simulator makes it possible to infer the parameters of a theoretical model directly from real and simulated observations when coupled with machine learning. We introduce an extension of the recently proposed likelihood-free frequentist inference (LF2I) approach that makes it possible to construct confidence sets with thep-value function and to use the same function to check the coverage explicitly at any given parameter point. LikeLF2I, this extension yields provably valid confidence sets in parameter inference problems for which a high-fidelity simulator is available. The utility of our algorithm is illustrated by applying it to three pedagogically interesting examples: the first is from cosmology, the second from high-energy physics and astronomy, both with tractable likelihoods, while the third, with an intractable likelihood, is from epidemiology33Code to reproduce all of our results is available onhttps://github.com/AliAlkadhim/ALFFI..
more »
« less
Constraining effective field theories with machine learning
An important part of the Large Hadron Collider (LHC) legacy will be precise limits on indirect effects of new physics, framed for instance in terms of an effective field theory. These measurements often involve many theory parameters and observables, which makes them challenging for traditional analysis methods. We discuss the underlying problem of “likelihood-free” inference and present powerful new analysis techniques that combine physics insights, statistical methods, and the power of machine learning. We have developed MadMiner, a new Python package that makes it straightforward to apply these techniques. In example LHC problems we show that the new approach lets us put stronger constraints on theory parameters than established methods, demonstrating its potential to improve the new physics reach of the LHC legacy measurements. While we present techniques optimized for particle physics, the likelihood-free inference formulation is much more general, and these ideas are part of a broader movement that is changing scientific inference in fields as diverse as cosmology, genetics, and epidemiology.
more »
« less
- Award ID(s):
- 1836650
- PAR ID:
- 10256982
- Editor(s):
- Doglioni, C.; Kim, D.; Stewart, G.A.; Silvestris, L.; Jackson, P.; Kamleh, W.
- Date Published:
- Journal Name:
- EPJ Web of Conferences
- Volume:
- 245
- ISSN:
- 2100-014X
- Page Range / eLocation ID:
- 06026
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Analysis of phylogenetic trees has become an essential tool in epidemiology. Likelihood-based methods fit models to phylogenies to draw inferences about the phylodynamics and history of viral transmission. However, these methods are often computationally expensive, which limits the complexity and realism of phylodynamic models and makes them ill-suited for informing policy decisions in real-time during rapidly developing outbreaks. Likelihood-free methods using deep learning are pushing the boundaries of inference beyond these constraints. In this paper, we extend, compare, and contrast a recently developed deep learning method for likelihood-free inference from trees. We trained multiple deep neural networks using phylogenies from simulated outbreaks that spread among 5 locations and found they achieve close to the same levels of accuracy as Bayesian inference under the true simulation model. We compared robustness to model misspecification of a trained neural network to that of a Bayesian method. We found that both models had comparable performance, converging on similar biases. We also implemented a method of uncertainty quantification called conformalized quantile regression that we demonstrate has similar patterns of sensitivity to model misspecification as Bayesian highest posterior density (HPD) and greatly overlap with HPDs, but have lower precision (more conservative). Finally, we trained and tested a neural network against phylogeographic data from a recent study of the SARS-Cov-2 pandemic in Europe and obtained similar estimates of region-specific epidemiological parameters and the location of the common ancestor in Europe. Along with being as accurate and robust as likelihood-based methods, our trained neural networks are on average over 3 orders of magnitude faster after training. Our results support the notion that neural networks can be trained with simulated data to accurately mimic the good and bad statistical properties of the likelihood functions of generative phylogenetic models.more » « less
-
Abernethy, Jacob; Agarwal, Shivani (Ed.)We study a variant of the sparse PCA (principal component analysis) problem in the “hard” regime, where the inference task is possible yet no polynomial-time algorithm is known to exist. Prior work, based on the low-degree likelihood ratio, has conjectured a precise expression for the best possible (sub-exponential) runtime throughout the hard regime. Following instead a statistical physics inspired point of view, we show bounds on the depth of free energy wells for various Gibbs measures naturally associated to the problem. These free energy wells imply hitting time lower bounds that corroborate the low-degree conjecture: we show that a class of natural MCMC (Markov chain Monte Carlo) methods (with worst-case initialization) cannot solve sparse PCA with less than the conjectured runtime. These lower bounds apply to a wide range of values for two tuning parameters: temperature and sparsity misparametrization. Finally, we prove that the Overlap Gap Property (OGP), a structural property that implies failure of certain local search algorithms, holds in a significant part of the hard regime.more » « less
-
A<sc>bstract</sc> We develop the idea that the unprecedented precision in Standard Model (SM) measurements, with further improvement at the HL-LHC, enables new searches for physics Beyond the Standard Model (BSM). As an illustration, we demonstrate that the measured kinematic distributions of theℓ+ Image missing<#comment/>final state not only determine the mass of theWboson, but are also sensitive to light new physics. Such a search for new physics thus requires asimultaneousfit to the BSM and SM parameters, “unifying” searches and measurements at the LHC and Tevatron. In this paper, we complete the program initiated in our earlier work [1]. In particular, we analyze (i) novel decay modes of theWboson with a neutrinophilic invisible scalar or with a heavy neutrino; (ii) modified production ofWbosons, namely, associated with a hadrophilic invisibleZ′ gauge boson; and (iii) scenarios without an on-shellWboson, such as slepton-sneutrino production in the Minimal Supersymmetric Standard Model (MSSM). Here, we complement our previous MSSM analysis in [1] by considering a different kinematic region. Our results highlight that new physics can still be directly discovered at the LHC, including light new physics, via SM precision measurements. Furthermore, we illustrate that such BSM signals are subtle, yet potentially large enough to affect the precision measurements of SM parameters themselves, such as theWboson mass.more » « less
-
This review provides a conceptual and technical survey of methods for parameter estimation of gravitational-wave signals in ground-based interferometers such as Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo. We introduce the framework of Bayesian inference and provide an overview of models for the generation and detection of gravitational waves from compact binary mergers, focusing on the essential features that are observable in the signals. Within the traditional likelihood-based paradigm, we describe various approaches for enhancing the efficiency and robustness of parameter inference. This includes techniques for accelerating likelihood evaluations, such as heterodyne/relative binning, reduced-order quadrature, multibanding, and interpolation. We also cover methods to simplify the analysis to improve convergence, via reparameterization, importance sampling, and marginalization. We end with a discussion of recent developments in the application of likelihood-free (simulation-based) inference methods to gravitational-wave data analysis.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1051/epjconf/202024506026
