Flow-Based Likelihoods for Non-Gaussian Inference

Abstract

We investigate the use of data-driven likelihoods to bypass a key assumption made in many scientific analyses, which is that the true likelihood of the data is Gaussian. In particular, we suggest using the optimization targets of flow-based generative models, a class of models that can capture complex distributions by transforming a simple base distribution through layers of nonlinearities. We call these flow-based likelihoods (FBL). We analyze the accuracy and precision of the reconstructed likelihoods on mock Gaussian data, and show that simply gauging the quality of samples drawn from the trained model is not a sufficient indicator that the true likelihood has been learned. We nevertheless demonstrate that the likelihood can be reconstructed to a precision equal to that of sampling error due to a finite sample size. We then apply FBLs to mock weak lensing convergence power spectra, a cosmological observable that is significantly non-Gaussian (NG). We find that the FBL captures the NG signatures in the data extremely well, while other commonly used data-driven likelihoods, such as Gaussian mixture models and independent component analysis, fail to do so. This suggests that works that have found small posterior shifts in NG data with data-driven likelihoods such as these could be underestimating the impact of non-Gaussianity in parameter constraints. By introducing a suite of tests that can capture different levels of NG in the data, we show that the success or failure of traditional data-driven likelihoods can be tied back to the structure of the NG in the data. Unlike other methods, the flexibility of the FBL makes it successful at tackling different types of NG simultaneously. Because of this, and consequently their likely applicability across datasets and domains, we encourage their use for inference when sufficient mock data are available for training.

arXiv comment14 pages, 6 figures + appendices. v2 matches published version

References in corpus (28)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• The cosmological simulation code GADGET-2
• Cosmological parameters from CMB and other data: a Monte-Carlo approach
• Tensions between the Early and the Late Universe
• Planck 2018 results. V. CMB power spectra and likelihoods
• CFHTLenS: The Canada-France-Hawaii Telescope Lensing Survey
• Dark Energy Survey Year 1 Results: Cosmological Constraints from Cosmic Shear
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Anisotropic galaxy clustering in Fourier-space
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the BOSS Final Data Release
• nbodykit: an open-source, massively parallel toolkit for large-scale structure
• Parameter inference with estimated covariance matrices
• CFHTLenS: The relation between galaxy dark matter haloes and baryons from weak gravitational lensing
• Planck intermediate results. LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters
• Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology
• Non-Gaussian information from weak lensing data via deep learning
• Nuisance hardened data compression for fast likelihood-free inference
• Dependence of cosmic shear covariances on cosmology - Impact on parameter estimation
• Mocking the Weak Lensing universe: the LensTools python computing package
• On the insufficiency of arbitrarily precise covariance matrices: non-Gaussian weak lensing likelihoods
• The skewed weak lensing likelihood: why biases arise, despite data and theory being sound
• Gravitational wave population inference with deep flow-based generative network
• Cosmic Shear: Inference from Forward Models
• Likelihood Non-Gaussianity in Large-Scale Structure Analyses
• Flows for simultaneous manifold learning and density estimation
• On estimating cosmology-dependent covariance matrices
• Debiasing inference with approximate covariance matrices and other unidentified biases
• Constraining the Reionization History using Bayesian Normalizing Flows
• Including parameter dependence in the data and covariance for cosmological inference

Cited by in corpus (14)

• Likelihood-free inference with neural compression of DES SV weak lensing map statistics
• Non-Gaussian estimates of tensions in cosmological parameters
• Weak lensing scattering transform: dark energy and neutrino mass sensitivity
• Beyond Gaussian Noise: A Generalized Approach to Likelihood Analysis with non-Gaussian Noise
• Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys
• Machine Learning and Cosmology
• Quantification of high dimensional non-Gaussianities and its implication to Fisher analysis in cosmology
• The impact of signal-to-noise, redshift, and angular range on the bias of weak lensing 2-point functions
• Normalizing flows for random fields in cosmology
• Weak Lensing Trispectrum and Kurt-Spectra
• What does a cosmological experiment really measure? Covariant posterior decomposition with normalizing flows
• Constraining cosmology with thermal Sunyaev-Zel'dovich maps: Minkowski functionals, peaks, minima, and moments
• Inference and De-Noising of Non-Gaussian Particle Distribution Functions: A Generative Modeling Approach
• Non-Gaussian likelihood of weak lensing power spectra