Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology

Abstract

Many statistical models in cosmology can be simulated forwards but have intractable likelihood functions. Likelihood-free inference methods allow us to perform Bayesian inference from these models using only forward simulations, free from any likelihood assumptions or approximations. Likelihood-free inference generically involves simulating mock data and comparing to the observed data; this comparison in data-space suffers from the curse of dimensionality and requires compression of the data to a small number of summary statistics to be tractable. In this paper we use massive asymptotically-optimal data compression to reduce the dimensionality of the data-space to just one number per parameter, providing a natural and optimal framework for summary statistic choice for likelihood-free inference. Secondly, we present the first cosmological application of Density Estimation Likelihood-Free Inference (\textsc{delfi}), which learns a parameterized model for joint distribution of data and parameters, yielding both the parameter posterior and the model evidence. This approach is conceptually simple, requires less tuning than traditional Approximate Bayesian Computation approaches to likelihood-free inference and can give high-fidelity posteriors from orders of magnitude fewer forward simulations. As an additional bonus, it enables parameter inference and Bayesian model comparison simultaneously. We demonstrate Density Estimation Likelihood-Free Inference with massive data compression on an analysis of the joint light-curve analysis supernova data, as a simple validation case study. We show that high-fidelity posterior inference is possible for full-scale cosmological data analyses with as few as $\sim 10^4$ simulations, with substantial scope for further improvement, demonstrating the scalability of likelihood-free inference to large and complex cosmological datasets.

11 pages, 6 figures, updated to MNRAS accepted version (26 Mar 2018)

References in corpus (8)

• Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems
• The star formation histories of galaxies in the Sloan Digital Sky Survey
• Constraining the thick disc formation scenario of the Milky Way
• Generalized massive optimal data compression
• Massive data compression for parameter-dependent covariance matrices
• Maximal compression of the redshift space galaxy power spectrum and bispectrum
• Sequential Monte Carlo with Adaptive Weights for Approximate Bayesian Computation
• An investigation into the Multiple Optimised Parameter Estimation and Data compression algorithm

Cited by in corpus (111)

• Machine learning and the physical sciences
• The frontier of simulation-based inference
• Normalizing Flows for Probabilistic Modeling and Inference
• Fast likelihood-free cosmology with neural density estimators and active learning
• Mining gold from implicit models to improve likelihood-free inference
• Cosmological constraints with deep learning from KiDS-450 weak lensing maps
• Likelihood-free inference with neural compression of DES SV weak lensing map statistics
• Nuisance hardened data compression for fast likelihood-free inference
• Automatic physical inference with information maximising neural networks
• Generalized massive optimal data compression
• Bayesian optimisation for likelihood-free cosmological inference
• Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows
• Simulation-Based Inference of Reionization Parameters From 3D Tomographic 21 cm Lightcone Images
• Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps -- validation on simulations
• Constraining Neutrino Mass with the Tomographic Weak Lensing Bispectrum
• Inference of the optical depth to reionization from low multipole temperature and polarisation Planck data
• Fast and Credible Likelihood-Free Cosmology with Truncated Marginal Neural Ratio Estimation
• Translation and Rotation Equivariant Normalizing Flow (TRENF) for Optimal Cosmological Analysis
• Enhancing BOSS bispectrum cosmological constraints with maximal compression
• Neural posterior estimation for exoplanetary atmospheric retrieval
• FlowPM: Distributed TensorFlow Implementation of the FastPM Cosmological N-body Solver
• Conditional Density Estimation Tools in Python and R with Applications to Photometric Redshifts and Likelihood-Free Cosmological Inference
• k-cut Cosmic Shear: Tunable Power Spectrum Sensitivity to Test Gravity
• The integrated 3-point correlation function of cosmic shear
• Accurate Analytic Model for the Weak Lensing Convergence One-Point Probability Distribution Function and its Auto-Covariance
• Implicit Likelihood Inference of Reionization Parameters from the 21 cm Power Spectrum
• Cosmic Shear: Inference from Forward Models
• Exploring the likelihood of the 21-cm power spectrum with simulation-based inference
• LtU-ILI: An All-in-One Framework for Implicit Inference in Astrophysics and Cosmology
• Kernel-Based Emulator for the 3D Matter Power Spectrum from CLASS
• 21cmEMU: an emulator of 21cmFAST summary observables
• Likelihood Non-Gaussianity in Large-Scale Structure Analyses
• The sum of the masses of the Milky Way and M31: a likelihood-free inference approach
• $\mathrm{S}\mathrm{IM}\mathrm{BIG}$: Mock Challenge for a Forward Modeling Approach to Galaxy Clustering
• Simulation-based inference of dynamical galaxy cluster masses with 3D convolutional neural networks
• Forward modeling of galaxy populations for cosmological redshift distribution inference
• On the accuracy and precision of correlation functions and field-level inference in cosmology
• Likelihood methods for CMB experiments
• Robust Simulation-Based Inference in Cosmology with Bayesian Neural Networks
• Measurement of the B-band Galaxy Luminosity Function with Approximate Bayesian Computation
• Likelihood-free Cosmological Constraints with Artificial Neural Networks: An Application on Hubble Parameters and SNe Ia
• KiDS-SBI: Simulation-based inference analysis of KiDS-1000 cosmic shear
• Promise of Future Searches for Cosmic Topology
• GLASS: Generator for Large Scale Structure
• Parameter Inference for Weak Lensing using Gaussian Processes and MOPED
• EFTofLSS meets simulation-based inference: ${\sigma }_8$ from biased tracers
• Mapping quasar light echoes in 3D with Lyα forest tomography
• The PAU Survey: Measurement of Narrow-band galaxy properties with Approximate Bayesian Computation
• Primordial non-Gaussianity and non-Gaussian Covariance
• LINNA: Likelihood Inference Neural Network Accelerator
• Neural Approximate Sufficient Statistics for Implicit Models
• Effective LHC measurements with matrix elements and machine learning
• Likelihood-free Inference with Mixture Density Network
• 21st Century Statistical and Computational Challenges in Astrophysics
• Calibrating cosmological simulations with implicit likelihood inference using galaxy growth observables
• Single frequency CMB B-mode inference with realistic foregrounds from a single training image
• Primordial power spectrum and cosmology from black-box galaxy surveys
• Unbiased likelihood-free inference of the Hubble constant from light standard sirens
• An Accurate Analytic Model for the Thermal Sunyaev-Zel'dovich One-Point PDF
• CoLFI: Cosmological Likelihood-free Inference with Neural Density Estimators
• Likelihood-free inference with an improved cross-entropy estimator
• Thermodynamics of Einstein-Euler-Heisenberg Black Holes with Thermal Fluctuations and Nonlinear Electromagnetic Fields
• Cosmological constraints from weak lensing scattering transform using HSC Y1 data
• Deriving the star formation histories of galaxies from spectra with simulation-based inference
• Teaching neural networks to generate Fast Sunyaev Zel'dovich Maps
• Cosmological Parameter Estimation and Inference using Deep Summaries
• Scalable inference with Autoregressive Neural Ratio Estimation
• Machine Learning and Cosmology
• Evidence Networks: simple losses for fast, amortized, neural Bayesian model comparison
• Flow-Based Likelihoods for Non-Gaussian Inference
• A Framework for Obtaining Accurate Posteriors of Strong Gravitational Lensing Parameters with Flexible Priors and Implicit Likelihoods using Density Estimation
• Debiasing Standard Siren Inference of the Hubble Constant with Marginal Neural Ratio Estimation
• Perfectly parallel cosmological simulations using spatial comoving Lagrangian acceleration
• Likelihood-free Forward Modeling for Cluster Weak Lensing and Cosmology
• Forecasting the power of Higher Order Weak Lensing Statistics with automatically differentiable simulations
• GEOMAX: beyond linear compression for 3pt galaxy clustering statistics
• Parameter inference and model comparison using theoretical predictions from noisy simulations
• Bayesian evidence-driven likelihood selection for sky-averaged 21-cm signal extraction
• An uncertainty-aware Digital Shadow for underground multimodal CO2 storage monitoring
• Fast likelihood-free inference in the LSS Stage IV era
• Estimation of HII Bubble Size Distribution from 21cm Power Spectrum with Artificial Neural Networks
• Inferring subhalo effective density slopes from strong lensing observations with neural likelihood-ratio estimation
• Characterizing the Conditional Galaxy Property Distribution using Gaussian Mixture Models
• Efficient simulation of discrete galaxy populations and associated radiation fields during the first billion years
• Towards fast machine-learning-assisted Bayesian posterior inference of microseismic event location and source mechanism
• Neural Density Estimation and Likelihood-free Inference
• Cosmological constraints from low redshift 21 cm intensity mapping with machine learning
• Measuring the thermal and ionization state of the low-$z$ IGM using likelihood free inference
• Full-waveform earthquake source inversion using simulation-based inference
• Efficient Bayesian Experimental Design for Implicit Models
• Gaussian Processes and Nested Sampling Applied to Kepler's Small Long-period Exoplanet Candidates
• A Simulation Based Inference Approach to the Dynamics of the MW-LMC System -- Validation
• Cosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes
• Simulation-based inference has its own Dodelson-Schneider effect (but it knows that it does)
• Lightweight starshade position sensing with convolutional neural networks and simulation-based inference
• The Initial Magnetic Field Distribution in AB Stars
• Constraining Star Formation Histories of Blue Galaxies using the Scatter between Stellar Mass and Halo Mass
• Simulation-based inference of Bayesian hierarchical models while checking for model misspecification
• ParamANN: A Neural Network to Estimate Cosmological Parameters for $\Lambda$CDM Universe Using Hubble Measurements
• Galaxy mass profiles with convolutional neural networks
• Gaussbock: Fast parallel-iterative cosmological parameter estimation with Bayesian nonparametrics
• 3D ScatterNet: Inference from 21 cm Light-cones
• Parameter estimation from Ly$\alpha$ forest in Fourier space using Information Maximising Neural Network
• Probabilistic Spectral Reconstruction of Trans-Neptunian Objects from Sparse Photometry: A Framework for Taxonomy, Survey Optimization, and Outlier Detection
• Skew-spectra: a generalization to spin-$s$
• GalSBI-SPS: a stellar population synthesis-based galaxy population model for cosmology and galaxy evolution applications
• Functional Data Analysis for Extracting the Intrinsic Dimensionality of Spectra: Application to Chemical Homogeneity in the Open Cluster M67
• On the Connection between Field-Level Inference and $n$-point Correlation Functions
• Diagnosing Systematic Effects Using the Inferred Initial Power Spectrum
• IQ Collaboratory III: The Empirical Dust Attenuation Framework -- Taking Hydrodynamical Simulations with a Grain of Dust
• Generative modeling of convergence maps based on predicted one-point statistics