The future of cosmological likelihood-based inference: accelerated high-dimensional parameter estimation and model comparison

• URL: http://arxiv.org/abs/2405.12965v2
• Date: Wed, 4 Sep 2024 14:10:43 GMT
• Title: The future of cosmological likelihood-based inference: accelerated high-dimensional parameter estimation and model comparison
• Abstract summary: We advocate for a new paradigm of cosmological likelihood-based inference, leveraging recent developments in machine learning and its underlying technology. We demonstrate the application of this paradigm on a simulated cosmic shear analysis for a Stage IV survey in 37- and 39-dimensional parameter spaces. We recover posterior contours and evidence estimates that are in excellent agreement with those computed by the traditional nested sampling approach.
• Score: 5.79711608843279
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We advocate for a new paradigm of cosmological likelihood-based inference, leveraging recent developments in machine learning and its underlying technology, to accelerate Bayesian inference in high-dimensional settings. Specifically, we combine (i) emulation, where a machine learning model is trained to mimic cosmological observables, e.g. CosmoPower-JAX; (ii) differentiable and probabilistic programming, e.g. JAX and NumPyro, respectively; (iii) scalable Markov chain Monte Carlo (MCMC) sampling techniques that exploit gradients, e.g. Hamiltonian Monte Carlo; and (iv) decoupled and scalable Bayesian model selection techniques that compute the Bayesian evidence purely from posterior samples, e.g. the learned harmonic mean implemented in harmonic. This paradigm allows us to carry out a complete Bayesian analysis, including both parameter estimation and model selection, in a fraction of the time of traditional approaches. First, we demonstrate the application of this paradigm on a simulated cosmic shear analysis for a Stage IV survey in 37- and 39-dimensional parameter spaces, comparing $\Lambda$CDM and a dynamical dark energy model ($w_0w_a$CDM). We recover posterior contours and evidence estimates that are in excellent agreement with those computed by the traditional nested sampling approach while reducing the computational cost from 8 months on 48 CPU cores to 2 days on 12 GPUs. Second, we consider a joint analysis between three simulated next-generation surveys, each performing a 3x2pt analysis, resulting in 157- and 159-dimensional parameter spaces. Standard nested sampling techniques are simply unlikely to be feasible in this high-dimensional setting, requiring a projected 12 years of compute time on 48 CPU cores; on the other hand, the proposed approach only requires 8 days of compute time on 24 GPUs. All packages used in our analyses are publicly available.

Related papers

• FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale [91.84761739154366]
  FourCastNet 3 advances global weather modeling by implementing a scalable, geometric machine learning (ML) approach to probabilistic ensemble forecasting.<n>FourCastNet 3 delivers forecasting accuracy that surpasses leading conventional ensemble models and rivals the best diffusion-based methods.<n>Its computational efficiency, medium-range probabilistic skill, spectral fidelity, and rollout stability at subseasonal timescales make it a strong candidate for improving meteorological forecasting and early warning systems through large ensemble predictions.
  arXiv  Detail & Related papers  (2025-07-16T11:22:18Z)
• Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review [59.856222854472605]
  This tutorial provides an in-depth guide on inference-time guidance and alignment methods for optimizing downstream reward functions in diffusion models. practical applications in fields such as biology often require sample generation that maximizes specific metrics. We discuss (1) fine-tuning methods combined with inference-time techniques, (2) inference-time algorithms based on search algorithms such as Monte Carlo tree search, and (3) connections between inference-time algorithms in language models and diffusion models.
  arXiv  Detail & Related papers  (2025-01-16T17:37:35Z)
• Parallel simulation for sampling under isoperimetry and score-based diffusion models [56.39904484784127]
  As data size grows, reducing the iteration cost becomes an important goal. Inspired by the success of the parallel simulation of the initial value problem in scientific computation, we propose parallel Picard methods for sampling tasks. Our work highlights the potential advantages of simulation methods in scientific computation for dynamics-based sampling and diffusion models.
  arXiv  Detail & Related papers  (2024-12-10T11:50:46Z)
• von Mises Quasi-Processes for Bayesian Circular Regression [57.88921637944379]
  We explore a family of expressive and interpretable distributions over circle-valued random functions. The resulting probability model has connections with continuous spin models in statistical physics. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Markov Chain Monte Carlo sampling.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
  Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
  arXiv  Detail & Related papers  (2024-04-11T09:23:36Z)
• Fusion of Gaussian Processes Predictions with Monte Carlo Sampling [61.31380086717422]
  In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and integrate their outcomes.
  arXiv  Detail & Related papers  (2024-03-03T04:21:21Z)
• GPS-Gaussian: Generalizable Pixel-wise 3D Gaussian Splatting for Real-time Human Novel View Synthesis [70.24111297192057]
  We present a new approach, termed GPS-Gaussian, for synthesizing novel views of a character in a real-time manner. The proposed method enables 2K-resolution rendering under a sparse-view camera setting.
  arXiv  Detail & Related papers  (2023-12-04T18:59:55Z)
• CosmoPower-JAX: high-dimensional Bayesian inference with differentiable cosmological emulators [0.0]
  We present CosmoPower-JAX, a JAX-based implementation of the CosmoPower framework, which accelerates cosmological inference. We show how, using the automatic differentiation, batch evaluation and just-in-time compilation features of JAX, parameter estimation can be accelerated by orders of magnitude. We show how CosmoPower-JAX provides converged posterior contours in 3 days, as opposed to the estimated 6 years required by standard methods.
  arXiv  Detail & Related papers  (2023-05-10T17:54:10Z)
• Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements [62.997667081978825]
  characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in dMRI. We propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model.
  arXiv  Detail & Related papers  (2021-11-15T09:08:27Z)
• Reversible Gromov-Monge Sampler for Simulation-Based Inference [3.725559762520257]
  This paper introduces a new simulation-based inference procedure to model and sample from multi-dimensional probability distributions. Motivated by the work of M'emoli (2011) and Sturm (2012) on distance and isomorphism between metric measure spaces, we propose a new notion called the Reversible Gromov-Monge (RGM) distance.
  arXiv  Detail & Related papers  (2021-09-28T23:09:24Z)
• Compressed particle methods for expensive models with application in Astronomy and Remote Sensing [15.874578163779047]
  We introduce a novel approach where the expensive model is evaluated only in some well-chosen samples. We provide theoretical results supporting the novel algorithms and give empirical evidence of the performance of the proposed method in several numerical experiments. Two of them are real-world applications in astronomy and satellite remote sensing.
  arXiv  Detail & Related papers  (2021-07-18T14:45:23Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Linear-time inference for Gaussian Processes on one dimension [17.77516394591124]
  We investigate data sampled on one dimension for which state-space models are popular due to their linearly-scaling computational costs. We provide the first general proof of conjecture that state-space models are general, able to approximate any one-dimensional Gaussian Processes. We develop parallelized algorithms for performing inference and learning in the LEG model, test the algorithm on real and synthetic data, and demonstrate scaling to datasets with billions of samples.
  arXiv  Detail & Related papers  (2020-03-11T23:20:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.