Fast likelihood-free cosmology with neural density estimators and active learning (1903.00007v1)

Abstract: Likelihood-free inference provides a framework for performing rigorous Bayesian inference using only forward simulations, properly accounting for all physical and observational effects that can be successfully included in the simulations. The key challenge for likelihood-free applications in cosmology, where simulation is typically expensive, is developing methods that can achieve high-fidelity posterior inference with as few simulations as possible. Density-estimation likelihood-free inference (DELFI) methods turn inference into a density estimation task on a set of simulated data-parameter pairs, and give orders of magnitude improvements over traditional Approximate Bayesian Computation approaches to likelihood-free inference. In this paper we use neural density estimators (NDEs) to learn the likelihood function from a set of simulated datasets, with active learning to adaptively acquire simulations in the most relevant regions of parameter space on-the-fly. We demonstrate the approach on a number of cosmological case studies, showing that for typical problems high-fidelity posterior inference can be achieved with just $\mathcal{O}(10^3)$ simulations or fewer. In addition to enabling efficient simulation-based inference, for simple problems where the form of the likelihood is known, DELFI offers a fast alternative to MCMC sampling, giving orders of magnitude speed-up in some cases. Finally, we introduce \textsc{pydelfi} -- a flexible public implementation of DELFI with NDEs and active learning -- available at \url{https://github.com/justinalsing/pydelfi}.

• The paper introduces neural density estimators within the DELFI framework to achieve efficient posterior inference with significantly fewer simulations.
• It leverages active learning to dynamically select simulation points, enhancing parameter space exploration and inference precision.
• The study validates its approach by attaining high-fidelity results with as few as 1,000 simulations and provides the open-source tool pydelfi for practical application.

Insights into Fast Likelihood-Free Cosmology with Neural Density Estimators

The paper "Fast Likelihood-Free Cosmology with Neural Density Estimators and Active Learning" by Alsing et al. explores the evolution of likelihood-free inference methodologies tailored for cosmology, a field where traditional methods often fall short due to the complexity and computational demands of simulating cosmological models. The researchers investigate the implementation of density-estimation likelihood-free inference (DELFI), using neural density estimators (NDEs) as a scalable solution to address these challenges.

Key Contributions and Approaches

The core challenge in likelihood-free cosmology is achieving precise posterior estimates while minimizing the number of simulations conducted, as simulations in cosmology are resource-intensive. While Approximate Bayesian Computation (ABC) methods have historically been employed, they demand an extensive number of simulations which scales poorly with the number of parameters. DELFI offers a robust alternative, significantly reducing such computational costs.

1. Neural Density Estimators: They adopt NDEs to infer the likelihood function from simulated datasets. This step crucially transforms inference into a more manageable density estimation task. The paper leverages two prominent classes of NDEs: Mixture Density Networks (MDNs) and Masked Autoregressive Flows (MAFs). Each NDE is trained to model the conditional distribution of simulated data given the parameters, thus learning how the simulated data behaves across the parameter space.
2. Active Learning: To further optimize resource allocation, the study incorporates active learning, allowing the model to dynamically query new simulations based on the current estimations of the parameter space. This adaptive mechanism ensures simulations are concentrated in parameter regions that most enhance the fidelity of posterior inference.
3. Efficient Simulation Strategy: The research demonstrates that high-fidelity posterior estimates can be achieved with as few as 1000 simulations. This mark is notably low compared to traditional methods, supporting the feasibility of leveraging DELFI for cosmological tasks.
4. pydelfi: They introduce pydelfi, an open-source, flexible implementation allowing researchers to utilize DELFI effectively in cosmological analysis. The introduction of pydelfi highlights the paper's emphasis on not only advancing theoretical methods but also on ensuring practical utility and accessibility.

Implications and Future Directions

The implications of adopting DELFI in cosmology could be profound. By reducing simulation costs significantly, this method allows cosmologists to address previously infeasible problems involving complex models with numerous parameters. Moreover, the integration of active learning explores new grounds for iterative model refinement, potentially leading to more precise cosmological predictions.

In terms of practical applications, DELFI may influence how future cosmic surveys are designed and analyzed. Adaptive learning strategies could enable real-time analysis of data from upcoming space missions, leading to swifter refinements in cosmological models.

Looking ahead, further developments in NDE architecture and active learning rules could enhance DELFI's efficiency and robustness. There is also potential for DELFI to be extended beyond cosmology, where simulation-based inference underpins many scientific inquiries. Future work might explore these models in radically different contexts, leveraging high-dimensional data compression and sophisticated simulation techniques.

This paper delineates a promising advancement in statistical methods for cosmology, paving the way for more efficient and accurate inferences from complex generative models. By harnessing the power of neural networks and adaptive simulations, the research stands to profoundly impact computational approaches in scientific fields reliant on intricate simulations.