Uroš Seljak

Biwei Dai, Po-Wen Chang, Wahid Bhimji et al.

Weak gravitational lensing, the correlated distortion of background galaxy shapes by foreground structures, is a powerful probe of the matter distribution in our universe and allows accurate constraints on the cosmological model. In recent years, high-order statistics and machine learning (ML) techniques have been applied to weak lensing data to extract the nonlinear information beyond traditional two-point analysis. However, these methods typically rely on cosmological simulations, which poses several challenges: simulations are computationally expensive, limiting most realistic setups to a low training data regime; inaccurate modeling of systematics in the simulations create distribution shifts that can bias cosmological parameter constraints; and varying simulation setups across studies make method comparison difficult. To address these difficulties, we present the first weak lensing benchmark dataset with several realistic systematics and launch the FAIR Universe Weak Lensing Machine Learning Uncertainty Challenge. The challenge focuses on measuring the fundamental properties of the universe from weak lensing data with limited training set and potential distribution shifts, while providing a standardized benchmark for rigorous comparison across methods. Organized in two phases, the challenge will bring together the physics and ML communities to advance the methodologies for handling systematic uncertainties, data efficiency, and distribution shifts in weak lensing analysis with ML, ultimately facilitating the deployment of ML approaches into upcoming weak lensing survey analysis.

Minas Karamanis, Uroš Seljak

Sequential Monte Carlo (SMC) samplers are powerful tools for Bayesian inference but suffer from high computational costs due to their reliance on large particle ensembles for accurate estimates. We introduce persistent sampling (PS), an extension of SMC that systematically retains and reuses particles from all prior iterations to construct a growing, weighted ensemble. By leveraging multiple importance sampling and resampling from a mixture of historical distributions, PS mitigates the need for excessively large particle counts, directly addressing key limitations of SMC such as particle impoverishment and mode collapse. Crucially, PS achieves this without additional likelihood evaluations-weights for persistent particles are computed using cached likelihood values. This framework not only yields more accurate posterior approximations but also produces marginal likelihood estimates with significantly lower variance, enhancing reliability in model comparison. Furthermore, the persistent ensemble enables efficient adaptation of transition kernels by leveraging a larger, decorrelated particle pool. Experiments on high-dimensional Gaussian mixtures, hierarchical models, and non-convex targets demonstrate that PS consistently outperforms standard SMC and related variants, including recycled and waste-free SMC, achieving substantial reductions in mean squared error for posterior expectations and evidence estimates, all at reduced computational cost. PS thus establishes itself as a robust, scalable, and efficient alternative for complex Bayesian inference tasks.

Reuben Cohn-Gordon, Uroš Seljak, Dries Sels

Hamiltonian Monte Carlo (HMC) is a state of the art method for sampling from distributions with differentiable densities, but can converge slowly when applied to challenging multimodal problems. Running HMC with a time varying Hamiltonian, in order to interpolate from an initial tractable distribution to the target of interest, can address this problem. In conjunction with a weighting scheme to eliminate bias, this can be viewed as a special case of Sequential Monte Carlo (SMC) sampling \cite{doucet2001introduction}. However, this approach can be inefficient, since it requires slow change between the initial and final distribution. Inspired by \cite{sels2017minimizing}, where a learned \emph{counterdiabatic} term added to the Hamiltonian allows for efficient quantum state preparation, we propose \emph{Counterdiabatic Hamiltonian Monte Carlo} (CHMC), which can be viewed as an SMC sampler with a more efficient kernel. We establish its relationship to recent proposals for accelerating gradient-based sampling with learned drift terms, and demonstrate on simple benchmark problems.

Vanessa Böhm, Uroš Seljak

Principal Component Analysis (PCA) minimizes the reconstruction error given a class of linear models of fixed component dimensionality. Probabilistic PCA adds a probabilistic structure by learning the probability distribution of the PCA latent space weights, thus creating a generative model. Autoencoders (AE) minimize the reconstruction error in a class of nonlinear models of fixed latent space dimensionality and outperform PCA at fixed dimensionality. Here, we introduce the Probabilistic Autoencoder (PAE) that learns the probability distribution of the AE latent space weights using a normalizing flow (NF). The PAE is fast and easy to train and achieves small reconstruction errors, high sample quality, and good performance in downstream tasks. We compare the PAE to Variational AE (VAE), showing that the PAE trains faster, reaches a lower reconstruction error, and produces good sample quality without requiring special tuning parameters or training procedures. We further demonstrate that the PAE is a powerful model for performing the downstream tasks of probabilistic image reconstruction in the context of Bayesian inference of inverse problems for inpainting and denoising applications. Finally, we identify latent space density from NF as a promising outlier detection metric.

He Jia, Uroš Seljak

Normalizing constant (also called partition function, Bayesian evidence, or marginal likelihood) is one of the central goals of Bayesian inference, yet most of the existing methods are both expensive and inaccurate. Here we develop a new approach, starting from posterior samples obtained with a standard Markov Chain Monte Carlo (MCMC). We apply a novel Normalizing Flow (NF) approach to obtain an analytic density estimator from these samples, followed by Optimal Bridge Sampling (OBS) to obtain the normalizing constant. We compare our method which we call Gaussianized Bridge Sampling (GBS) to existing methods such as Nested Sampling (NS) and Annealed Importance Sampling (AIS) on several examples, showing our method is both significantly faster and substantially more accurate than these methods, and comes with a reliable error estimation.

Vanessa Böhm, François Lanusse, Uroš Seljak

We develop a generative model-based approach to Bayesian inverse problems, such as image reconstruction from noisy and incomplete images. Our framework addresses two common challenges of Bayesian reconstructions: 1) It makes use of complex, data-driven priors that comprise all available information about the uncorrupted data distribution. 2) It enables computationally tractable uncertainty quantification in the form of posterior analysis in latent and data space. The method is very efficient in that the generative model only has to be trained once on an uncorrupted data set, after that, the procedure can be used for arbitrary corruption types.