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1. Marginalized Stochastic Natural Gradients for Black-Box Variational Inference

   Ji, Geng; Sujono, Debora; Sudderth, Erik B. (July 2021, International Conference on Machine Learning)

   Meila, Marina; Zhang, Tong (Ed.)

   Black-box variational inference algorithms use stochastic sampling to analyze diverse statistical models, like those expressed in probabilistic programming languages, without model-specific derivations. While the popular score-function estimator computes unbiased gradient estimates, its variance is often unacceptably large, especially in models with discrete latent variables. We propose a stochastic natural gradient estimator that is as broadly applicable and unbiased, but improves efficiency by exploiting the curvature of the variational bound, and provably reduces variance by marginalizing discrete latent variables. Our marginalized stochastic natural gradients have intriguing connections to classic coordinate ascent variational inference, but allow parallel updates of variational parameters, and provide superior convergence guarantees relative to naive Monte Carlo approximations. We integrate our method with the probabilistic programming language Pyro and evaluate real-world models of documents, images, networks, and crowd-sourcing. Compared to score-function estimators, we require far fewer Monte Carlo samples and consistently convergence orders of magnitude faster. 

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2. Clustering time series with nonlinear dynamics: A Bayesian non-parametric and particle-based approach

   Lin, A.; Zhang, Y.; Heng, J.; Allsop, S.; Tye, K.; Jacob, P.; Ba, D. (April 2019, AISTATS)

   We propose a statistical framework for clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of sub-groups that each comprise time series with similar dynamics. Our motivation comes from neuroscience where an important problem is to identify, within a large assembly of neurons, sub-groups that respond similarly to a stimulus or contingency. In the neural setting, conditioned on cluster membership and the parameters governing the dynamics, time series within a cluster are assumed independent and generated according to a nonlinear binomial state-space model. We derive a Metropolis-within-Gibbs algorithm for full Bayesian inference that alternates between sampling of cluster membership and sampling of parameters of interest. The Metropolis step is a PMMH iteration that requires an unbiased, low variance estimate of the likelihood function of a nonlinear state- space model. We leverage recent results on controlled sequential Monte Carlo to estimate likelihood functions more efficiently compared to the bootstrap particle filter. We apply the framework to time series acquired from the prefrontal cortex of mice in an experiment designed to characterize the neural underpinnings of fear. 

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3. An Invitation to Sequential Monte Carlo Samplers

   https://doi.org/10.1080/01621459.2022.2087659  

   Dai, Chenguang; Heng, Jeremy; Jacob, Pierre E.; Whiteley, Nick (June 2022, Journal of the American Statistical Association)

   Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to approximate distributions of interest and their normalizing constants. These samplers originate from particle filtering for state space models and have become general and scalable sampling techniques. This article describes sequential Monte Carlo samplers and their possible implementations, arguing that they remain under-used in statistics, despite their ability to perform sequential inference and to leverage parallel processing resources among other potential benefits. Supplementary materials for this article are available online. 

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4. Slice Sampling Reparameterization Gradients

   Zoltowski, David; Cai, Diana; Adams, Ryan P. (January 2021, Advances in neural information processing systems)

   Many probabilistic modeling problems in machine learning use gradient-based optimization in which the objective takes the form of an expectation. These problems can be challenging when the parameters to be optimized determine the probability distribution under which the expectation is being taken, as the na\"ive Monte Carlo procedure is not differentiable. Reparameterization gradients make it possible to efficiently perform optimization of these Monte Carlo objectives by transforming the expectation to be differentiable, but the approach is typically limited to distributions with simple forms and tractable normalization constants. Here we describe how to differentiate samples from slice sampling to compute \textit{slice sampling reparameterization gradients}, enabling a richer class of Monte Carlo objective functions to be optimized. Slice sampling is a Markov chain Monte Carlo algorithm for simulating samples from probability distributions; it only requires a density function that can be evaluated point-wise up to a normalization constant, making it applicable to a variety of inference problems and unnormalized models. Our approach is based on the observation that when the slice endpoints are known, the sampling path is a deterministic and differentiable function of the pseudo-random variables, since the algorithm is rejection-free. We evaluate the method on synthetic examples and apply it to a variety of applications with reparameterization of unnormalized probability distributions. 

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5. Investigating the crust of neutron stars with neural-network quantum states

   https://doi.org/10.1038/s42005-025-02015-2  

   Fore, Bryce; Kim, Jane; Hjorth-Jensen, Morten; Lovato, Alessandro (March 2025, Communications Physics)

   Abstract An accurate description of low-density nuclear matter is crucial for explaining the physics of neutron star crusts. In the density range between approximately 0.01 fm⁻³and 0.1 fm⁻³, matter transitions from neutron-rich nuclei to various higher-density pasta shapes, before ultimately reaching a uniform liquid. In this work, we introduce a variational Monte Carlo method based on a neural Pfaffian-Jastrow quantum state, which allows us to model the transition from the liquid phase to neutron-rich nuclei microscopically. At low densities, nuclear clusters dynamically emerge from the microscopic interactions among protons and neutrons, which we model based on pionless effective field theory. Our variational Monte Carlo approach represents a significant improvement over the state-of-the-art auxiliary-field diffusion Monte Carlo method, which is severely hindered by the fermion-sign problem in this low-density regime and cannot capture the onset of clusters. In addition to computing the energy per particle of symmetric nuclear matter and pure neutron matter, we analyze an intermediate isospin-asymmetry configuration to elucidate the formation of nuclear clusters. We also provide evidence that the presence of such nuclear clusters influences the amount of protons in the crust compared to protons in beta-equilibrated, neutrino-transparent matter. 

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