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1. 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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2. 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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3. Path-Dependent Reliability and Resiliency of Critical Infrastructure via Particle Integration Methods

   Paredes, R. ; Talebiyan, H. ; Dueñas-Osorio, L. ( January 2022 , The 13th International Conference on Structural Safety and Reliability (ICOSSAR 2021-2022))

   Critical infrastructure is the backbone of modern societies. To meet increasing demand under resource-constrained and multihazard conditions, policy-makers are tapping into infrastructure resiliency: its capacity to withstand and recover from disruptions. Thus, resiliency-aware uncertainty quantification is key to identify tipping points, yet it remains computationally inaccessible. This paper maps resiliency measures to well understood time-dependent reliability computations, porting insights and methods from reliability theory to the service of critical infrastructure resiliency and upkeep efforts. For large-scale applications, we use particle integration methods (PIMs)—a family of sequential Monte Carlo methods with wide-ranging applications—and propose their optimal tuning in terms of their variance and number of limit-state function evaluations. We obtain consistent and unbiased probability estimates in applications to dynamical systems, network reliability, and resilience analysis, demonstrating PIMs as practical yet under-appreciated tools. For example, we obtain probability estimates of order 10−14 in networks with over 10,000 random variables. 

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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. Dynamics of Coordinate Ascent Variational Inference: A Case Study in 2D Ising Models

   https://doi.org/10.3390/e22111263  

   Plummer, Sean ; Pati, Debdeep ; Bhattacharya, Anirban ( November 2020 , Entropy)

   null (Ed.)

   Variational algorithms have gained prominence over the past two decades as a scalable computational environment for Bayesian inference. In this article, we explore tools from the dynamical systems literature to study the convergence of coordinate ascent algorithms for mean field variational inference. Focusing on the Ising model defined on two nodes, we fully characterize the dynamics of the sequential coordinate ascent algorithm and its parallel version. We observe that in the regime where the objective function is convex, both the algorithms are stable and exhibit convergence to the unique fixed point. Our analyses reveal interesting discordances between these two versions of the algorithm in the region when the objective function is non-convex. In fact, the parallel version exhibits a periodic oscillatory behavior which is absent in the sequential version. Drawing intuition from the Markov chain Monte Carlo literature, we empirically show that a parameter expansion of the Ising model, popularly called the Edward–Sokal coupling, leads to an enlargement of the regime of convergence to the global optima. 

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