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1. Bayesian function registration with random truncation

   https://doi.org/10.1371/journal.pone.0287734  

   Lu, Yi; Herbei, Radu; Kurtek, Sebastian (July 2023, PLOS ONE)

   Yang, Junyuan (Ed.)

   In this work, we develop a new set of Bayesian models to perform registration of real-valued functions. A Gaussian process prior is assigned to the parameter space of time warping functions, and a Markov chain Monte Carlo (MCMC) algorithm is utilized to explore the posterior distribution. While the proposed model can be defined on the infinite-dimensional function space in theory, dimension reduction is needed in practice because one cannot store an infinite-dimensional function on the computer. Existing Bayesian models often rely on some pre-specified, fixed truncation rule to achieve dimension reduction, either by fixing the grid size or the number of basis functions used to represent a functional object. In comparison, the new models in this paper randomize the truncation rule. Benefits of the new models include the ability to make inference on the smoothness of the functional parameters, a data-informative feature of the truncation rule, and the flexibility to control the amount of shape-alteration in the registration process. For instance, using both simulated and real data, we show that when the observed functions exhibit more local features, the posterior distribution on the warping functions automatically concentrates on a larger number of basis functions. Supporting materials including code and data to perform registration and reproduce some of the results presented herein are available online. 

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2. Estimation of time-varying graph topologies from graph signals

   Y. Liu, C. Cui (January 2023, Conference record IEEE International Conference on Acoustics Speech and Signal Processing)

   In science and engineering, we often deal with signals that are acquired from time-varying systems represented by dynamic graphs. We observe these signals, and the interest is in finding the time-varying topology of the graphs. We propose two Bayesian methods for estimating these topologies without assuming any specific functional relationships among the signals on the graphs. The two methods exploit Gaussian processes, where the first method uses the length scale of the kernel and relies on variational inference for optimization, and the second method is based on derivatives of the functions and Monte Carlo sampling. Both methods estimate the time-varying topologies of the graphs sequentially. We provide numerical tests that show the performance of the methods in two settings. 

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3. Sequential Monte Carlo testing by betting

   https://doi.org/10.1093/jrsssb/qkaf014  

   Fischer, Lasse; Ramdas, Aaditya (April 2025, Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Abstract In a Monte Carlo test, the observed dataset is fixed, and several resampled or permuted versions of the dataset are generated in order to test a null hypothesis that the original dataset is exchangeable with the resampled/permuted ones. Sequential Monte Carlo tests aim to save computational resources by generating these additional datasets sequentially one by one and potentially stopping early. While earlier tests yield valid inference at a particular prespecified stopping rule, our work develops a new anytime-valid Monte Carlo test that can be continuously monitored, yielding a p-value or e-value at any stopping time possibly not specified in advance. It generalizes the well-known method by Besag and Clifford, allowing it to stop at any time, but also encompasses new sequential Monte Carlo tests that tend to stop sooner under the null and alternative without compromising power. The core technical advance is the development of new test martingales for testing exchangeability against a very particular alternative based on a testing by betting technique. The proposed betting strategies are guided by the derivation of a simple log-optimal betting strategy, have closed-form expressions for the wealth process, provable guarantees on resampling risk, and display excellent power in practice. 

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4. Programmable MCMC with Soundly Composed Guide Programs

   https://doi.org/10.1145/3689748  

   Pham, Long; Wang, Di; Saad, Feras A; Hoffmann, Jan (October 2024, Proceedings of the ACM on Programming Languages)

   Probabilistic programming languages (PPLs) provide language support for expressing flexible probabilistic models and solving Bayesian inference problems. PPLs withprogrammable inferencemake it possible for users to obtain improved results by customizing inference engines usingguideprograms that are tailored to a correspondingmodelprogram. However, errors in guide programs can compromise the statistical soundness of the inference. This article introduces a novel coroutine-based framework for verifying the correctness of user-written guide programs for a broad class of Markov chain Monte Carlo (MCMC) inference algorithms. Our approach rests on a novel type system for describing communication protocols between a model program and a sequence of guides that each update only a subset of random variables. We prove that, by translating guide types to context-free processes with finite norms, it is possible to check structural type equality between models and guides in polynomial time. This connection gives rise to an efficienttype-inference algorithmfor probabilistic programs with flexible constructs such as general recursion and branching. We also contribute acoverage-checking algorithmthat verifies the support of sequentially composed guide programs agrees with that of the model program, which is a key soundness condition for MCMC inference with multiple guides. Evaluations on diverse benchmarks show that our type-inference and coverage-checking algorithms efficiently infer types and detect sound and unsound guides for programs that existing static analyses cannot handle. 

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5. MFBO-SSM: Multi-Fidelity Bayesian Optimization for Fast Inference in State-Space Models

   Imani, M; Ghoreishi, S.F.; Allaire, D.; Braga-Neto, U (July 2019, Proceedings of the ... AAAI Conference on Artificial Intelligence)

   Nonlinear state-space models are ubiquitous in modeling real-world dynamical systems. Sequential Monte Carlo (SMC) techniques, also known as particle methods, are a well-known class of parameter estimation methods for this general class of state-space models. Existing SMC-based techniques rely on excessive sampling of the parameter space, which makes their computation intractable for large systems or tall data sets. Bayesian optimization techniques have been used for fast inference in state-space models with intractable likelihoods. These techniques aim to find the maximum of the likelihood function by sequential sampling of the parameter space through a single SMC approximator. Various SMC approximators with different fidelities and computational costs are often available for sample- based likelihood approximation. In this paper, we propose a multi-fidelity Bayesian optimization algorithm for the inference of general nonlinear state-space models (MFBO-SSM), which enables simultaneous sequential selection of parameters and approximators. The accuracy and speed of the algorithm are demonstrated by numerical experiments using synthetic gene expression data from a gene regulatory network model and real data from the VIX stock price index. 

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