Stabilised weighted data subsampling for accelerated inference in models with recursive likelihoods

Statistics > Methodology [Submitted on 13 May 2026 (v1), last revised 1 Jun 2026 (this version, v2)] Title:Stabilised weighted data subsampling for accelerated inference in models with recursive likelihoods View PDFAbstract:Inference for models with recursively defined likelihoods is computationally demanding, limiting scalability to large datasets. We propose a stabilised weighted subsampling methodology for accelerated inference based on an unbiased estimator of the log-likelihood. By assigning higher sampling probabilities to early observations, the method reduces the effective depth of recursive likelihood evaluations and hence computational cost. However, sampling probabilities that decay too slowly yield limited savings, while overly aggressive decay can substantially inflate estimator variance. We develop a stabilisation framework, supported by theory, that restricts the decay to avoid both computational and variance pathologies through principled hyperparameter tuning. We also derive an unbiased subsampling estimator of the log-likelihood gradient, enabling gradient-based inference. The methodology can be embedded within a range of inferential frameworks. We illustrate its use in variational Bayes and subsampling Markov chain Monte Carlo for conditional volatility models, including leverage effects. Empirical results show substantial computational speed-ups relative to full-data methods while maintaining inferential accuracy. We also compare with recent stochastic gradient MCMC and divide-and-conquer MCMC methods for temporally dependent data, observing favourable empirical performance. Submission history From: Matias Quiroz [view email][v1] Wed, 13 May 2026 11:53:57 UTC (3,065 KB) [v2] Mon, 1 Jun 2026 03:19:33 UTC (3,012 KB) Current browse context: stat.ME References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.