Abstract: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.
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)
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