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Abstract:
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In many modern applications, discretely-observed data may be naturally understood as a set of functions. Functional data often exhibit two confounded sources of variability: amplitude (y-axis) and phase (x-axis). The extraction of amplitude and phase, a process referred to as registration, is essential in exploring the underlying structure of functional data. While such data are often gathered sequentially with new functional observations arriving over time, most available registration procedures are only applicable to batch learning, leading to inefficient computation. To address these challenges, we introduce a Bayesian framework for sequential registration of functional data, which updates statistical inference as new sets of functions are assimilated. This Bayesian model-based sequential learning approach utilizes sequential Monte Carlo sampling to recursively update the alignment of functions. Consequently, distributed computing, which is not generally an option in batch learning, significantly reduces computational cost. Simulations and applications to real data reveal that the proposed approach performs well even when the target distribution has a challenging structure.
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