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Abstract:
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Gaussian processes, a class of nonparametric models, are widely used in geometric data modeling due to their flexibility in adapting to the data’s structure. However, collections of curves and surfaces often share structural similarities. Therefore, effective modeling of the dependence between objects can help aid in the efficient extraction of this information. In this work, we propose a multiple-output, multidimensional Gaussian process framework. This model more adequately captures dependence at multiple levels, allowing for proper characterization of uncertainty in closed curve fitting. We illustrate the proposed methodological advances, and demonstrate the utility of meaningful uncertainty quantification on several curve and shape-related tasks. This model-based approach not only addresses the problem of inference on closed curves (and their shapes) with kernel constructions, but also opens doors to nonparametric modeling of multi-level dependence for functional objects.
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