BAMIFun provides Bayesian multiple imputation for functional data via low-rank penalized spline models, achieving accurate imputation and improved coverage in simulations and real datasets compared to single-imputation FPCA methods.
arXiv preprint arXiv:1708.06897 , year=
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abstract
In an era where big and high-dimensional data is readily available, data scientists are inevitably faced with the challenge of reducing this data for expensive downstream computation or analysis. To this end, we present here a new method for reducing high-dimensional big data into a representative point set, called projected support points (PSPs). A key ingredient in our method is the so-called sparsity-inducing (SpIn) kernel, which encourages the preservation of low-dimensional features when reducing high-dimensional data. We begin by introducing a unifying theoretical framework for data reduction, connecting PSPs with fundamental sampling principles from experimental design and Quasi-Monte Carlo. Through this framework, we then derive sparsity conditions under which the curse-of-dimensionality in data reduction can be lifted for our method. Next, we propose two algorithms for one-shot and sequential reduction via PSPs, both of which exploit big data subsampling and majorization-minimization for efficient optimization. Finally, we demonstrate the practical usefulness of PSPs in two real-world applications, the first for data reduction in kernel learning, and the second for reducing Markov Chain Monte Carlo (MCMC) chains.
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UNVERDICTED 2representative citing papers
SKMD adapts Stein variational gradient descent into molecular dynamics with asynchronous updates and global atomic descriptor kernels to acquire non-redundant training configurations while preserving the Boltzmann distribution, yielding higher MLIP accuracy with fewer samples than baselines.
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BAMIFun: Bayesian Multiple Imputation for Functional Data
BAMIFun provides Bayesian multiple imputation for functional data via low-rank penalized spline models, achieving accurate imputation and improved coverage in simulations and real datasets compared to single-imputation FPCA methods.
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Stein Kernelized Molecular Dynamics for Active Learning of Interatomic Potentials
SKMD adapts Stein variational gradient descent into molecular dynamics with asynchronous updates and global atomic descriptor kernels to acquire non-redundant training configurations while preserving the Boltzmann distribution, yielding higher MLIP accuracy with fewer samples than baselines.