From Low- to High-Dimensional Moments Without Magic |
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Authors: | Bernhard G. Bodmann Martin Ehler Manuel Gräf |
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Affiliation: | 1.Department of Mathematics,University of Houston,Houston,USA;2.Department of Mathematics,University of Vienna,Vienna,Austria;3.Acoustics Research Institute,Austrian Academy of Sciences,Vienna,Austria |
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Abstract: | We aim to compute the first few moments of a high-dimensional random vector from the first few moments of a number of its low-dimensional projections. To this end, we identify algebraic conditions on the set of low-dimensional projectors that yield explicit reconstruction formulas. We also provide a computational framework, with which suitable projectors can be derived by solving an optimization problem. Finally, we show that randomized projections permit approximate recovery. |
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