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#REDIRECT [[Nonlinear dimensionality reduction]]
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The '''probabilistic learning on manifolds''' (PLoM)<ref>[https://www.aimsciences.org/article/doi/10.3934/fods.2020013 Probabilistic learning on manifolds ]</ref> is a novel type [[machine learning]] technique to construct learned datasets from a given small dataset.
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Originally proposed by [[Christian Soize]] and [[Roger Ghanem]] in 2016,<ref>[https://www.sciencedirect.com/science/article/pii/S0021999116301899 Data-driven probability concentration and sampling on manifold]</ref> the methodology has been gaining ground in several [[machine learning]] applications<ref>[https://www.sciencedirect.com/science/article/abs/pii/S0045782521001134 Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets]</ref> in [[computational science and engineering]], especially in [[inverse problems]], [[optimization]], and [[uncertainty quantification]], where it is often necessary to evaluate an extremely costly function defined by a computational model. In this context, initially, the expensive computational model is used to generate a small initial dataset, which is used in the learning process of the PLoM technique, which therefore generates (in a cheap way) a large secondary dataset whose distribution emulates the baseline dataset distribution.
== References ==
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[[Category:Applied mathematics]]
[[Category:Probability theory]]
[[Category:Statistical theory]]
[[Category:Machine learning]]
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