Extended regression on manifolds estimation

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    4 Citations (Scopus)

    Abstract

    Let f(X) be unknown smooth function which maps p-dimensional manifold-valued inputs X, whose values lie on unknown Input manifold M of lower dimensionality q < p embedded in an ambient high-dimensional space Rp, to m-dimensional outputs. Regression on manifold problem is to estimate a triple (f(X), Jf(X), M), which includes Jacobian Jf of the mapping f, from given sample consisting of ‘input-output’ pairs. If some mapping h transforms Input manifold M to q-dimensional Feature space Yh = h(M) and satisfies certain conditions, initial estimating problem can be reduced to Regression on feature space problem consisting in estimating of triple (gf(y), Jg,f(y), Yh) in which unknown function gf(y) depends on low-dimensional features y = h(X) and satisfies the condition gf(h(X)) ≈ f(X), and Jg,f is its Jacobian. The paper considers such Extended problem and presents geometrically motivated method for estimating both triples from given sample.

    Original languageEnglish
    Title of host publicationConformal and Probabilistic Prediction with Applications - 5th International Symposium, COPA 2016, Proceedings
    EditorsJesus Vega, Alexander Gammerman, Zhiyuan Luo, Vladimir Vovk
    PublisherSpringer Verlag
    Pages208-228
    Number of pages21
    ISBN (Print)9783319333946
    DOIs
    Publication statusPublished - 2016
    Event5th International Symposium on Conformal and Probabilistic Prediction with Applications, COPA 2016 - Madrid, Spain
    Duration: 20 Apr 201622 Apr 2016

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume9653
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Conference

    Conference5th International Symposium on Conformal and Probabilistic Prediction with Applications, COPA 2016
    Country/TerritorySpain
    CityMadrid
    Period20/04/1622/04/16

    Keywords

    • Input manifold estimation
    • Jacobian estimation
    • Regression on feature space
    • Regression on manifolds
    • Tangent bundle manifold learning

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