Entropy-based sliced inverse regression

Hideitsu Hino, Keigo Wakayama, Noboru Murata

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    Abstract The importance of dimension reduction has been increasing according to the growth of the size of available data in many fields. An appropriate dimension reduction method of raw data helps to reduce computational time and to expose the intrinsic structure of complex data. Sliced inverse regression is a well-known dimension reduction method for regression, which assumes an elliptical distribution for the explanatory variable, and ingeniously reduces the problem of dimension reduction to a simple eigenvalue problem. Sliced inverse regression is based on the strong assumptions on the data distribution and the form of regression function, and there are a number of methods to relax or remove these assumptions to extend the applicability of the inverse regression method. However, each method is known to have its drawbacks either theoretically or empirically. To alleviate drawbacks in the existing methods, a dimension reduction method for regression based on the notion of conditional entropy minimization is proposed. Using entropy as a measure of dispersion of data, a low dimensional subspace is estimated without assuming any specific distribution nor any regression function. The proposed method is shown to perform comparable or superior to the conventional methods through experiments using artificial and real-world datasets.

    Original languageEnglish
    Pages (from-to)105-114
    Number of pages10
    JournalComputational Statistics and Data Analysis
    Volume67
    DOIs
    Publication statusPublished - 2013

    Fingerprint

    Sliced Inverse Regression
    Dimension Reduction
    Entropy
    Reduction Method
    Regression Function
    Regression
    Inverse Regression
    Elliptical Distribution
    Conditional Entropy
    Data Distribution
    Eigenvalue Problem
    Subspace
    Experiments
    Experiment

    Keywords

    • Keywords Sliced inverse regression Dimension reduction Entropy

    ASJC Scopus subject areas

    • Computational Mathematics
    • Computational Theory and Mathematics
    • Statistics and Probability
    • Applied Mathematics

    Cite this

    Entropy-based sliced inverse regression. / Hino, Hideitsu; Wakayama, Keigo; Murata, Noboru.

    In: Computational Statistics and Data Analysis, Vol. 67, 2013, p. 105-114.

    Research output: Contribution to journalArticle

    Hino, Hideitsu ; Wakayama, Keigo ; Murata, Noboru. / Entropy-based sliced inverse regression. In: Computational Statistics and Data Analysis. 2013 ; Vol. 67. pp. 105-114.
    @article{a5839adbf57e4b908158e6cbdc1d25a4,
    title = "Entropy-based sliced inverse regression",
    abstract = "Abstract The importance of dimension reduction has been increasing according to the growth of the size of available data in many fields. An appropriate dimension reduction method of raw data helps to reduce computational time and to expose the intrinsic structure of complex data. Sliced inverse regression is a well-known dimension reduction method for regression, which assumes an elliptical distribution for the explanatory variable, and ingeniously reduces the problem of dimension reduction to a simple eigenvalue problem. Sliced inverse regression is based on the strong assumptions on the data distribution and the form of regression function, and there are a number of methods to relax or remove these assumptions to extend the applicability of the inverse regression method. However, each method is known to have its drawbacks either theoretically or empirically. To alleviate drawbacks in the existing methods, a dimension reduction method for regression based on the notion of conditional entropy minimization is proposed. Using entropy as a measure of dispersion of data, a low dimensional subspace is estimated without assuming any specific distribution nor any regression function. The proposed method is shown to perform comparable or superior to the conventional methods through experiments using artificial and real-world datasets.",
    keywords = "Keywords Sliced inverse regression Dimension reduction Entropy",
    author = "Hideitsu Hino and Keigo Wakayama and Noboru Murata",
    year = "2013",
    doi = "10.1016/j.csda.2013.05.017",
    language = "English",
    volume = "67",
    pages = "105--114",
    journal = "Computational Statistics and Data Analysis",
    issn = "0167-9473",
    publisher = "Elsevier",

    }

    TY - JOUR

    T1 - Entropy-based sliced inverse regression

    AU - Hino, Hideitsu

    AU - Wakayama, Keigo

    AU - Murata, Noboru

    PY - 2013

    Y1 - 2013

    N2 - Abstract The importance of dimension reduction has been increasing according to the growth of the size of available data in many fields. An appropriate dimension reduction method of raw data helps to reduce computational time and to expose the intrinsic structure of complex data. Sliced inverse regression is a well-known dimension reduction method for regression, which assumes an elliptical distribution for the explanatory variable, and ingeniously reduces the problem of dimension reduction to a simple eigenvalue problem. Sliced inverse regression is based on the strong assumptions on the data distribution and the form of regression function, and there are a number of methods to relax or remove these assumptions to extend the applicability of the inverse regression method. However, each method is known to have its drawbacks either theoretically or empirically. To alleviate drawbacks in the existing methods, a dimension reduction method for regression based on the notion of conditional entropy minimization is proposed. Using entropy as a measure of dispersion of data, a low dimensional subspace is estimated without assuming any specific distribution nor any regression function. The proposed method is shown to perform comparable or superior to the conventional methods through experiments using artificial and real-world datasets.

    AB - Abstract The importance of dimension reduction has been increasing according to the growth of the size of available data in many fields. An appropriate dimension reduction method of raw data helps to reduce computational time and to expose the intrinsic structure of complex data. Sliced inverse regression is a well-known dimension reduction method for regression, which assumes an elliptical distribution for the explanatory variable, and ingeniously reduces the problem of dimension reduction to a simple eigenvalue problem. Sliced inverse regression is based on the strong assumptions on the data distribution and the form of regression function, and there are a number of methods to relax or remove these assumptions to extend the applicability of the inverse regression method. However, each method is known to have its drawbacks either theoretically or empirically. To alleviate drawbacks in the existing methods, a dimension reduction method for regression based on the notion of conditional entropy minimization is proposed. Using entropy as a measure of dispersion of data, a low dimensional subspace is estimated without assuming any specific distribution nor any regression function. The proposed method is shown to perform comparable or superior to the conventional methods through experiments using artificial and real-world datasets.

    KW - Keywords Sliced inverse regression Dimension reduction Entropy

    UR - http://www.scopus.com/inward/record.url?scp=84879054518&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84879054518&partnerID=8YFLogxK

    U2 - 10.1016/j.csda.2013.05.017

    DO - 10.1016/j.csda.2013.05.017

    M3 - Article

    AN - SCOPUS:84879054518

    VL - 67

    SP - 105

    EP - 114

    JO - Computational Statistics and Data Analysis

    JF - Computational Statistics and Data Analysis

    SN - 0167-9473

    ER -