The Lookup Table Regression Model for Histogram-Valued Symbolic Data

Manabu Ichino ()
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Manabu Ichino: School of Science and Engineering, Tokyo Denki University, Hatoyama, Saitama 350-0394, Japan

Stats, 2022, vol. 5, issue 4, 1-23

Abstract: This paper presents the Lookup Table Regression Model (LTRM) for histogram-valued symbolic data. We first transform the given symbolic data to a numerical data table by the quantile method. Then, under the selected response variable, we apply the Monotone Blocks Segmentation (MBS) to the obtained numerical data table. If the selected response variable and some remained explanatory variable(s) organize a monotone structure, the MBS generates a Lookup Table composed of interval values. For a given object, we search the nearest value of an explanatory variable, then the corresponding value of the response variable becomes the estimated value. If the response variable and the explanatory variable(s) are covariate but they follow to a non-monotonic structure, we need to divide the given data into several monotone substructures. For this purpose, we apply the hierarchical conceptual clustering to the given data, and we obtain Multiple Lookup Tables by applying the MBS to each of substructures. We show the usefulness of the proposed method by using an artificial data set and real data sets.

Keywords: quantile method; Lookup Table Regression Model (LTRM); Monotone Blocks Segmentation (MBS); feature selection; hierarchical clustering; Multi-Lookup Table Regression Model (M-LTRM) (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
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