Regression Analysis for Continuous Variables via Segmentation
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Solution Overview
Problem
Existing regression analysis methods fail to accurately estimate the mean and variance of a response variable when both are dependent on an explanatory variable, especially when the explanatory variable is continuous, and they assume homogeneity of variance or discrete time-series data.
Innovation Solution
An information processing device that partitions the domain of the explanatory variable into ranges, calculates the mean and variance for each range using observed data, selects an optimal partition based on an information criterion, and smooths the functions representing the mean and variance across the domain.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If regression analysis assumes homogeneity of variance, then the analysis is simple and straightforward, but it cannot accurately estimate mean and variance when they depend on the explanatory variable
Solution Approach 1:
The patent divides the domain of the explanatory variable into multiple ranges (segments) and performs separate mean and variance estimation for each range. This segmentation allows the model to capture non-homogeneous variance and mean dependencies without requiring complex global models, thus improving estimation accuracy while maintaining computational feasibility.
Solution Approach 2:
The patent estimates different mean and variance parameters for different ranges of the explanatory variable, allowing each local region to have its own statistical characteristics. This local quality approach enables accurate modeling of mean and variance dependence on the explanatory variable without assuming global homogeneity.
2Measurement precision
If discrete time-series data is used for regression analysis, then the analysis is computationally manageable, but it cannot estimate mean and variance when the explanatory variable is continuous
Solution Approach 1:
The patent segments the continuous domain of the explanatory variable into discrete ranges, allowing the use of discrete-like processing methods while maintaining the ability to handle continuous data. This segmentation transforms the continuous estimation problem into a series of manageable discrete range analyses.
Solution Approach 2:
The patent changes the approach by estimating mean and variance as functions of the explanatory variable through range-based partitioning, allowing continuous explanatory variables to be handled through discrete range assignments. This parameter estimation approach bridges the gap between discrete computational methods and continuous data requirements.
3Measurement precision
If the domain of explanatory variable is partitioned into multiple ranges, then mean and variance can be estimated for each range, but the number of parameters to estimate increases
Solution Approach 1:
The patent estimates mean and variance parameters for each range while using information criteria to determine the optimal number of ranges. This parameter estimation approach with model selection allows the system to adapt the number of parameters to the data, preventing overfitting while maintaining sufficient accuracy.
Solution Approach 2:
The patent uses information criteria (such as AIC or BIC) as feedback mechanisms to evaluate and select the optimal number of ranges. This feedback loop allows the system to automatically adjust the number of parameters based on data characteristics, balancing model complexity with estimation accuracy.
Data Source
AI summary
An information processing device calculates a mean and a variance of a response variable for each range determined based on a partition candidate being information on partitioning a domain of an explanatory variable into a plurality of ranges based on observed data and the mean and the variance are dependent on the explanatory variable, selects a specific partition candidate among a plurality of the partition candidates using an information criterion calculated based on the observed data and the calculated mean and variance of the response variable, and calculates a smooth function representing the variance of the response variable in the domain of the explanatory variable and a smooth function representing the mean of the response variable in the domain of the explanatory variable based on the mean and the variance calculated for each range determined based on the specific partition candidate.