Explanatory Variable Selection Using Sign Condition Constraints
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Solution Overview
Problem
Existing statistical models face challenges in efficiently selecting appropriate explanatory variables, especially when dealing with a large number of candidate variables, as traditional methods like brute-force regression and stepwise regression are computationally intensive or do not always yield optimal results.
Innovation Solution
An apparatus and method that utilize a variable selecting model to acquire sign conditions for coefficients, estimate coefficients and constants, and select explanatory variables based on non-zero estimates, allowing for efficient selection even from a large set of candidates while ensuring sign consistency and flexibility.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If brute-force regression is used to select explanatory variables, then the precision of variable selection is improved, but the computational load increases exponentially
Solution Approach 1:
The invention transforms the variable selection problem from a combinatorial optimization problem into a parameter estimation problem by introducing sign conditions on coefficients. Instead of evaluating all possible variable combinations, the method estimates coefficients under constrained sign conditions, changing the problem parameters from discrete variable selection to continuous parameter optimization with constraints.
Solution Approach 2:
The invention applies local quality by focusing the search space through sign conditions on individual coefficients. Rather than treating all variable combinations equally, it imposes local constraints (sign conditions) on coefficient estimates, allowing efficient exploration of promising regions in the parameter space while avoiding exhaustive enumeration of all possibilities.
2Productivity
If stepwise regression is used to reduce computational load, then the computational efficiency is improved, but the precision of variable selection deteriorates
Solution Approach 1:
The invention performs preliminary action by establishing sign conditions on coefficients before conducting the estimation. These pre-specified sign constraints guide the estimation process toward theoretically plausible solutions, ensuring that the computationally efficient method does not sacrifice precision by exploring implausible regions of the parameter space.
Solution Approach 2:
The method incorporates feedback through the sign condition constraints that guide the estimation process. By continuously checking whether coefficient estimates satisfy the predetermined sign conditions, the method provides feedback that steers the optimization toward valid solutions, maintaining precision while achieving computational efficiency.
3Use of energy by moving object
If lasso regression or elastic net is used for variable selection, then the computational load is reduced, but the selection accuracy deteriorates due to hyperparameter dependency
Solution Approach 1:
The invention extracts the sign condition constraints from the estimation process and applies them as preliminary conditions. By separating the sign condition specification from the coefficient estimation, the method eliminates the need for hyperparameter tuning that plagues lasso and elastic net methods, achieving both computational efficiency and selection accuracy without arbitrary parameter choices.
Data Source
AI summary
Provided is an apparatus which selects desired explanatory variables from a plurality of candidate explanatory variables in a statistical model that expresses, by a predetermined function, a relationship between a linear predictor and an expectation value of a response variable or a probability of the response variable having certain values, by using a variable selecting model that expresses the linear predictor as a sum of a constant and a linear combination of the candidate explanatory variables and their corresponding coefficients, the apparatus including a sign condition acquisition unit for acquiring sign conditions for at least one of the coefficients; an estimator for calculating an estimate of the respective coefficients and an estimate of the constant under the sign conditions, using plural data; and a selection unit for selecting, as the desired explanatory variable, the candidate explanatory variable corresponding to the coefficient of which the estimate is calculated to be non-zero.