Streamwise Feature Selection for Generalized Linear Models
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Solution Overview
Problem
Generalized Linear Models (GLMs) face challenges with computational intensity and multicollinearity as the number of attributes increases, leading to inefficiencies and decreased interpretability, particularly in high-dimensional datasets.
Innovation Solution
The streamwise feature selection method is extended to provide efficient and scalable model selection for GLMs by constructing and scoring candidate features singly, using adaptive penalties and statistical hints to reorder features based on correlation with the target attribute and model residuals, and implementing caching strategies to optimize computational efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If the number of input attributes increases to model larger datasets, then the model's coverage and applicability improve, but computational intensity increases with cubic scaling
Solution Approach 1:
The patent segments the feature selection process into iterative steps where features are added one at a time to the GLM model. Instead of evaluating all possible feature combinations simultaneously, the method divides the problem into sequential stages: (1) identify candidate features, (2) add one feature to the model, (3) evaluate model fit, (4) repeat until stopping criteria is met. This segmentation reduces computational intensity from cubic to linear scaling with the number of attributes.
Solution Approach 2:
The patent performs preliminary filtering and scoring of candidate features before they are added to the model. Features are pre-evaluated based on their individual correlation with the target variable and their potential contribution to model fit. This preliminary action allows the method to prioritize promising features and avoid exhaustive evaluation of all possible combinations, thereby reducing computational burden while maintaining model coverage.
2Adaptability or versatility
If the number of input attributes increases, then more candidate features can be constructed, but the likelihood of encountering multicollinearity increases causing numerical instability
Solution Approach 1:
The patent employs a dynamic feature selection process that adaptively adjusts the model composition based on the current state of feature inclusion. At each iteration, the method evaluates candidate features in the context of already-selected features, dynamically determining which features to add next. This dynamic approach allows the model to maintain feature diversity while monitoring for multicollinearity, as features that would cause numerical instability can be identified and excluded through iterative evaluation of model fit and feature correlations.
Solution Approach 2:
The patent incorporates feedback mechanisms where the model continuously evaluates the impact of adding each candidate feature. After each feature addition, the system assesses model performance metrics and feature correlations to determine whether the new feature contributes meaningfully or introduces multicollinearity. This feedback loop enables the method to maintain numerical stability by rejecting features that would cause instability while preserving feature diversity through selective inclusion of beneficial features.
3Loss of information
If the number of attributes increases, then more information is available for modeling, but interpretability of the GLM declines
Solution Approach 1:
The patent extracts and selects only the most relevant features from the large set of candidate features, rather than including all available attributes in the final model. By iteratively evaluating and selecting features based on their individual contribution to model fit, the method extracts the essential information needed for accurate prediction while excluding redundant or less important features. This extraction process maintains information retention for key predictors while improving interpretability by reducing the total number of features in the final model.
4Measurement precision
If all candidate features are evaluated simultaneously, then the best model can be identified, but the computational cost becomes prohibitive
Solution Approach 1:
The patent segments the model selection process into iterative steps where features are evaluated and added one at a time. Instead of simultaneously evaluating all candidate features and their combinations, the method divides the problem into sequential stages: (1) identify candidate features, (2) evaluate each candidate's contribution, (3) add the best candidate, (4) repeat until stopping criteria. This segmentation maintains model selection accuracy by systematically evaluating features while improving computational efficiency from cubic to linear scaling.
Solution Approach 2:
The patent applies partial action by evaluating only a subset of candidate features at each iteration rather than all possible features simultaneously. The method prioritizes features based on preliminary scoring and evaluates them in order of expected importance, performing full model fitting only for the most promising candidates. This partial evaluation approach maintains sufficient model selection accuracy while dramatically reducing computational cost compared to exhaustive evaluation of all feature combinations.
Data Source
AI summary
Systems, methods, and other embodiments associated with feature generation and model selection for generalized linear models are described. In one embodiment, a method includes ordering candidate features in a dataset being considered by a streamwise feature selection process according to an inclusion score that reflects a likelihood that a given candidate feature will be included in the GLM. The ordered candidate features are provided to the streamwise feature selection process for acceptance testing. In one embodiment, the method also includes selecting penalty criterion for use in the acceptance testing that is based on characteristics of the dataset.