Regression Analysis With Inexact Feedback Using Approximate Parameters
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Solution Overview
Problem
Traditional mathematical regression methods are hindered by the difficulty or impossibility of obtaining exact feedback on desired output values, which can be costly, unreliable, or ambiguous, limiting their effectiveness in providing accurate regression analysis.
Innovation Solution
A method for conducting regression analysis using inexact feedback, involving the selection of a regression model, initial parameters, and iterative optimization with the ability to update and change loss functions and optimization methods based on user feedback, allowing for improved regression value generation and prevention of overfitting.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional regression methods use exact feedback on desired output values, then measurement precision is improved, but ease of operation deteriorates due to difficulty in obtaining exact feedback
Solution Approach 1:
The patent uses approximate or placeholder values instead of requiring exact desired output values. These approximate values serve as temporary substitutes that allow the regression process to continue without needing precise feedback, effectively using 'cheap' approximations rather than 'expensive' exact measurements.
Solution Approach 2:
The patent changes the parameter requirements from exact desired output values to approximate values or relative comparisons. By modifying the input parameters from precise numerical values to less stringent specifications (such as relative rankings or approximate ranges), the system makes regression feasible when exact feedback is unavailable.
2Manufacturing precision
If regression analysis requires exact desired dependent variables, then manufacturing precision is improved, but productivity deteriorates due to time and resource costs
Solution Approach 1:
The patent applies partial action by not requiring complete exactness for all desired output values. Instead of demanding precise values for every data point, the system accepts approximate values or relative comparisons for some points, allowing the regression process to proceed with incomplete but sufficient information.
Solution Approach 2:
The patent substitutes expensive exact measurements with cheaper approximate values or relative comparisons. These approximate values are sufficient for training the regression model without requiring the time and resources needed to obtain precise desired output values for every sample.
3Measurement precision
If regression models are trained with strict loss functions requiring exact values, then measurement precision is improved, but adaptability deteriorates for ambiguous or relative values
Solution Approach 1:
The patent modifies the loss function parameters to accommodate approximate values and relative comparisons. Instead of using traditional loss functions that require exact target values, the system employs modified loss functions that can handle ambiguous data, relative rankings, or incomplete information, thereby increasing adaptability.
Solution Approach 2:
The patent creates a universal regression framework that can handle multiple types of input data including exact values, approximate values, relative comparisons, and ambiguous information. This multi-functional approach allows the same regression system to adapt to different data quality levels and feedback types.
Data Source
AI summary
The present invention provides methods for providing mathematical regression analysis. In particular, the method for conducting regression analysis comprises the steps of: selecting a regression model; selecting an initial set of regression parameters; applying the regression model to the initial set of regression parameters to create an initial set of regression values; selecting an improved set of regression values, wherein the improved set of regression values is selected from the set of initial regression values; generating a loss function based on the improved set; applying an iterative optimization method to the loss function and the improved set of regression values to generate a resultant set of regression values; and outputting the resultant set of regression values.