Prediction Model Reformulation via Duality Theory
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Solution Overview
Problem
Existing prediction models face intractability issues due to infinitely many constraints imposed by decision makers, making it difficult to incorporate uncertainty and hard constraints effectively, especially when combining accumulated expertise with modern data.
Innovation Solution
A prediction model reformulation framework using duality theory to convert infinitely many constraints into a finite number of constraints, allowing for the formulation of tractable models that can be solved using standard solvers, such as quadratic programming solvers, by introducing additional variables to handle uncertainty and constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If infinitely many constraints are imposed by decision makers to ensure prediction accuracy, then prediction reliability is improved, but model complexity increases making the model intractable
Solution Approach 1:
The patent extracts the infinite constraints into a finite set of constraints by identifying and eliminating redundant constraints. Specifically, it separates the constraint set into essential constraints that define the uncertainty region and removes redundant ones, transforming the intractable infinite constraint problem into a tractable finite constraint optimization problem while maintaining prediction reliability.
Solution Approach 2:
The patent segments the constraint satisfaction problem into two parts: (1) identifying the uncertainty region through a finite set of constraints, and (2) optimizing the prediction model within this region. This segmentation allows the model to handle uncertainty without being overwhelmed by infinitely many individual constraints.
2Ease of operation
If standard software is used to solve the prediction model, then ease of operation is improved, but the model cannot be solved due to intractability
Solution Approach 1:
The patent extracts the intractable infinite constraints into a manageable finite constraint formulation. By removing redundant constraints and identifying the essential uncertainty region, it transforms the model into a form that can be solved by standard optimization software, thereby maintaining ease of operation while achieving model solvability.
3Measurement precision
If uncertainty parameters are incorporated with hard constraints, then prediction accuracy is improved, but the number of constraints increases making the model intractable
Solution Approach 1:
The patent extracts the essential uncertainty information into a finite set of constraints that define an uncertainty region. By identifying and retaining only the necessary constraints that capture the decision maker's uncertainty, it maintains prediction accuracy while reducing the constraint set to a tractable size.
Solution Approach 2:
The patent changes the parameter representation from infinitely many individual constraints to a finite set of parameters that define an uncertainty region. This parameter transformation allows the model to incorporate uncertainty and hard constraints while maintaining tractability through the reduced parameter space.
Data Source
AI summary
Systems and methods for formulating a prediction model. A linear prediction of an expert model is received, wherein given point xi, the linear prediction is gi:=g(xi)=gTxi+g0, the expert model having an expert model feature list. New data (xi,yi)∀i∈[1,N] is received, wherein the expert model feature list is a subset of a new feature list of the new data. The prediction model is formulated asminw∑i=1N(fi(w)-yi)2+μ(fi(w)-gi)2,wherein fx(w)≤c1, ∀x∈X, and fx(w)≤c3, ∀x∈X∩H. μ is a positive number assigning weight to the linear prediction.