Parameter Vector Proposal via Low-Dimensional Subspace Extraction
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Solution Overview
Problem
Current parameter optimization methods face challenges in efficiently searching for optimal parameter vector values in high-dimensional spaces due to increased computational costs and reduced prediction accuracy, particularly in Gaussian process regression, which affects the search efficiency and accuracy of parameter vector values.
Innovation Solution
The proposed method involves determining a low-dimensional affine subspace within the D-dimensional space and extracting data points with high similarity to this subspace for use in Gaussian process regression, reducing the number of points used for inversion and improving prediction accuracy while controlling computational costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Gaussian process regression is used to search for optimal parameter vector values in high-dimensional spaces, then prediction accuracy can be maintained, but computational costs increase significantly
Solution Approach 1:
The patent extracts only the most relevant data points that are similar to the low-dimensional affine subspace from the entire high-dimensional observation data. By selecting a subset of data points with high similarity to the subspace, the method reduces the number of points used for inversion while maintaining prediction accuracy, thus lowering computational costs.
Solution Approach 2:
The patent transforms the high-dimensional parameter space into a low-dimensional affine subspace by determining an R-dimensional subspace (where R < D) that captures the essential structure of the data. This dimensionality reduction allows the Gaussian process regression to operate on a lower-dimensional representation, significantly reducing computational complexity while preserving predictive performance.
2Loss of time
If the number of data points used for Gaussian process regression is reduced to lower computational costs, then inversion time decreases, but prediction accuracy may deteriorate
Solution Approach 1:
The patent applies local quality by focusing computational resources on the specific region of the parameter space that is most relevant - the low-dimensional affine subspace. Instead of treating all data points equally, the method identifies and uses only those data points with high similarity to the subspace, creating a localized subset that maintains predictive accuracy while reducing computation time.
3Reliability
If the search space for parameter vector values is expanded to cover the entire D-dimensional space, then optimization completeness improves, but search efficiency decreases
Solution Approach 1:
The patent segments the high-dimensional parameter space into a low-dimensional affine subspace and the remaining space. By identifying the subspace that contains the essential structure of the objective function, the method effectively searches only within this segmented region, achieving both completeness (by capturing the essential structure) and efficiency (by avoiding redundant search in irrelevant regions).
Data Source
AI summary
A storage stores observation data (a set of pairs each consists of a parameter vector value representing a point in a D-dimensional space and an observation value of an objective function at the point). A processor determines a low-dimensional search space (R (2≤R<D)-dimensional affine subspace passes through a point represented by a parameter vector value in the D-dimensional space), extracts data (a set of pairs corresponding to points at which similarity to a point included in the search space are more than a predetermined value. The points are among points in the D-dimensional space represented by parameter vector values included in the observation data), and proposes a parameter vector value representing a next point based on the extracted data.