Privacy-Preserving Multicollinearity Detection via Matrix Segmentation
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Solution Overview
Problem
In machine learning, severe multicollinearity between predictive features in regression models leads to unstable and less interpretable results, especially in multi-party joint modeling scenarios where privacy security is a concern, as it increases variance of regression coefficients and reduces modeling accuracy.
Innovation Solution
A privacy protection-based multicollinearity detection method that aligns local feature data across member devices to construct a joint feature matrix, performs multi-party matrix multiplication, and determines variance inflation factors using inverse matrices, ensuring privacy security through secret sharing and data sharding techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multi-party joint modeling is performed to improve modeling accuracy, then modeling accuracy is improved, but privacy security of modeling data deteriorates
Solution Approach 1:
The patent segments the joint feature matrix into multiple submatrices and distributes them to different member devices. Each device holds only a portion of the data, preventing any single device from accessing complete private information while collectively enabling multicollinearity detection across all parties' data.
Solution Approach 2:
The patent introduces an intermediary computation mechanism where member devices perform matrix multiplication on their respective submatrices and share only the computational results (submatrices of the product matrix) rather than raw data. This intermediary step enables collaboration while maintaining privacy boundaries.
2Measurement precision
If traditional multicollinearity detection is performed on joint data, then detection accuracy is improved, but computational complexity and data security deteriorate
Solution Approach 1:
The patent divides the large-scale matrix computation into segmented submatrix operations. Each member device computes on smaller submatrices locally, reducing individual computational burden. The overall detection accuracy is maintained because the segmented operations collectively process the complete joint feature space.
Solution Approach 2:
The patent performs partial matrix multiplication operations where each device computes only the necessary submatrices of the product matrix required for variance inflation factor calculation, rather than computing the entire matrix. This partial action reduces computational complexity while sufficient for detection purposes.
3Measurement precision
If complete joint feature matrix is processed, then detection precision is improved, but privacy exposure increases
Solution Approach 1:
The patent segments the joint feature matrix X into submatrices X1, X2, ..., Xn held by different member devices. The segmentation enables processing of the complete matrix for accurate detection while ensuring no single device possesses the complete matrix, thereby preventing privacy exposure.
Solution Approach 2:
The patent transforms the privacy-sensitive raw data into privacy-protected representations through matrix operations. By working with submatrices and their products rather than original data, the patent changes the parameter representation to maintain detection precision while reducing privacy exposure.
Data Source
AI summary
One or more embodiments of the present specification provide privacy protection-based multicollinearity detection methods, apparatuses, and systems. Data alignment is performed by a member device on respective local feature data with other member devices to construct a joint feature matrix. Privacy protection-based multi-party matrix multiplication computation is performed to compute a product matrix of a transposed matrix of the joint feature matrix and the joint feature matrix. An inverse matrix of the product matrix is determined based on respective submatrices of the product matrix. A variance inflation factor of each attribute feature is determined by the member device with the other member devices using respective submatrices of the inverse matrix and the respective local feature data. Multicollinearity is determined by the member device with the other member devices based on fragment data of the variance inflation factor of each attribute feature.