Aggregate Data Resolution Enhancement Using Area-Integral Gaussian Processes
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Solution Overview
Problem
Existing methods for enhancing the resolution of aggregate data face issues such as incorrect evaluation of spatial correlation, underutilization of low-resolution auxiliary data, and inability to handle aggregate data associated with regions of varying shapes and sizes, leading to inaccurate high-resolution data prediction.
Innovation Solution
The proposed solution involves a Gaussian process model that estimates spatial scale and noise variance parameters using maximum likelihood estimation, allowing for high-resolution data computation through area integrals, and employs a multivariate Gaussian process to model multiple aggregate data sets, optimizing parameters for enhanced resolution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional Gaussian process methods are used to enhance aggregate data resolution, then high-resolution data can be predicted, but spatial correlation is evaluated incorrectly for regions with peculiar shapes
Solution Approach 1:
The patent applies local quality by using area integral operators that are specifically adapted to the geometry of each region. Instead of using a universal correlation function, the method computes area integrals of the correlation function over the specific spatial domain of each region, allowing the spatial correlation evaluation to be tailored to the local geometry of peculiar-shaped regions while maintaining overall prediction accuracy.
2Quantity of substance
If low-resolution auxiliary data is used in training, then more data is available for modeling, but the data is incorrectly deemed low reliability and ignored
Solution Approach 1:
The patent applies parameter changes by introducing a resolution-invariant reliability assessment mechanism. The method transforms the reliability evaluation from being resolution-dependent to resolution-independent by using area integral operators that normalize the correlation function over the region area. This allows low-resolution auxiliary data to be properly weighted and utilized in training without being incorrectly discarded, while still maintaining appropriate reliability assessment.
3Measurement precision
If aggregate data from multiple granularities are modeled simultaneously, then high-resolution predictions can be achieved, but the model complexity increases
Solution Approach 1:
The patent applies universality by developing a unified Gaussian process framework that can handle aggregate data from multiple granularities simultaneously. The area integral operator serves as a universal tool that works across different resolution levels, allowing the model to process both low-resolution auxiliary data and high-resolution target data through the same mathematical framework. This multi-functional approach enables high-resolution predictions while keeping the model structure relatively simple and consistent.
Data Source
AI summary
A parameter estimation section 106 is configured to perform estimation, for aggregate data in which values are associated with respective regions obtained by subdividing a space and for a Gaussian process model that expresses a plurality of aggregate data of differing partition granularity. The estimation is performed based on the Gaussian process model including a spatial scale parameter of a correlation function between regions of the aggregate data and including a noise variance parameter of the correlation function, by estimating the spatial scale parameter and the noise variance parameter so as to maximize a function expressing values of the aggregate data by area integrals of a Gaussian process. A high resolution data computation section111 is configured to perform computation in the Gaussian process model including the estimated spatial scale parameter and noise variance parameter by computing high resolution data in which the resolution of the subject aggregate data is enhanced by taking area integrals of the values of the aggregate data subject to enhancement, by computation for each region obtained by subdividing the space at the granularity indicated by the target partition.