Kernel Mean Construction for High-Dimensional Parameter Estimation
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Solution Overview
Problem
Existing parameter estimation methods, such as Approximate Bayesian Computation (ABC), face challenges with high-dimensional parameters, inefficient search for significant candidates, and acceptance of unnecessary parameters based on mistaken knowledge, leading to decreased accuracy and increased calculation time. Additionally, previous methods struggle with estimating pedestrian-flow patterns without preliminary data on individual activities and may invade privacy or fail to provide detailed round-trip behavior analysis.
Innovation Solution
A parameter estimation system using a machine learning device that acquires samples from a prior distribution, constructs a kernel mean of a posterior distribution, and evaluates new samples based on similarity to correct data, reducing the number of simulations required and improving accuracy by repetitive learning with Kernel ABC and Kernel Herding techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Approximate Bayesian Computation (ABC) is used to estimate high-dimensional parameters, then parameter estimation can be performed, but the calculation time increases significantly and accuracy decreases
Solution Approach 1:
The patent applies Automatic Relevance Determination (ARD) as a preliminary action to identify and prioritize significant parameters before performing the main ABC estimation process. This preliminary filtering reduces the dimensionality of the parameter space, allowing the subsequent ABC algorithm to operate more efficiently with fewer calculations while maintaining or improving accuracy.
Solution Approach 2:
The patent extracts and removes redundant or less significant parameters from the high-dimensional parameter set using ARD. By taking out only the essential parameters that contribute meaningfully to the estimation accuracy, the system reduces computational burden and calculation time while preserving the core estimation quality.
2Productivity
If ABC performs simulation with randomly selected parameters, then parameter estimation can be conducted, but inefficient search occurs on less significant parameter candidates
Solution Approach 1:
ARD is applied as a preliminary action to rank and identify significant parameters before the ABC simulation process. This preliminary classification allows the system to focus computational resources on parameters that matter most, eliminating useless calculation time spent on insignificant parameters.
Solution Approach 2:
The patent applies different treatment to different parameters based on their significance. Significant parameters identified by ARD receive focused attention and more rigorous evaluation in the ABC process, while less significant parameters are either simplified or excluded. This local differentiation of quality and effort improves overall productivity.
3Measurement precision
If ABC accepts parameters based on prior knowledge, then estimation can proceed, but unnecessary parameters are accepted due to mistaken knowledge
Solution Approach 1:
The patent implements a feedback mechanism where ARD continuously evaluates parameter significance based on the data and estimation results. This feedback loop allows the system to correct mistaken prior knowledge by identifying which parameters actually contribute to accuracy and which do not, dynamically adjusting the parameter set to eliminate unnecessary dimensions.
Solution Approach 2:
The system dynamically changes the effective parameter dimensionality by using ARD to identify and retain only the significant parameters. This parameter transformation reduces the complexity from the original high-dimensional space to a lower-dimensional space containing only the essential parameters, improving both accuracy and manageability.
Data Source
AI summary
A first sample acquisition unit acquires a parameter sample from a prior distribution. A function execution unit acquires data from a distribution by supplying the sample to a function. A degree-of-similarity calculation unit calculates the degree of similarity between the data and correct data using a kernel function. A kernel mean construction unit constructs a kernel mean of a posterior distribution from the degree of similarity, the sample, and the kernel function. A second sample acquisition unit acquires a new parameter sample from the kernel mean and the kernel function. A sample evaluation unit determines whether the difference between new data obtained by supplying one sample selected from the new samples to the function and the correct data is less than a prescribed threshold value. When it is determined that the difference is less than the prescribed threshold value, the sample evaluation unit estimates the selected sample as a parameter. The present invention enables estimation of a high-dimensional parameter of the function, thus making it possible to reduce calculation time.