Kernel Selection via Symbolic Representation for Bayesian Optimization
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Solution Overview
Problem
Current machine learning models for predicting variables in technical systems are inefficient in terms of computing resource consumption, particularly in Bayesian optimization processes, as they require extensive calculations to determine kernel differences in functional spaces.
Innovation Solution
The method involves representing kernels using symbols that characterize operators and their applications, allowing for the calculation of distances between kernels based on symbol frequencies, which reduces computational complexity and speeds up the Bayesian optimization process by using a condensed statistical representation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If kernel differences are determined in functional spaces using traditional methods, then measurement precision is improved, but computing time and resource consumption increase significantly
Solution Approach 1:
The patent creates a symbolic representation (copy) of kernels that captures their essential characteristics without requiring full functional space computations. This symbolic copy enables distance determination through simpler operations while preserving the necessary information for accurate kernel difference determination.
Solution Approach 2:
The patent replaces the mechanical computation of kernel differences in functional spaces with a symbolic processing system. Instead of performing complex mathematical operations in functional spaces, the system uses symbol manipulation and frequency-based distance calculations, which are computationally more efficient.
2Measurement precision
If traditional Bayesian optimization is used for kernel selection, then selection accuracy is improved, but device complexity and computing resources increase
Solution Approach 1:
The patent extracts the essential characteristics of kernels into symbolic representations, separating the critical information needed for selection from the computationally intensive functional space descriptions. This extraction enables simpler comparison operations while maintaining selection accuracy.
Solution Approach 2:
The patent changes the parameters used for kernel comparison from full functional space representations to symbolic frequency-based parameters. This parameter transformation reduces the dimensionality and computational complexity of the selection process while preserving the ability to accurately distinguish between kernels.
3Measurement precision
If full kernel comparisons are performed in functional spaces, then prediction accuracy is improved, but computing resources and energy consumption increase
Solution Approach 1:
The patent creates compact symbolic copies of kernels that retain the essential information needed for accurate predictions. These symbolic representations require significantly fewer computing resources to process while maintaining the predictive capability of the original full-kernel approach.
Solution Approach 2:
The patent performs partial comparisons using symbolic representations rather than complete functional space computations. This partial action approach provides sufficient information for accurate predictions without the excessive computational resources required by full kernel comparisons.
Data Source
AI summary
A device and a computer-implemented method for determining a variable of a technical system, using a machine learning model. A kernel for the model is selected from a set of kernels as a function of a selection criterion, and a first data set which includes mutually assigned input variables and output variables of the technical system. The selection criterion is determined for a kernel that is selected from the set of kernels as a function of an acquisition function, the acquisition function being determined as a function of a second data set that includes pairs of kernels from the set of kernels and a selection criterion. The pairs of kernels are determined over respectively one pair of kernels from the set of kernels and as a function of the second data set. Representations of a first and second kernel are provided.