Probability Function Estimation via Fluctuation
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Solution Overview
Problem
Existing methods for estimating probability functions based on data face challenges such as over-learning with small data sets, difficulty in setting objective prior beliefs, and lack of theoretical coherence, especially in multivariate cases, leading to suboptimal estimations and accuracy issues.
Innovation Solution
An information processing apparatus and method that calculates a probability function with highest likelihood and canonical distribution, using fluctuation as a parameter, without setting additional parameters, allowing for robust estimation of probability functions through recursive calculations and statistical hypothesis testing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If relative frequency is used to estimate probability function, then estimation can be performed without prior knowledge, but over-learning occurs when data amount is small
Solution Approach 1:
The patent changes the parameter from relative frequency to fluctuation (standard deviation), and introduces a transformation function that maps fluctuation to a probability distribution. This transformation automatically adjusts the estimation based on the amount of data, preventing over-learning when data is scarce while maintaining ease of operation without requiring prior knowledge setting.
2Reliability
If Bayesian statistics with prior distribution is used, then over-learning can be avoided, but objective prior belief cannot be set when analyzer has no prior knowledge
Solution Approach 1:
The patent enables the system to automatically determine the appropriate probability distribution and parameters based on the data itself through fluctuation calculation and transformation function application. This self-service mechanism eliminates the need for external prior knowledge or subjective prior belief setting, allowing objective analysis while maintaining estimation robustness.
3Adaptability or versatility
If equivalent sample size parameter is used for Bayesian network structure, then multivariable estimation can be performed, but optimum value varies considerably for each data set and optimization is difficult
Solution Approach 1:
The patent extracts the essential information needed for probability estimation from the data through fluctuation calculation, and applies a universal transformation function that handles both univariate and multivariable cases. This approach eliminates the need for separate optimization procedures for different data sets, reducing complexity while maintaining versatility.
4Reliability
If free energy minimization principle is used for probability estimation, then robust estimation can be achieved, but temperature parameter must be set and optimization is not achieved
Solution Approach 1:
The patent calculates fluctuation from the data itself and uses this self-determined value as the basis for probability distribution transformation. This eliminates the need for external temperature parameter setting while maintaining the robust estimation capabilities of free energy minimization approaches.
Data Source
AI summary
A probability function with highest likelihood is calculated based on data. A canonical distribution in statistical physics and a temperature parameter of the canonical distribution are calculated as a fluctuation of the data. A probability function is estimated using the calculated probability function with the highest likelihood, the calculated fluctuation, and the canonical distribution. The present technology is applicable to an apparatus that estimates and uses a probability function.