Mixture Model Estimation via Hidden Variable Variation Probability
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for estimating the number and types of mixture models in multivariate data face challenges such as nonregular Fisher information matrices, improper criteria selection, and excessive computational complexity, especially when dealing with exponentially increasing model candidates.
Innovation Solution
A mixture model estimation device and method that calculates the variation probability of a hidden variable to optimize the types and parameters of components, maximizing the lower bound of the model posterior probability for each component, thereby enabling rapid and proper model selection.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the number and types of mixture models are increased to improve model selection accuracy, then the model selection accuracy is improved, but the computational complexity increases exponentially
Solution Approach 1:
The patent segments the model selection process into two distinct stages: (1) a rough selection stage using a simplified criterion to filter candidate models, and (2) a precise selection stage using the lower bound criterion to select from the filtered candidates. This segmentation reduces computational complexity by avoiding exhaustive evaluation of all possible models while maintaining selection accuracy through the two-stage approach.
Solution Approach 2:
The patent performs preliminary filtering of candidate models using a computationally simpler criterion before applying the more accurate but computationally intensive lower bound criterion. This preliminary action eliminates obviously suboptimal models early in the process, reducing the number of models that require full evaluation and thus lowering overall computational complexity.
2Adaptability or versatility
If the number of candidate models increases to cover more possibilities, then the model selection comprehensiveness is improved, but the time required for evaluation increases exponentially
Solution Approach 1:
The patent divides the evaluation process into two phases: an initial rapid filtering phase that quickly eliminates poor candidates, and a detailed evaluation phase for the remaining candidates. This segmentation allows comprehensive model coverage without requiring full evaluation of all candidates, thus reducing evaluation time while maintaining comprehensiveness.
Solution Approach 2:
The patent performs preliminary filtering using a simplified criterion to identify a subset of promising candidate models before applying the full lower bound criterion. This preliminary action reduces the number of models requiring time-consuming detailed evaluation, thereby reducing overall evaluation time while still maintaining comprehensive model selection capability.
3Measurement precision
If the Fisher information matrix is used for model selection, then the model selection criterion is established, but the matrix becomes nonregular and proper criteria cannot be defined
Solution Approach 1:
The patent introduces a lower bound criterion as an intermediary that avoids the mathematical problems of the Fisher information matrix. Instead of directly using the problematic Fisher matrix, the patent derives a lower bound criterion that provides reliable model selection without encountering the nonregularity issues, thus maintaining both criterion establishment and validity.
Data Source
AI summary
With respect to the model selection issue of a mixture model, the present invention performs high-speed model selection under an appropriate standard regarding the number of model candidates which exponentially increases as the number and the types to be mixed increase. A mixture model estimation device comprises: a data input unit to which data of a mixture model to be estimated, candidate values of the number of mixtures which are required for estimating the mixture model of the data, and types of components configuring the mixture model and parameters thereof, are input; a processing unit which sets the number of mixtures from the candidate values, calculates, with respect to the set number of mixtures, a variation probability of a hidden variable for a random variable which becomes a target for mixture model estimation of the data, and estimates the optimal mixture model by optimizing the types of the components and the parameters therefor using the calculated variation probability of the hidden variable so that the lower bound of the posterior probabilities of the model separated for each component of the mixture model can be maximized; and a model estimation result output unit which outputs the model estimation result obtained by the processing unit.