Log-Likelihood Matrix Shifting for Forward Probability Calculation
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Solution Overview
Problem
Conventional methods for calculating forward probabilities in Gaussian process-hidden semi-Markov models are inefficient, leading to prolonged computation times and difficulties in tuning hyperparameters or performing real-time analysis.
Innovation Solution
An information processing device and method that store and manipulate log-likelihood matrices to efficiently calculate forward probabilities by shifting and rotating matrix components, allowing for parallel computation and reducing the need for repeated calculations across timesteps, lengths, and classes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If repeated calculation is performed for each variable (timestep, length, class) in forward filtering, then calculation accuracy is maintained, but calculation time increases significantly
Solution Approach 1:
The patent combines the separate calculations for different variables (timestep, length, class) into a unified matrix operation. By representing the forward filtering process as matrix multiplications where dimensions correspond to these variables, the system performs all necessary calculations simultaneously rather than iteratively, maintaining accuracy while reducing computational time.
Solution Approach 2:
The patent transforms the iterative calculation approach into a dimensional transformation problem. By organizing data into matrices where rows and columns represent different variables (timestep, length, class), the system solves the problem in a higher-dimensional space where parallel computation becomes feasible, converting sequential operations into concurrent matrix operations.
2Reliability
If conventional forward filtering is used to calculate forward probabilities, then theoretical correctness is ensured, but real-time analysis and hyperparameter tuning become difficult
Solution Approach 1:
The patent replaces the mechanical iterative calculation system with a mathematical matrix operation system. By substituting the step-by-step computational process with closed-form matrix expressions, the system eliminates the sequential bottleneck while preserving the theoretical correctness of the forward filtering algorithm, enabling real-time processing and efficient hyperparameter tuning.
3Loss of information
If detailed calculations are performed for all combinations of timesteps, lengths, and classes, then comprehensive results are obtained, but computational complexity increases
Solution Approach 1:
The patent segments the computational problem into distinct matrix components that represent different aspects of the calculation (transition probabilities, emission probabilities, state vectors). By dividing the overall computation into these manageable matrix segments that can be independently constructed and then combined through multiplication, the system maintains comprehensive results while reducing the apparent complexity of the implementation.
Data Source
AI summary
An information processing device that stores a log-likelihood matrix consisting of log-likelihoods as components arranged in ascending order of lengths of unit series and timesteps; that generates a shifted log-likelihood matrix by performing a shifting process of shifting the log-likelihoods to align along each line in ascending order of the lengths when the lengths and the timesteps are each increased by one unit; that generates a successive-generation probability matrix by adding the log-likelihoods from the top of each line to the respective components in the shifted log-likelihood matrix; a matrix-rotation operating unit that generates a shifted successive-generation probability matrix by shifting the successive generation probabilities in the successive-generation-probability matrix in such a manner that shift destinations and shift sources of components whose values have been shifted through the shifting process; and that calculates forward probabilities using the shifted successive-generation probability matrix.