Parallel Difference Calculation for MCMC Convergence
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Solution Overview
Problem
When parallelizing the Markov Chain Monte Carlo method, convergence to the target probability distribution is violated, and high parallelization efficiency cannot be obtained, as seen in existing techniques that do not guarantee convergence and often reject results except for one variable, leading to inefficiencies in sampling methods.
Innovation Solution
An information processing device and method that calculate differences between evaluation functions in parallel and modify these differences to cancel errors, ensuring convergence of the dynamical system while maintaining high parallelization efficiency by replicating sequential difference calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the Markov Chain Monte Carlo method is parallelized by calculating differences for multiple variables simultaneously, then parallelization efficiency is improved, but convergence to the target probability distribution is violated
Solution Approach 1:
The patent applies preliminary action by calculating the differences between evaluation functions for all selected variables in parallel before any state updates are performed. This ensures that all difference calculations are based on the same initial state, preventing the convergence violation that occurs when calculations are done sequentially and intermediate updates affect subsequent calculations.
Solution Approach 2:
The patent uses copying by creating a snapshot of the current state and using this copied state as the basis for all parallel difference calculations. This ensures that each parallel calculation thread operates on an identical copy of the state, maintaining the mathematical properties required for convergence while achieving parallelization efficiency.
2Reliability
If difference calculations are performed sequentially for each variable, then convergence is maintained, but processing time increases
Solution Approach 1:
The patent performs all necessary difference calculations in advance before state updates, allowing these calculations to be executed in parallel rather than sequentially. This preliminary parallel calculation phase maintains convergence properties while dramatically reducing the total processing time compared to sequential execution.
Solution Approach 2:
The patent transitions from sequential single-threaded difference calculation to parallel multi-threaded calculation by adding the dimension of parallel execution. Multiple difference calculations that would traditionally be performed one after another are instead executed simultaneously across multiple processing units, reducing processing time while maintaining mathematical correctness through the use of state snapshots.
Data Source
AI summary
In order to satisfy both of convergence of a dynamical system and high parallelization efficiency when obtaining samples that follow a probability distribution, the information processing device 10 includes a processing unit 20 having a difference calculator 11 which calculates differences between evaluation functions in parallel when changing a state of each of variables selected from a plurality of variables, and a difference modification unit 12 which modifies the difference calculated by the difference calculator 11 so as to cancel an error between a sequentially calculated difference.