MAP Sample Size Estimation Using Convex Cost Flow
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Solution Overview
Problem
Existing methods fail to provide a means for estimating the sample size M in Collective Graphical Models (CGMs) when it is not given in advance, making efficient MAP estimation difficult.
Innovation Solution
A sample size estimation device and method that linearly approximates the concave function part of the MAP estimation problem using a minimum convex cost flow problem, allowing for simultaneous estimation of the sample size M and MAP solution through a discrete DC algorithm.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the MAP estimation problem is solved directly without sample size estimation, then the estimation accuracy is improved, but the computational complexity increases because the sample size M is not given in advance
Solution Approach 1:
The patent segments the MAP estimation problem into two parts: first estimating the sample size M using the concave-convex procedure, then performing the actual MAP estimation with the estimated M. This segmentation reduces the overall computational complexity by breaking down the intractable problem into manageable subproblems.
Solution Approach 2:
The patent changes the parameter M (sample size) from an unknown variable to an estimated value through the concave-convex procedure. By estimating M first and then using it in the MAP estimation, the method transforms the original intractable problem into a solvable one while maintaining estimation accuracy.
2Speed
If the concave function part is linearly approximated using minimum convex cost flow problem, then the convergence speed is improved, but the approximation error increases
Solution Approach 1:
The patent introduces a minimum convex cost flow problem as an intermediary to approximate the concave function part of the MAP estimation problem. This intermediary formulation enables efficient computation through convex optimization techniques while maintaining sufficient accuracy for practical applications.
Solution Approach 2:
The patent transforms the concave optimization problem into a convex cost flow problem by changing the mathematical formulation. This parameter transformation allows the use of efficient convex optimization algorithms that converge faster while providing acceptable approximation accuracy.
Data Source
AI summary
A sample size estimation device includes an input unit, a cost function approximation unit, a network construction unit, a minimum convex cost flow problem solving unit, an estimation control unit, and an output unit. The network construction unit creates an instance of a minimum convex cost flow problem from a linearly approximated objective function approximated by the cost function approximation unit. The minimum convex cost flow problem solving unit obtains an optimum solution of the instance of the minimum convex cost flow problem. The estimation control unit controls and executes a whole MAP estimation by issuing a command while exchanging data with the cost function approximation unit, the network construction unit, and the minimum convex cost flow problem solving unit. The estimation control unit also obtains a MAP estimation solution from the optimum solution of the instance. The output unit outputs the obtained MAP estimation solution.