# Sampler for Composition Ratio by Markov Chain Monte Carlo

## TL;DR

This paper introduces a novel MCMC algorithm tailored for generating composition ratios with fixed sum and sparsity constraints, facilitating creative combination of knowledge in tasks like cocktail creation.

## Contribution

It proposes a new MCMC method that effectively samples composition ratios with specific constraints, addressing limitations of existing algorithms.

## Key findings

- Successfully generated composition ratios for cocktail creation.
- Combined MCMC with supervised learning for creative problem solving.
- Demonstrated effectiveness in a practical creative task.

## Abstract

Invention involves combination, or more precisely, ratios of composition. According to Thomas Edison, "Genius is one percent inspiration and 99 percent perspiration" is an example. In many situations, researchers and inventors already have a variety of data and manage to create something new by using it, but the key problem is how to select and combine knowledge. In this paper, we propose a new Markov chain Monte Carlo (MCMC) algorithm to generate composition ratios, nonnegative-integer-valued vectors with two properties: (i) the sum of the elements of each vector is constant, and (ii) only a small number of elements is nonzero. These constraints make it difficult for existing MCMC algorithms to sample composition ratios. The key points of our approach are (1) designing an appropriate target distribution by using a condition on the number of nonzero elements, and (2) changing values only between a certain pair of elements in each iteration. Through an experiment on creating a new cocktail, we show that the combination of the proposed method with supervised learning can solve a creative problem.