  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.
