A simple mechanism for the roommate problem

Gale and Shapley (1962) proposed that there is a similar game to the marriage problem called "the roommate problem". And, they showed that unlike the marriage problem, the roommate problem may have unstable solutions. In other words, the stability theorem fails for the roommate problem. In this paper, we propose a new mechanism for the roommate problem. The mechanism is successful in determining the reason of instability in our game scenario. And, we show that our mechanism implements the full set of stable matchings in the existence of stability, and it ends up with Pareto Optimal matching in the instance of instability

A new dynamic mechanism to the marriage problem with a variant

We know from Gale and Shapley (1962) that every Two-Sided Matching Game has a stable solution. It is also well-known that the number of stable matchings increases with the number of agents on both sides. In this paper, we propose two mechanisms, one of which is a variant of the other, to the marriage problem. Our original mechanism implements the full set of stable matchings for any preference profile. On the other hand, the variant mechanism parititons the domain of preference profiles into two; for one set, it implements the full set of stable matchings like the original mechanism and for the other, it ends up with a proper subset of the set of stable matchings. Besides, for some profiles with multi stability, it gives one of the optimal stable matchings. Namely, the second mechanism coincides either with the original mechanism or it is an improvement for one side; and in some profiles, the algortihm induces Gale and Shapley's algorithm for some profiles. Thus, it is a "middle" mechanism

Calibration of conditional composite likelihood for Bayesian inference on Gibbs random fields

Gibbs random fields play an important role in statistics, however, the resulting likelihood is typically unavailable due to an intractable normalizing constant. Composite likelihoods offer a principled means to construct useful approximations. This paper provides a mean to calibrate the posterior distribution resulting from using a composite likelihood and illustrate its performance in several examples.Comment: JMLR Workshop and Conference Proceedings, 18th International Conference on Artificial Intelligence and Statistics (AISTATS), San Diego, California, USA, 9-12 May 2015 (Vol. 38, pp. 921-929). arXiv admin note: substantial text overlap with arXiv:1207.575