Efficiency of Stochastic Transfers in a Directed Graph

A mathematical model of a directed graph with stochastic transfers is presented. It will be used to analyze the optimality (or "competitiveness") properties of a network of transactions involving risky transfers of assets in an economic system. These properties are discussed in a model with some specific directed graph structures which result in a decomposition of the graph into parts with "narrow" linkage.

Free resolutions of Dynkin format and the licci property of grade 3 perfect ideals

Recent work on generic free resolutions of length 3 attaches to every resolution a graph and suggests that resolutions whose associated graph is a Dynkin diagram are distinguished. We conjecture that in a regular local ring, every grade 3 perfect ideal whose minimal free resolution is distinguished in this way is in the linkage class of a complete intersection.Comment: Minor edits. Final version, to appear in Math. Scand., 13 p

Use of graph theory measures to identify errors in record linkage

Ensuring high linkage quality is important in many record linkage applications. Current methods for ensuring quality are manual and resource intensive. This paper seeks to determine the effectiveness of graph theory techniques in identifying record linkage errors. A range of graph theory techniques was applied to two linked datasets, with known truth sets. The ability of graph theory techniques to identify groups containing errors was compared to a widely used threshold setting technique. This methodology shows promise; however, further investigations into graph theory techniques are required. The development of more efficient and effective methods of improving linkage quality will result in higher quality datasets that can be delivered to researchers in shorter timeframes

A Bayesian Approach to Graphical Record Linkage and De-duplication

We propose an unsupervised approach for linking records across arbitrarily many files, while simultaneously detecting duplicate records within files. Our key innovation involves the representation of the pattern of links between records as a bipartite graph, in which records are directly linked to latent true individuals, and only indirectly linked to other records. This flexible representation of the linkage structure naturally allows us to estimate the attributes of the unique observable people in the population, calculate transitive linkage probabilities across records (and represent this visually), and propagate the uncertainty of record linkage into later analyses. Our method makes it particularly easy to integrate record linkage with post-processing procedures such as logistic regression, capture-recapture, etc. Our linkage structure lends itself to an efficient, linear-time, hybrid Markov chain Monte Carlo algorithm, which overcomes many obstacles encountered by previously record linkage approaches, despite the high-dimensional parameter space. We illustrate our method using longitudinal data from the National Long Term Care Survey and with data from the Italian Survey on Household and Wealth, where we assess the accuracy of our method and show it to be better in terms of error rates and empirical scalability than other approaches in the literature.Comment: 39 pages, 8 figures, 8 tables. Longer version of arXiv:1403.0211, In press, Journal of the American Statistical Association: Theory and Methods (2015