Binary data fusion using undirected probabilistic graphical models: Combining statisticalmatching and the Ising model

Graphical models can prove quite powerful for statistical matching, making secondary data analysis feasible also in situations where joint information about variables that were not collected together is sought. Without any constraints regarding the direction of influence of variables, we develop a method that uses the graphical Ising model to merge two or more data files containing binary data only. To this end, we rely on the conditional independence assumption commonly made in statistical matching to learn a joint Markov network graph structure over all variables from the given data. Based on this joint graph, the probability distribution is estimated by an adapted version of the Ising model. The quality of our new data fusion method is assessed on basis of a simulation study, sampling data from random Ising models. We investigate which parameters influence the quality of data integration, and how violations of the conditional independence assumption affect the results

Graphical Reasoning in Compact Closed Categories for Quantum Computation

Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof system with a fixed logical kernel for equational reasoning about compact closed categories. Automating this reasoning process is motivated by the slow and error prone nature of manual graph manipulation. A salient feature of our system is that it provides a formal and declarative account of derived results that can include `ellipses'-style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation.Comment: 21 pages, 9 figures. This is the journal version of the paper published at AIS

Graph kernels between point clouds

Point clouds are sets of points in two or three dimensions. Most kernel methods for learning on sets of points have not yet dealt with the specific geometrical invariances and practical constraints associated with point clouds in computer vision and graphics. In this paper, we present extensions of graph kernels for point clouds, which allow to use kernel methods for such ob jects as shapes, line drawings, or any three-dimensional point clouds. In order to design rich and numerically efficient kernels with as few free parameters as possible, we use kernels between covariance matrices and their factorizations on graphical models. We derive polynomial time dynamic programming recursions and present applications to recognition of handwritten digits and Chinese characters from few training examples