Random networks, graphical models and exchangeability

Building Measurement Models from Scratch: Graphical Models, Exchangeability Models, and Log-linear Models

Exchangeability and regression models

Sir David Cox’s statistical career and his lifelong interest in the theory and application of stochastic processes began with problems in the wool industry. The problem of drafting a strand of wool yarn to near uniform width is not an auspicious starting point, but an impressive array of temporal and spectral methods from stationary time series were brought to bear on the problem in Cox (1949)....

"Infinite Exchangeability and Random Set Partitions"

This talk aims to introduce a Bayesian idea on multiple comparisons or simultaneous inference. Instead of constructing statistics for comparing variety means in pairs, we start with an infinitely exchangeable Gaussian prior for the variety effects such that each pair of varieties is equal with positive prior probability. Consistency conditions on joint exchangeable priors involving set partitio...

Missing at Random in Graphical Models

The notion of missing at random (MAR) plays a central role in the theory underlying current methods for handling missing data. However the standard definition of MAR is difficult to interpret in practice. In this paper, we assume the missing data model is represented as a directed acyclic graph that not only encodes the dependencies among the variables but also explicitly portrays the causal me...

Duality of Graphical Models and Tensor Networks

In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a hypergraph exactly corresponds to the graphical model given by the dual hypergraph. We translate various notions under duality. For example, marginalization in a...