A lower bound for the Graver complexity of the incidence matrix of a complete bipartite graph

Incidence weighting estimation under bipartite incidence graph sampling

Bipartite incidence graph sampling provides a unified representation of many sampling situations for the purpose of estimation, including the existing unconventional sampling methods, such as indirect, network or adaptive cluster sampling, which are not originally described as graph problems. We develop a large class of linear estimators based on the edges in the sample bipartite incidence graph, subjected to a general condition of design unbiasedness. The class contains as special cases the classic Horvitz-Thompson estimator, as well as the other unbiased estimators in the literature of uncon…

论二部关联图抽样中的容许性

On Admissibility in Bipartite Incidence Graph Sampling

本文研究二部关联图抽样中估计量的容许性，在研究单元可经多条抽样路径观测的一般框架下，证明除 Horvitz–Thompson 估计量外还存在其他容许估计量，并涵盖有限总体抽样结论。

The Four Point Permutation Test for Latent Block Structure in Incidence Matrices

Transactional data may be represented as a bipartite graph $G:=(L \cup R, E)$, where $L$ denotes agents, $R$ denotes objects visible to many agents, and an edge in $E$ denotes an interaction between an agent and an object. Unsupervised learning seeks to detect block structures in the adjacency matrix $Z$ between $L$ and $R$, thus grouping together sets of agents with similar object interactions. New results on quasirandom permutations suggest a non-parametric \textbf{four point test} to measure the amount of block structure in $G$, with respect to vertex orderings on $L$ and $R$. Take disjoint…