6,653 research outputs found
Gains in Power from Structured Two-Sample Tests of Means on Graphs
We consider multivariate two-sample tests of means, where the location shift
between the two populations is expected to be related to a known graph
structure. An important application of such tests is the detection of
differentially expressed genes between two patient populations, as shifts in
expression levels are expected to be coherent with the structure of graphs
reflecting gene properties such as biological process, molecular function,
regulation, or metabolism. For a fixed graph of interest, we demonstrate that
accounting for graph structure can yield more powerful tests under the
assumption of smooth distribution shift on the graph. We also investigate the
identification of non-homogeneous subgraphs of a given large graph, which poses
both computational and multiple testing problems. The relevance and benefits of
the proposed approach are illustrated on synthetic data and on breast cancer
gene expression data analyzed in context of KEGG pathways
Estimating Graphlet Statistics via Lifting
Exploratory analysis over network data is often limited by the ability to
efficiently calculate graph statistics, which can provide a model-free
understanding of the macroscopic properties of a network. We introduce a
framework for estimating the graphlet count---the number of occurrences of a
small subgraph motif (e.g. a wedge or a triangle) in the network. For massive
graphs, where accessing the whole graph is not possible, the only viable
algorithms are those that make a limited number of vertex neighborhood queries.
We introduce a Monte Carlo sampling technique for graphlet counts, called {\em
Lifting}, which can simultaneously sample all graphlets of size up to
vertices for arbitrary . This is the first graphlet sampling method that can
provably sample every graphlet with positive probability and can sample
graphlets of arbitrary size . We outline variants of lifted graphlet counts,
including the ordered, unordered, and shotgun estimators, random walk starts,
and parallel vertex starts. We prove that our graphlet count updates are
unbiased for the true graphlet count and have a controlled variance for all
graphlets. We compare the experimental performance of lifted graphlet counts to
the state-of-the art graphlet sampling procedures: Waddling and the pairwise
subgraph random walk
Network Sampling: From Static to Streaming Graphs
Network sampling is integral to the analysis of social, information, and
biological networks. Since many real-world networks are massive in size,
continuously evolving, and/or distributed in nature, the network structure is
often sampled in order to facilitate study. For these reasons, a more thorough
and complete understanding of network sampling is critical to support the field
of network science. In this paper, we outline a framework for the general
problem of network sampling, by highlighting the different objectives,
population and units of interest, and classes of network sampling methods. In
addition, we propose a spectrum of computational models for network sampling
methods, ranging from the traditionally studied model based on the assumption
of a static domain to a more challenging model that is appropriate for
streaming domains. We design a family of sampling methods based on the concept
of graph induction that generalize across the full spectrum of computational
models (from static to streaming) while efficiently preserving many of the
topological properties of the input graphs. Furthermore, we demonstrate how
traditional static sampling algorithms can be modified for graph streams for
each of the three main classes of sampling methods: node, edge, and
topology-based sampling. Our experimental results indicate that our proposed
family of sampling methods more accurately preserves the underlying properties
of the graph for both static and streaming graphs. Finally, we study the impact
of network sampling algorithms on the parameter estimation and performance
evaluation of relational classification algorithms
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