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Abstract:
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With the ubiquitous presence of networks in all areas of science and technology, it has become increasingly important to develop methods for statistical inference for graph-valued data. Although network analysis has been an area of active interest in statistics and machine learning, most classical approaches for graph testing are applicable in the relatively low-dimensional setting, where the sample size (number of graphs) is larger than the size of the graphs (number of vertices).
In this talk we will discuss the problem of testing equality of two random graph models, given samples from the respective distributions, in the high-dimensional regime. In particular, we will present theoretically optimal and computationally efficient methods for two-sample testing in inhomogeneous random graph models, which include various commonly studied network models, such as stochastic block models and random dot product graphs. We will also discuss the problem of testing equality of motif counts (such as edges and triangles) in random graphon models.
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