Testing and estimation for relational data

Alex Volfovsky, Harvard, Statistics
Recent years have seen a dramatic rise in social media, networks, and other settings in which the relationships and interactions between individuals, countries or objects are observed. These types of relational data are often represented as a square matrix, the entries of which record the relationships between pairs of objects. Statistical methods for such data range from network regression where entries are frequently assumed to be independent to latent space methods that assume some degree of similarity or dependence between objects in terms of the way they relate to each other. However, formal tests for such dependence have not been developed. First, we provide a test (based on the observation of a single relational data matrix) for such dependence using the framework of the matrix normal model, a type of multivariate normal distribution parameterized in terms of row- and column-specific covariance matrices. Second, we develop an estimation procedure (still based on the observation of a single relational data matrix) that captures the variability in such data by leveraging the identical index sets of the rows and columns.
February, 8 2016 | 12:30 p.m. - 2:00 p.m. | 270 Gross Hall

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