Σεμινάριο ΕΜΠ ΣΕΜΦΕ 8/11/2024: Deviance Matrix Factorization by Luis Carvalho (Boston University)

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Παρασκευή 8/11 στην αίθουσα σεμιναρίων του Τομέα Μαθηματικών στο ΕΜΠ στις 14.00

Speaker: Luis Carvalho, Department of Mathematics and Statistics, Boston University

Title: Deviance Matrix Factorization

Abstract:
The singular value decomposition can be used to find a low-rank representation of a matrix under the Frobenius norm (entrywise square-error loss) and, for this reason, it enjoys an ubiquitous presence in many areas, including in Statistics with principal component and factor analyses. In this talk, we discuss a generalization of this matrix factorization, the deviance matrix factorization (DMF), that assumes broader deviance losses and thus allows for more meaningful and representative decompositions under different data domains and variance assumptions. We provide an efficient algorithm for the DMF and discuss using entrywise weights to represent missing data. We propose two tests to identify suitable decomposition ranks and data distributions and prove a few theoretical guarantees such as consistency. To showcase the practical performance of the proposed decomposition, we present a number of case studies in genetics, network analysis, and image classification. Finally, we offer a few directions for future work. This is joint work with Liang Wang.