Variance Reduction for Inverse Trace Estimation via Random Spanning ForestsDownload PDF

23 Jun 2022, 13:07 (modified: 12 Sept 2022, 18:06)ECMLPKDD 2022 Workshop MLG SubmissionReaders: Everyone
Keywords: trace estimation, graph signal processing, sampling, random spanning forests
Abstract: The trace $tr(q(\mathsf{L}+q\mathsf{I})^{-1})$, where $\mathsf{L}$ is a symmetric diagonally dominant matrix, is the quantity of interest in some machine learning problems. However, its direct computation is impractical if the matrix size is large. State-of-the-art methods include Hutchinson's estimator combined with iterative solvers, as well as the estimator based on random spanning forests (a random process on graphs). In this work, we show two ways of improving the forest-based estimator via well-known variance reduction techniques, namely control variates and strati ed sampling. Implementing these techniques is easy, and provides substantial variance reduction, yielding comparable or better performance relative to state-of-the-art algorithms.
Dual Submission: It is accepted to GRETSI 2022.
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