| Autor: |
Pilavci, Yusuf Yigit, Amblard, Pierre-Olivier, Barthelme, Simon, Tremblay, Nicolas |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
GRETSI 2022 - XXVIII{\`e}me Colloque Francophone de Traitement du Signal et des Images, Sep 2022, Nancy, France |
| Druh dokumentu: |
Working Paper |
| Popis: |
The trace $\tr(q(\ma{L} + q\ma{I})^{-1})$, where $\ma{L}$ 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 stratified sampling. Implementing these techniques is easy, and provides substantial variance reduction, yielding comparable or better performance relative to state-of-the-art algorithms. |
| Databáze: |
arXiv |
| Externí odkaz: |
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