Some data analysis problems require the computation of (regularised) inverse traces, i.e. quantities of the form Tr(qI + L)−1. For large matrices, direct methods are unfeasible and one must resort to approximations, for example using a conjugate gradient solver combined with Girard’s trace estimator (also known as Hutchinson’s trace estimator). Here we describe an unbiased estimator of the regularized inverse trace, based on Wilson’s algorithm, an algorithm that was initially designed to draw uniform spanning trees in graphs. Our method is fast, easy to implement, and scales to very large matrices. Its main drawback is that it is limited to diagonally dominant matrices L.
Estimating the inverse trace using random forests on graphs / Barthelme S; Tremblay N; Gaudilliere A; Avena L; Amblard P-O. - (2019). (Intervento presentato al convegno GRETSI 2019 - XXVIIème Colloque francophone de traitement du signal et des images tenutosi a Lille, France. nel August 2019).
Estimating the inverse trace using random forests on graphs
Avena L;
2019
Abstract
Some data analysis problems require the computation of (regularised) inverse traces, i.e. quantities of the form Tr(qI + L)−1. For large matrices, direct methods are unfeasible and one must resort to approximations, for example using a conjugate gradient solver combined with Girard’s trace estimator (also known as Hutchinson’s trace estimator). Here we describe an unbiased estimator of the regularized inverse trace, based on Wilson’s algorithm, an algorithm that was initially designed to draw uniform spanning trees in graphs. Our method is fast, easy to implement, and scales to very large matrices. Its main drawback is that it is limited to diagonally dominant matrices L.
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