Dynamic Trace EstimationDownload PDF

21 May 2021, 20:48 (edited 26 Oct 2021)NeurIPS 2021 PosterReaders: Everyone
  • Keywords: randomized numerical linear algebra, trace estimation, dynamic algorithms
  • Abstract: We study a dynamic version of the implicit trace estimation problem. Given access to an oracle for computing matrix-vector multiplications with a dynamically changing matrix A, our goal is to maintain an accurate approximation to A's trace using as few multiplications as possible. We present a practical algorithm for solving this problem and prove that, in a natural setting, its complexity is quadratically better than the standard solution of repeatedly applying Hutchinson's stochastic trace estimator. We also provide an improved algorithm assuming additional common assumptions on A's dynamic updates. We support our theory with empirical results, showing significant computational improvements on three applications in machine learning and network science: tracking moments of the Hessian spectral density during neural network optimization, counting triangles and estimating natural connectivity in a dynamically changing graph.
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