2016/06/16 by Boram Yoon, Yoon, Boram
Computer Science · #Algorithms and Data Compression #Cellular Automata and Applications #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1606.05560
openalex publication_date 2016/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We present a new trace estimator of the matrix whose explicit form is not given but its matrix multiplication to a vector is available. The form of the estimator is similar to the Hutchison stochastic trace estimator, but instead of the random noise vectors in Hutchison estimator, we use small number of probing vectors determined by machine learning. Evaluation of the quality of estimates and bias correction are discussed. An unbiased estimator is proposed for the calculation of the expectation value of a function of traces. In the numerical experiments with random matrices, it is shown that the precision of trace estimates with O(10) probing vectors determined by the machine learning is similar to that with O(10000) random noise vectors.