Sensitivity of Leverage Scores
نویسنده
چکیده
The sampling strategies in many randomized matrix algorithms are, either explicitly or implicitly, controlled by statistical quantities called leverage scores. We present four bounds for the sensitivity of leverage scores as well as an upper bound for the principal angles between two matrices. These bounds are expressed by considering two real m×n matrices of full column rank, A and B. Our bounds shows that if the principal angles between A and B are small, then the leverage scores of B are close to the leverage scores of A. Next, we show that the principal angles can be bounded above by the two-norm condition number of A, κ(A) and ‖B − A‖2. Finally, we combine these bounds and derive bounds for the leverage scores of B in terms of κ(A) and ‖B − A‖2/‖A‖2 and show that if ‖B − A‖2/‖A‖2 and κ(A) are small, then the leverage scores of B are close to the leverage scores of A.
منابع مشابه
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تاریخ انتشار 2014