论文标题
量化数据矩阵的强大最小二乘
Robust Least Squares for Quantized Data Matrices
论文作者
论文摘要
在本文中，我们为在数据矩阵中受量化误差的线性方程系统制定并解决了可靠的最小二乘问题。普通最小二乘无法考虑操作员的不确定性，为观察到的信号中的所有噪声建模。与普通最小二乘相比，总和的总正方形说明了数据矩阵的不确定性，但必定会增加操作员的状况数量。经常采用Tikhonov正则化或脊回归来打击不良条件，但需要参数调整，这提出了许多挑战，并且对参数先验分布进行了强有力的假设。所提出的方法还需要选择一个参数，但是可以自然的方式选择它，例如，圆形到第四位的矩阵使用0.5e-4的不确定性边界参数。我们在这里表明，我们的鲁棒方法在理论上是适当的，可进行的，并且对普通和最小二乘的表现有利。
In this paper we formulate and solve a robust least squares problem for a system of linear equations subject to quantization error in the data matrix. Ordinary least squares fails to consider uncertainty in the operator, modeling all noise in the observed signal. Total least squares accounts for uncertainty in the data matrix, but necessarily increases the condition number of the operator compared to ordinary least squares. Tikhonov regularization or ridge regression is frequently employed to combat ill-conditioning, but requires parameter tuning which presents a host of challenges and places strong assumptions on parameter prior distributions. The proposed method also requires selection of a parameter, but it can be chosen in a natural way, e.g., a matrix rounded to the 4th digit uses an uncertainty bounding parameter of 0.5e-4. We show here that our robust method is theoretically appropriate, tractable, and performs favorably against ordinary and total least squares.
