论文标题
盲型多项式回归
Blind Polynomial Regression
论文作者
论文摘要
在许多信号处理和机器学习任务（例如插值和预测）中，将多项式拟合到观察到的数据是无处不在的任务。在这种情况下，输入和输出对可用，目标是找到多项式的系数。但是，在许多应用中，输入可能是部分已知的或根本不知道的，因此渲染常规回归方法不适用。在本文中，我们正式陈述了（可能部分的）盲目回归问题，说明了其一些理论特性，并提出了解决该问题的算法方法。作为案例研究，我们将方法应用于抖动纠正问题并证实其绩效。
Fitting a polynomial to observed data is an ubiquitous task in many signal processing and machine learning tasks, such as interpolation and prediction. In that context, input and output pairs are available and the goal is to find the coefficients of the polynomial. However, in many applications, the input may be partially known or not known at all, rendering conventional regression approaches not applicable. In this paper, we formally state the (potentially partial) blind regression problem, illustrate some of its theoretical properties, and propose algorithmic approaches to solve it. As a case-study, we apply our methods to a jitter-correction problem and corroborate its performance.
