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.
翻译:在许多信号处理和机器学习任务(如内插和预测)中,将多元数据适用于观测到的数据是一项普遍存在的任务,例如内插和预测。在这方面,有输入和输出对对,目标是找到多元系数。然而,在许多应用中,输入可能部分为人所知或根本不为人所知,使得常规回归方法不适用。在本文中,我们正式指出(可能为部分)盲目回归问题,说明其理论属性,并提出解决该问题的算法方法。作为案例研究,我们运用我们的方法解决急躁的纠正问题,并证实其表现。