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On a Class of Optimization-Based Robust Estimators

机译：关于基于优化的一类鲁棒估计器

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摘要

In this paper, we consider the problem of estimating a parameter matrix from observations which are affected by two types of noise components: (i) a sparse noise sequence which, whenever nonzero can have arbitrarily large amplitude (ii) and a dense and bounded noise sequence of “moderate” amount. This is termed a robust regression problem. To tackle it, a quite general optimization-based framework is proposed and analyzed. When only the sparse noise is present, a sufficient bound is derived on the number of nonzero elements in the sparse noise sequence that can be accommodated by the estimator while still returning the true parameter matrix. While almost all the restricted isometry-based bounds from the literature are not verifiable, our bound can be easily computed through solving a convex optimization problem. Moreover, empirical evidence tends to suggest that it is generally tight. If in addition to the sparse noise sequence, the training data are affected by a bounded dense noise, we derive an upper bound on the estimation error.
机译：在本文中，我们考虑从受两种噪声成分影响的观测值估计参数矩阵的问题：（i）稀疏噪声序列，每当非零时，其振幅都可以任意大（ii）以及密集且有界的噪声“适度”金额的顺序。这被称为鲁棒回归问题。为了解决这个问题，提出并分析了一个非常通用的基于优化的框架。当仅存在稀疏噪声时，在稀疏噪声序列中非零元素的数量上可以得出足够的界限，该数量可以由估算器容纳，同时仍返回真实参数矩阵。尽管文献中几乎所有基于等轴测图的受限边界均不可验证，但可以通过解决凸优化问题轻松地计算出我们的边界。而且，经验证据倾向于表明它通常是紧密的。如果除稀疏噪声序列之外，训练数据还受有界密集噪声的影响，我们可以得出估计误差的上限。

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