Outlier-robust estimation is a fundamental problem and has been extensively investigated by statisticians and practitioners. The last few years have seen a convergence across research fields towards "algorithmic robust statistics", which focuses on developing tractable outlier-robust techniques for high-dimensional estimation problems. Despite this convergence, research efforts across fields have been mostly disconnected from one another. This monograph bridges recent work on certifiable outlier-robust estimation for geometric perception in robotics and computer vision with parallel work in robust statistics. In particular, we adapt and extend recent results on robust linear regression (applicable to the low-outlier regime with << 50% outliers) and list-decodable regression (applicable to the high-outlier regime with >> 50% outliers) to the setup commonly found in robotics and vision, where (i) variables (e.g., rotations, poses) belong to a non-convex domain, (ii) measurements are vector-valued, and (iii) the number of outliers is not known a priori. The emphasis here is on performance guarantees: rather than proposing radically new algorithms, we provide conditions on the input measurements under which modern estimation algorithms (possibly after small modifications) are guaranteed to recover an estimate close to the ground truth in the presence of outliers. These conditions are what we call an "estimation contract". Besides the proposed extensions of existing results, we believe the main contributions of this monograph are (i) to unify parallel research lines by pointing out commonalities and differences, (ii) to introduce advanced material (e.g., sum-of-squares proofs) in an accessible and self-contained presentation for the practitioner, and (iii) to point out a few immediate opportunities and open questions in outlier-robust geometric perception.
翻译:远紫外线估算是一个根本性问题,统计学家和从业者对此进行了广泛调查。 过去几年中,各研究领域在“ 高度强强度统计”方面趋于趋同, 重点是为高度估算问题开发可移动的外紫外线技术。 尽管这种趋同,各领域的研究工作大多是相互脱节的。 这个专论将最近关于对机器人和计算机视觉中的几何感知进行可验证的外部紫外线估算的工作与对稳健统计的平行工作联系起来。 特别是,我们调整和扩展了强力直线回归的最新结果( 适用于低度直线回归制度, 最高值强度强度强度统计 ) 以及列表可辨别的回归( 重于高度超值的外部估算 ) 。 这里强调的是( 直线性变量( 例如, 轮值) 直径直线估算是一个非直线域域域域, 测量为矢量, 并且( ) 直径直径直线回归, 以及( 三) 显示我们之前不知道多少次线线线线线线回归的结果 。 这里强调业绩的自我保障: 而不是直接的算算算算算, 。