RODIAN: Robustified Median

TL;DR

RODIAN is a deterministic, efficient robust averaging method that accurately estimates the true mean in data contaminated with over 50% outliers, outperforming existing techniques.

Contribution

We introduce RODIAN, a novel robust mean estimation method that handles high outlier proportions without prior inlier error bounds, inspired by MINPRAN.

Findings

RODIAN accurately estimates the mean with >50% outliers.

RODIAN outperforms median and least-median-of-squares in robustness.

RODIAN remains effective with non-uniform outlier distributions.

Abstract

We propose a robust method for averaging numbers contaminated by a large proportion of outliers. Our method, dubbed RODIAN, is inspired by the key idea of MINPRAN [1]: We assume that the outliers are uniformly distributed within the range of the data and we search for the region that is least likely to contain outliers only. The median of the data within this region is then taken as RODIAN. Our approach can accurately estimate the true mean of data with more than 50% outliers and runs in time $O(n\log n)$. Unlike other robust techniques, it is completely deterministic and does not rely on a known inlier error bound. Our extensive evaluation shows that RODIAN is much more robust than the median and the least-median-of-squares. This result also holds in the case of non-uniform outlier distributions.