STAR_outliers: a python package that separates univariate outliers from non-normal distributions

Abstract

Abstract There are not currently any univariate outlier detection algorithms that transform and model arbitrarily shaped distributions to remove univariate outliers. Some algorithms model skew, even fewer model kurtosis, and none of them model bimodality and monotonicity. To overcome these challenges, we have implemented an algorithm for Skew and Tail-heaviness Adjusted Removal of Outliers (STAR_outliers) that robustly removes univariate outliers from distributions with many different shape profiles, including extreme skew, extreme kurtosis, bimodality, and monotonicity. We show that STAR_outliers removes simulated outliers with greater recall and precision than several general algorithms, and it also models the outlier bounds of real data distributions with greater accuracy. Background Reliably removing univariate outliers from arbitrarily shaped distributions is a difficult task. Incorrectly assuming unimodality or overestimating tail heaviness fails to remove outliers, while underestimating tail heaviness incorrectly removes regular data from the tails. Skew often produces one heavy tail and one light tail, and we show that several sophisticated outlier removal algorithms often fail to remove outliers from the light tail. Multivariate outlier detection algorithms have recently become popular, but having tested PyOD’s multivariate outlier removal algorithms, we found them to be inadequate for univariate outlier removal. They usually do not allow for univariate input, and they do not fit their distributions of outliership scores with a model on which an outlier threshold can be accurately established. Thus, there is a need for a flexible outlier removal algorithm that can model arbitrarily shaped univariate distributions. Results In order to effectively model arbitrarily shaped univariate distributions, we have combined several well-established algorithms into a new algorithm called STAR_outliers. STAR_outliers removes more simulated true outliers and fewer non-outliers than several other univariate algorithms. These include several normality-assuming outlier removal methods, PyOD’s isolation forest (IF) outlier removal algorithm (ACM Transactions on Knowledge Discovery from Data (TKDD) 6:3, 2012) with default settings, and an IQR based algorithm by Verardi and Vermandele that removes outliers while accounting for skew and kurtosis (Verardi and Vermandele, Journal de la Société Française de Statistique 157:90–114, 2016). Since the IF algorithm’s default model poorly fit the outliership scores, we also compared the isolation forest algorithm with a model that entails removing as many datapoints as STAR_outliers does in order of decreasing outliership scores. We also compared these algorithms on the publicly available 2018 National Health and Nutrition Examination Survey (NHANES) data by setting the outlier threshold to keep values falling within the main 99.3 percent of the fitted model’s domain. We show that our STAR_outliers algorithm removes significantly closer to 0.7 percent of values from these features than other outlier removal methods on average. Conclusions STAR_outliers is an easily implemented python package for removing outliers that outperforms multiple commonly used methods of univariate outlier removal.

Keywords

• Outliers
• Statistics
• Software