Ordinary least square (OLS) estimation of a linear regression model is well-known to be highly sensitive to outliers. It is common practice to (1) identify and remove outliers by looking at the data and (2) to fit OLS and form confidence intervals and p-values on the remaining data as if this were the original data collected. This standard “detect-and-forget” approach has been shown to be problematic, and in this paper we highlight the fact that it can lead to invalid inference and show how recently developed tools in selective inference can be used to properly account for outlier detection and removal. Our inferential procedures apply to a general class of outlier removal procedures that includes several of the most commonly used approaches. We conduct simulations to corroborate the theoretical results, and we apply our method to three real data sets to illustrate how our inferential results can differ from the traditional detect-and-forget strategy. A companion R package, outference, implements these new procedures with an interface that matches the functions commonly used for inference with lm in R.

R code used for each data set to perform negative binomial regression, calculate overdispersion statistic, generate summary statistics, remove outliers

These data sets were originally created for the following publications:

M. E. Houle, H.-P. Kriegel, P. Kröger, E. Schubert, A. Zimek Can Shared-Neighbor Distances Defeat the Curse of Dimensionality? In Proceedings of the 22nd International Conference on Scientific and Statistical Database Management (SSDBM), Heidelberg, Germany, 2010.

H.-P. Kriegel, E. Schubert, A. Zimek Evaluation of Multiple Clustering Solutions In 2nd MultiClust Workshop: Discovering, Summarizing and Using Multiple Clusterings Held in Conjunction with ECML PKDD 2011, Athens, Greece, 2011.

The outlier data set versions were introduced in:

E. Schubert, R. Wojdanowski, A. Zimek, H.-P. Kriegel On Evaluation of Outlier Rankings and Outlier Scores In Proceedings of the 12th SIAM International Conference on Data Mining (SDM), Anaheim, CA, 2012.

They are derived from the original image data available at https://aloi.science.uva.nl/

The image acquisition process is documented in the original ALOI work: J. M. Geusebroek, G. J. Burghouts, and A. W. M. Smeulders, The Amsterdam library of object images, Int. J. Comput. Vision, 61(1), 103-112, January, 2005

Additional information is available at: https://elki-project.github.io/datasets/multi_view

The following views are currently available:

    Feature type
    Description
    Files


    Object number
    Sparse 1000 dimensional vectors that give the true object assignment
    objs.arff.gz


    RGB color histograms
    Standard RGB color histograms (uniform binning)
    aloi-8d.csv.gz aloi-27d.csv.gz aloi-64d.csv.gz aloi-125d.csv.gz aloi-216d.csv.gz aloi-343d.csv.gz aloi-512d.csv.gz aloi-729d.csv.gz aloi-1000d.csv.gz


    HSV color histograms
    Standard HSV/HSB color histograms in various binnings
    aloi-hsb-2x2x2.csv.gz aloi-hsb-3x3x3.csv.gz aloi-hsb-4x4x4.csv.gz aloi-hsb-5x5x5.csv.gz aloi-hsb-6x6x6.csv.gz aloi-hsb-7x7x7.csv.gz aloi-hsb-7x2x2.csv.gz aloi-hsb-7x3x3.csv.gz aloi-hsb-14x3x3.csv.gz aloi-hsb-8x4x4.csv.gz aloi-hsb-9x5x5.csv.gz aloi-hsb-13x4x4.csv.gz aloi-hsb-14x5x5.csv.gz aloi-hsb-10x6x6.csv.gz aloi-hsb-14x6x6.csv.gz


    Color similiarity
    Average similarity to 77 reference colors (not histograms) 18 colors x 2 sat x 2 bri + 5 grey values (incl. white, black)
    aloi-colorsim77.arff.gz (feature subsets are meaningful here, as these features are computed independently of each other)


    Haralick features
    First 13 Haralick features (radius 1 pixel)
    aloi-haralick-1.csv.gz


    Front to back
    Vectors representing front face vs. back faces of individual objects
    front.arff.gz


    Basic light
    Vectors indicating basic light situations
    light.arff.gz


    Manual annotations
    Manually annotated object groups of semantically related objects such as cups
    manual1.arff.gz

Outlier Detection Versions

Additionally, we generated a number of subsets for outlier detection:

    Feature type
    Description
    Files


    RGB Histograms
    Downsampled to 100000 objects (553 outliers)
    aloi-27d-100000-max10-tot553.csv.gz aloi-64d-100000-max10-tot553.csv.gz



    Downsampled to 75000 objects (717 outliers)
    aloi-27d-75000-max4-tot717.csv.gz aloi-64d-75000-max4-tot717.csv.gz



    Downsampled to 50000 objects (1508 outliers)
    aloi-27d-50000-max5-tot1508.csv.gz aloi-64d-50000-max5-tot1508.csv.gz

Causal effect estimates using Radial MVMR with and without outlier removal with varying levels of unbalanced pleiotropy.

RRegrs study for Growth Yield for original and corrected/filterred datasets: inputs training and test files, R scripts to split the datasets, plot for outlier removal.

Causal effect estimates obtained using radial MR and radial MVMR models, estimating the effect of lipid fractions (HDL, LDL, and triglycerides) on CHD.

In powder metallurgy materials, sintered density in Cu-Al alloy plays a critical role in detecting mechanical properties. Experimental measurement of this property is costly and time-consuming. In this study, adaptive boosting decision tree, support vector regression, k-nearest neighbors, extreme gradient boosting, and four multilayer perceptron (MLP) models tuned by resilient backpropagation, Levenberg–Marquardt (LM), scaled conjugate gradient, and Bayesian regularization were employed for predicting powder densification through sintering. Yield strength, Young’s modulus, volume variation caused by the phase transformation, hardness, liquid volume, liquidus temperature, the solubility ratio among the liquid phase and the solid phase, sintered temperature, solidus temperature, sintered atmosphere, holding time, compaction pressure, particle size, and specific shape factor were regarded as the input parameters of the suggested models. The cross plot, error distribution curve, and cumulative frequency diagram as graphical tools and average percent relative error (APRE), average absolute percent relative error (AAPRE), root mean square error (RMSE), standard deviation (SD), and coefficient of correlation (R) as the statistical evaluations were utilized to estimate the models’ accuracy. All of the developed models were compared with preexisting approaches, and the results exhibited that the developed models in the present work are more precise and valid than the existing ones. The designed MLP-LM model was found to be the most precise approach with AAPRE = 1.292%, APRE = −0.032%, SD = 0.020, RMSE = 0.016, and R = 0.989. Lately, outlier detection was applied performing the leverage technique to detect the suspected data points. The outlier detection discovered that few points are located out of the applicability domain of the proposed MLP-LM model.

**Correlation is significant at the 0.01 level (2-tailed).*Correlation is significant at the 0.05 level (2-tailed).'Correlation is significant at the 0.1 level (2-tailed).For each model, the two categories of sibling pairs are derived from Table 2. In each case, a possible fit (in bold) is indicated by the second correlation being less than the first.

MLR models of age at onset of T1D after removing outliers (N = 354).

Tests were carried out at three False Discovery Rate (FDR) thresholds using BayeScan 2.1 [70] and LOSITAN [72]. Jointly-identified loci were identified using both outlier detection platforms.