Here we present a dataset, MNIST4OD, of large size (number of dimensions and number of instances) suitable for Outliers Detection task.The dataset is based on the famous MNIST dataset (http://yann.lecun.com/exdb/mnist/).We build MNIST4OD in the following way:To distinguish between outliers and inliers, we choose the images belonging to a digit as inliers (e.g. digit 1) and we sample with uniform probability on the remaining images as outliers such as their number is equal to 10% of that of inliers. We repeat this dataset generation process for all digits. For implementation simplicity we then flatten the images (28 X 28) into vectors.Each file MNIST_x.csv.gz contains the corresponding dataset where the inlier class is equal to x.The data contains one instance (vector) in each line where the last column represents the outlier label (yes/no) of the data point. The data contains also a column which indicates the original image class (0-9).See the following numbers for a complete list of the statistics of each datasets ( Name | Instances | Dimensions | Number of Outliers in % ):MNIST_0 | 7594 | 784 | 10MNIST_1 | 8665 | 784 | 10MNIST_2 | 7689 | 784 | 10MNIST_3 | 7856 | 784 | 10MNIST_4 | 7507 | 784 | 10MNIST_5 | 6945 | 784 | 10MNIST_6 | 7564 | 784 | 10MNIST_7 | 8023 | 784 | 10MNIST_8 | 7508 | 784 | 10MNIST_9 | 7654 | 784 | 10

Kriging with interpolation is widely used in various noise-free areas, such as computer experiments. However, owing to its Gaussian assumption, it is susceptible to outliers, which affects statistical inference, and the resulting conclusions could be misleading. Little work has explored outlier detection for kriging. Therefore, we propose a novel kriging method for simultaneous outlier detection and prediction by introducing a normal-gamma prior, which results in an unbounded penalty on the biases to distinguish outliers from normal data points. We develop a simple and efficient method, avoiding the expensive computation of the Markov chain Monte Carlo algorithm, to simultaneously detect outliers and make a prediction. We establish the true identification property for outlier detection and the consistency of the estimated hyperparameters in kriging under the increasing domain framework as if the number and locations of the outliers were known in advance. Under appropriate regularity conditions, we demonstrate information consistency for prediction in the presence of outliers. Numerical studies and real data examples show that the proposed method generally provides robust analyses in the presence of outliers. Supplementary materials for this article are available online.

Here are six files that provide details for all 44,120 identified single nucleotide polymorphisms (SNPs) or the 215 outlier SNPs associated with the evolution of rapid character displacement among replicate islands with (2Spp) and without competition (1Spp) between two Anolis species. On 2Spp islands, A. carolinensis occurs higher in trees and have evolved larger toe pads. Among 1Spp and 2Spp island populations, we identify 44,120 SNPs, with 215-outlier SNPs with improbably large FST values, low nucleotide variation, greater linkage than expected, and these SNPs are enriched for animal walking behavior. Thus, we conclude that these 215-outliers are evolving by natural selection in response to the phenotypic convergent evolution of character displacement. There are two, non-mutually exclusive perspective of these nucleotide variants. One is character displacement is convergent: all 215 outlier SNPs are shared among 3 out of 5 2Spp island and 24% of outlier SNPS are shared among all five out of five 2Spp island. Second, character displacement is genetically redundant because the allele frequencies in one or more 2Spp are similar to 1Spp islands: among one or more 2Spp islands 33% of outlier SNPS are within the range of 1Spp MiAF and 76% of outliers are more similar to 1Spp island than mean MiAF of 2Spp islands. Focusing on convergence SNP is scientifically more robust, yet it distracts from the perspective of multiple genetic solutions that enhances the rate and stability of adaptive change. The six files include: a description of eight islands, details of 94 individuals, and four files on SNPs. The four SNP files include the VCF files for 94 individuals with 44KSNPs and two files (Excel sheet/tab-delimited file) with FST, p-values and outlier status for all 44,120 identified single nucleotide polymorphisms (SNPs) associated with the evolution of rapid character displacement. The sixth file is a detailed file on the 215 outlier SNPs. Complete sequence data is available at Bioproject PRJNA833453, which including samples not included in this study. The 94 individuals used in this study are described in “Supplemental_Sample_description.txt” Methods Anoles and genomic DNA: Tissue or DNA for 160 Anolis carolinensis and 20 A. sagrei samples were provided by the Museum of Comparative Zoology at Harvard University (Table S2). Samples were previously used to examine evolution of character displacement in native A. carolinensis following invasion by A. sagrei onto man-made spoil islands in Mosquito Lagoon Florida (Stuart et al. 2014). One hundred samples were genomic DNAs, and 80 samples were tissues (terminal tail clip, Table S2). Genomic DNA was isolated from 80 of 160 A. carolinensis individuals (MCZ, Table S2) using a custom SPRI magnetic bead protocol (Psifidi et al. 2015). Briefly, after removing ethanol, tissues were placed in 200 ul of GH buffer (25 mM Tris- HCl pH 7.5, 25 mM EDTA, , 2M GuHCl Guanidine hydrochloride, G3272 SIGMA, 5 mM CaCl2, 0.5% v/v Triton X-100, 1% N-Lauroyl-Sarcosine) with 5% per volume of 20 mg/ml proteinase K (10 ul/200 ul GH) and digested at 55º C for at least 2 hours. After proteinase K digestion, 100 ul of 0.1% carboxyl-modified Sera-Mag Magnetic beads (Fisher Scientific) resuspended in 2.5 M NaCl, 20% PEG were added and allowed to bind the DNA. Beads were subsequently magnetized and washed twice with 200 ul 70% EtOH, and then DNA was eluted in 100 ul 0.1x TE (10 mM Tris, 0.1 mM EDTA). All DNA samples were gel electrophoresed to ensure high molecular mass and quantified by spectrophotometry and fluorescence using Biotium AccuBlueTM High Sensitivity dsDNA Quantitative Solution according to manufacturer’s instructions. Genotyping-by-sequencing (GBS) libraries were prepared using a modified protocol after Elshire et al. (Elshire et al. 2011). Briefly, high-molecular-weight genomic DNA was aliquoted and digested using ApeKI restriction enzyme. Digests from each individual sample were uniquely barcoded, pooled, and size selected to yield insert sizes between 300-700 bp (Borgstrom et al. 2011). Pooled libraries were PCR amplified (15 cycles) using custom primers that extend into the genomic DNA insert by 3 bases (CTG). Adding 3 extra base pairs systematically reduces the number of sequenced GBS tags, ensuring sufficient sequencing depth. The final library had a mean size of 424 bp ranging from 188 to 700 bp . Anolis SNPs: Pooled libraries were sequenced on one lane on the Illumina HiSeq 4000 in 2x150 bp paired-end configuration, yielding approximately 459 million paired-end reads ( ~138 Gb). The medium Q-Score was 42 with the lower 10% Q-Scores exceeding 32 for all 150 bp. The initial library contained 180 individuals with 8,561,493 polymorphic sites. Twenty individuals were Anolis sagrei, and two individuals (Yan 1610 & Yin 1411) clustered with A. sagrei and were not used to define A. carolinesis’ SNPs. Anolis carolinesis reads were aligned to the Anolis carolinensis genome (NCBI RefSeq accession number:/GCF_000090745.1_AnoCar2.0). Single nucleotide polymorphisms (SNPs) for A. carolinensis were called using the GBeaSy analysis pipeline (Wickland et al. 2017) with the following filter settings: minimum read length of 100 bp after barcode and adapter trimming, minimum phred-scaled variant quality of 30 and minimum read depth of 5. SNPs were further filtered by requiring SNPs to occur in > 50% of individuals, and 66 individuals were removed because they had less than 70% of called SNPs. These filtering steps resulted in 51,155 SNPs among 94 individuals. Final filtering among 94 individuals required all sites to be polymorphic (with fewer individuals, some sites were no longer polymorphic) with a maximum of 2 alleles (all are bi-allelic), minimal allele frequency 0.05, and He that does not exceed HWE (FDR <0.01). SNPs with large He were removed (2,280 SNPs). These SNPs with large significant heterozygosity may result from aligning paralogues (different loci), and thus may not represent polymorphisms. No SNPs were removed with low He (due to possible demography or other exceptions to HWE). After filtering, 94 individual yielded 44,120 SNPs. Thus, the final filtered SNP data set was 44K SNPs from 94 indiviuals. Statistical Analyses: Eight A. carolinensis populations were analyzed: three populations from islands with native species only (1Spp islands) and 5 populations from islands where A. carolinesis co-exist with A. sagrei (2Spp islands, Table 1, Table S1). Most analyses pooled the three 1Spp islands and contrasted these with the pooled five 2Spp islands. Two approaches were used to define SNPs with unusually large allele frequency differences between 1Spp and 2Spp islands: 1) comparison of FST values to random permutations and 2) a modified FDIST approach to identify outlier SNPs with large and statistically unlikely FST values. Random Permutations: FST values were calculated in VCFTools (version 4.2, (Danecek et al. 2011)) where the p-value per SNP were defined by comparing FST values to 1,000 random permutations using a custom script (below). Basically, individuals and all their SNPs were randomly assigned to one of eight islands or to 1Spp versus 2Spp groups. The sample sizes (55 for 2Spp and 39 for 1Spp islands) were maintained. FST values were re-calculated for each 1,000 randomizations using VCFTools. Modified FDIST: To identify outlier SNPs with statistically large FST values, a modified FDIST (Beaumont and Nichols 1996) was implemented in Arlequin (Excoffier et al. 2005). This modified approach applies 50,000 coalescent simulations using hierarchical population structure, in which demes are arranged into k groups of d demes and in which migration rates between demes are different within and between groups. Unlike the finite island models, which have led to large frequencies of false positive because populations share different histories (Lotterhos and Whitlock 2014), the hierarchical island model avoids these false positives by avoiding the assumption of similar ancestry (Excoffier et al. 2009). References Beaumont, M. A. and R. A. Nichols. 1996. Evaluating loci for use in the genetic analysis of population structure. P Roy Soc B-Biol Sci 263:1619-1626. Borgstrom, E., S. Lundin, and J. Lundeberg. 2011. Large scale library generation for high throughput sequencing. PLoS One 6:e19119. Bradbury, P. J., Z. Zhang, D. E. Kroon, T. M. Casstevens, Y. Ramdoss, and E. S. Buckler. 2007. TASSEL: software for association mapping of complex traits in diverse samples. Bioinformatics 23:2633-2635. Cingolani, P., A. Platts, L. Wang le, M. Coon, T. Nguyen, L. Wang, S. J. Land, X. Lu, and D. M. Ruden. 2012. A program for annotating and predicting the effects of single nucleotide polymorphisms, SnpEff: SNPs in the genome of Drosophila melanogaster strain w1118; iso-2; iso-3. Fly (Austin) 6:80-92. Danecek, P., A. Auton, G. Abecasis, C. A. Albers, E. Banks, M. A. DePristo, R. E. Handsaker, G. Lunter, G. T. Marth, S. T. Sherry, G. McVean, R. Durbin, and G. Genomes Project Analysis. 2011. The variant call format and VCFtools. Bioinformatics 27:2156-2158. Earl, D. A. and B. M. vonHoldt. 2011. Structure Harvester: a website and program for visualizing STRUCTURE output and implementing the Evanno method. Conservation Genet Resour 4:359-361. Elshire, R. J., J. C. Glaubitz, Q. Sun, J. A. Poland, K. Kawamoto, E. S. Buckler, and S. E. Mitchell. 2011. A robust, simple genotyping-by-sequencing (GBS) approach for high diversity species. PLoS One 6:e19379. Evanno, G., S. Regnaut, and J. Goudet. 2005. Detecting the number of clusters of individuals using the software STRUCTURE: a simulation study. Mol Ecol 14:2611-2620. Excoffier, L., T. Hofer, and M. Foll. 2009. Detecting loci under selection in a hierarchically structured population. Heredity 103:285-298. Excoffier, L., G. Laval, and S. Schneider. 2005. Arlequin (version 3.0): An integrated software package for population genetics data analysis.

The number of samples in training and testing set after pre-processing.

Outlier detection is the key to the quality control of marine survey data. For the detection of outliers in Conductivity-Temperature-Depth (CTD) data, previous methods, such as the Wild Edit method and the Median Filter Combined with Maximum Deviation method, mostly set a threshold based on statistics. Values greater than the threshold are treated as outliers, but there is no clear specification for the selection of threshold, thus multiple attempts are required. The process is time-consuming and inefficient, and the results have high false negative and positive rates. In response to this problem, we proposed an outlier detection method in CTD conductivity data, based on a physical constraint, the continuity of seawater. The method constructs a cubic spline fitting function based on the independent points scheme and the cubic spline interpolation to fit the conductivity data. The maximum fitting residual points will be flagged as outliers. The fitting stops when the optimal number of iterations is reached, which is automatically obtained by the minimum value of the sequence of maximum fitting residuals. Verification of the accuracy and stability of the method by means of examples proves that it has a lower false negative rate (17.88%) and false positive rate (0.24%) than other methods. Indeed, rates for the Wild Edit method are 56.96% and 2.19%, while for the Median Filter Combined with Maximum Deviation method rates are 23.28% and 0.31%. The Cubic Spline Fitting method is simple to operate, the result is clear and definite, better solved the problem of conductivity outliers detection.

To perform accurate engineering predictions, a method which accounts for both Gaussian process regression (GPR) and possibilistic fuzzy c-means clustering (PFCM) is developed in this paper, where the Gaussian process regression method is used in relationship regressions and the corresponding prediction errors are utilised to determine the memberships of the training samples. On the basis of its memberships and the prediction errors of the clusters, the typicality of each training sample is computed and used to determine the existence of outliers. In actual applications, the identified outliers should be eliminated and predictive model could be developed with the rest of the training samples. In addition to the method of predictive model construction, the influence of key parameters on the model accuracy is also investigated using two numerical problems. The results indicate that compared with standard outlier detection approaches and Gaussian process regression, the proposed approach is able to identify outliers with more precision and generate more accurate prediction results. To further identify the ability and feasibility of the method proposed in this paper in actual engineering applications, a predictive model was developed which can be used to predict the inlet pressure of a nuclear control valve on the basis of its in-situ data. The findings show that the proposed approach outperforms Gaussian process regression. In comparison to the traditional Gaussian process regression, the proposed approach reduces the detrimental impact of outliers and generates a more precise prediction model.

The FST-heterozygosity outlier approach has been a popular method for identifying loci under balancing and positive selection since Beaumont and Nichols first proposed it in 1996 and recommended its use for studies sampling a large number of independent populations (at least 10). Since then, their program FDIST2 and a user-friendly program optimized for large datasets, LOSITAN, have been used widely in the population genetics literature, often without the requisite number of samples. We observed empirical datasets whose distributions could not be reconciled with the confidence intervals generated by the null coalescent island model. Here, we use forward-in-time simulations to investigate circumstances under which the FST-heterozygosity outlier approach performs poorly for next-generation single-nucleotide polymorphism (SNP) datasets. Our results show that samples involving few independent populations, particularly when migration rates are low, result in distributions of the FST-heterozygosity relationship that are not described by the null model implemented in LOSITAN. In addition, even under favorable conditions LOSITAN rarely provides confidence intervals that precisely fit SNP data, making the associated p-values only roughly valid at best. We present an alternative method, implemented in a new R package named fsthet, which uses the raw empirical data to generate smoothed outlier plots for the FST-heterozygosity relationship.

Outside Chaco Canyon, in the expansive San Juan Basin, Chacoan students have long noted the presence of sites exhibiting architecture and ceramics characteristic of the major Chaco Canyon sites. Chacoan architecture also occurs at sites with assemblages dominated by San Juan and Chuskan series ceramics. More recently, it has become apparent that many of these outlying sites occur within major Anasazi site aggregations or communities and are linked to Chaco Canyon via prehistoric roads. The term outlier has come into popular usage to emphasize the geographic location of these communities relative to Chaco Canyon.

Examples of widely recognized outlier sites with Chacoan architectural features and, in some instances, Chacoan (Cibolan) ceramics are Aztec Ruin (Morris 1928), Chimney Rock Pueblo, (Eddy 1977; Jeancon and Roberts 1924), Lowry Ruin (Martin 1936), Kin Ya'a (Bannister 1965; Holsinger 1901), Village of the Great Kivas (Roberts 1932), Allantown (Roberts 1939), and Salmon Ruin (Irwin-Williams 1972, 1975). A number of these sites are known to have associated smaller sites, and at a few, prehistoric roads have been documented.

While archaeologists have not doubted the "Chacoan" affinities of architectural features at these sites, debate continues concerning why sites up to 130 km distant from Chaco Canyon should display such striking morphological similarity. Early explanations included migration and resettlement of Chacoan groups or diffusion of Chacoan culture (Gladwin 1945:144-45; Martin 1936:103,205; Morris 1939:53,205; Roberts 1932: 157). The great number of contemporaneous Chacoan outliers documented in recent years, however, has eliminated migration as a valid explanation, while diffusion in its traditional sense has been abandoned by many anthropologists because of its lack of explanatory value (Martin and Plog 1973: 256-60).

The Controlled Anomalies Time Series (CATS) Dataset consists of commands, external stimuli, and telemetry readings of a simulated complex dynamical system with 200 injected anomalies.

The CATS Dataset exhibits a set of desirable properties that make it very suitable for benchmarking Anomaly Detection Algorithms in Multivariate Time Series [1]:

• Multivariate (17 variables) including sensors reading and control signals. It simulates the operational behaviour of an arbitrary complex system including:
  • 4 Deliberate Actuations / Control Commands sent by a simulated operator / controller, for instance, commands of an operator to turn ON/OFF some equipment.
  • 3 Environmental Stimuli / External Forces acting on the system and affecting its behaviour, for instance, the wind affecting the orientation of a large ground antenna.
  • 10 Telemetry Readings representing the observable states of the complex system by means of sensors, for instance, a position, a temperature, a pressure, a voltage, current, humidity, velocity, acceleration, etc.
• 5 million timestamps. Sensors readings are at 1Hz sampling frequency.
  • 1 million nominal observations (the first 1 million datapoints). This is suitable to start learning the "normal" behaviour.
  • 4 million observations that include both nominal and anomalous segments. This is suitable to evaluate both semi-supervised approaches (novelty detection) as well as unsupervised approaches (outlier detection).
• 200 anomalous segments. One anomalous segment may contain several successive anomalous observations / timestamps. Only the last 4 million observations contain anomalous segments.
• Different types of anomalies to understand what anomaly types can be detected by different approaches. The categories are available in the dataset and in the metadata.
• Fine control over ground truth. As this is a simulated system with deliberate anomaly injection, the start and end time of the anomalous behaviour is known very precisely. In contrast to real world datasets, there is no risk that the ground truth contains mislabelled segments which is often the case for real data.
• Suitable for root cause analysis. In addition to the anomaly category, the time series channel in which the anomaly first developed itself is recorded and made available as part of the metadata. This can be useful to evaluate the performance of algorithm to trace back anomalies to the right root cause channel.
• Affected channels. In addition to the knowledge of the root cause channel in which the anomaly first developed itself, we provide information of channels possibly affected by the anomaly. This can also be useful to evaluate the explainability of anomaly detection systems which may point out to the anomalous channels (root cause and affected).
• Obvious anomalies. The simulated anomalies have been designed to be "easy" to be detected for human eyes (i.e., there are very large spikes or oscillations), hence also detectable for most algorithms. It makes this synthetic dataset useful for screening tasks (i.e., to eliminate algorithms that are not capable to detect those obvious anomalies). However, during our initial experiments, the dataset turned out to be challenging enough even for state-of-the-art anomaly detection approaches, making it suitable also for regular benchmark studies.
• Context provided. Some variables can only be considered anomalous in relation to other behaviours. A typical example consists of a light and switch pair. The light being either on or off is nominal, the same goes for the switch, but having the switch on and the light off shall be considered anomalous. In the CATS dataset, users can choose (or not) to use the available context, and external stimuli, to test the usefulness of the context for detecting anomalies in this simulation.
• Pure signal ideal for robustness-to-noise analysis. The simulated signals are provided without noise: while this may seem unrealistic at first, it is an advantage since users of the dataset can decide to add on top of the provided series any type of noise and choose an amplitude. This makes it well suited to test how sensitive and robust detection algorithms are against various levels of noise.
• No missing data. You can drop whatever data you want to assess the impact of missing values on your detector with respect to a clean baseline.

Change Log

Version 2

• Metadata: we include a metadata.csv with information about:
  • Anomaly categories
  • Root cause channel (signal in which the anomaly is first visible)
  • Affected channel (signal in which the anomaly might propagate) through coupled system dynamics
• Removal of anomaly overlaps: version 1 contained anomalies which overlapped with each other resulting in only 190 distinct anomalous segments. Now, there are no more anomaly overlaps.
• Two data files: CSV and parquet for convenience.

[1] Example Benchmark of Anomaly Detection in Time Series: “Sebastian Schmidl, Phillip Wenig, and Thorsten Papenbrock. Anomaly Detection in Time Series: A Comprehensive Evaluation. PVLDB, 15(9): 1779 - 1797, 2022. doi:10.14778/3538598.3538602”

About Solenix

Solenix is an international company providing software engineering, consulting services and software products for the space market. Solenix is a dynamic company that brings innovative technologies and concepts to the aerospace market, keeping up to date with technical advancements and actively promoting spin-in and spin-out technology activities. We combine modern solutions which complement conventional practices. We aspire to achieve maximum customer satisfaction by fostering collaboration, constructivism, and flexibility.

IntroductionCreating training and testing datasets for machine learning algorithms to measure linear dimensions of organs is a tedious task. There are no universally accepted methods for evaluating outliers or anomalies in such datasets. This can cause errors in machine learning and compromise the quality of end products. The goal of this study is to identify optimal methods for detecting organ anomalies and outliers in medical datasets designed to train and test neural networks in morphometrics.MethodsA dataset was created containing linear measurements of the spleen obtained from CT scans. Labelling was performed by three radiologists. The total number of studies included in the sample was N = 197 patients. Using visual methods (1.5 interquartile range; heat map; boxplot; histogram; scatter plot), machine learning algorithms (Isolation forest; Density-Based Spatial Clustering of Applications with Noise; K-nearest neighbors algorithm; Local outlier factor; One-class support vector machines; EllipticEnvelope; Autoencoders), and mathematical statistics (z-score, Grubb’s test; Rosner’s test).ResultsWe identified measurement errors, input errors, abnormal size values and non-standard shapes of the organ (sickle-shaped, round, triangular, additional lobules). The most effective methods included visual techniques (including boxplots and histograms) and machine learning algorithms such is OSVM, KNN and autoencoders. A total of 32 outlier anomalies were found.DiscussionCuration of complex morphometric datasets must involve thorough mathematical and clinical analyses. Relying solely on mathematical statistics or machine learning methods appears inadequate.

The "Amsterdam Library of Object Images" is a collection of 110250 images of 1000 small objects, taken under various light conditions and rotation angles. All objects were placed on a black background. Thus the images are taken under rather uniform conditions, which means there is little uncontrolled bias in the data set (unless mixed with other sources). They do however not resemble a "typical" image collection. The data set has a rather unique property for its size: there are around 100 different images of each object, so it is well suited for clustering. By downsampling some objects it can also be used for outlier detection. For multi-view research, we offer a number of different feature vector sets for evaluating this data set.

Key Characteristics of Algorithms' Dynamics Beyond Accuracy - Evaluation Tests (v2) conducted for the paper: What do anomaly scores actually mean? Key characteristics of algorithms' dynamics beyond accuracy by F. Iglesias, H. O. Marques, A. Zimek, T. Zseby Context and methodology Anomaly detection is intrinsic to a large number of data analysis applications today. Most of the algorithms used assign an outlierness score to each instance prior to establishing anomalies in a binary form. The experiments in this repository study how different algorithms generate different dynamics in the outlierness scores and react in very different ways to possible model perturbations that affect data. The study elaborated in the referred paper presents new indices and coefficients to assess the dynamics and explores the responses of the algorithms as a function of variations in these indices, revealing key aspects of the interdependence between algorithms, data geometries and the ability to discriminate anomalies. Therefeore, this repository reproduces the conducted experiments, which study eight algorithms (ABOD, HBOS, iForest, K-NN, LOF, OCSVM, SDO and GLOSH), submitted to seven perturbations related to: cardinality, dimensionality, outlier proportion, inlier-outlier density ratio, density layers, clusters and local outliers, and collects behavioural profiles with eleven measurements (Adjusted Average Precission, ROC-AUC, Perini's Confidence [1], Perini's Stability [2], S-curves, Discriminant Power, Robust Coefficients of Variations for Inliers and Outliers, Coherence, Bias and Robustness) under two types of normalization: linear and Gaussian, the latter aiming to standardize the outlierness scores issued by different algorithms [3]. This repository is framed within the research on the following domains: algorithm evaluation, outlier detection, anomaly detection, unsupervised learning, machine learning, data mining, data analysis. Datasets and algorithms can be used for experiment replication and for further evaluation and comparison. References [1] Perini, L., Vercruyssen, V., Davis, J.: Quantifying the confidence of anomaly detectors in their example-wise predictions. In: The European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases. Springer Verlag (2020). [2] Perini, L., Galvin, C., Vercruyssen, V.: A Ranking Stability Measure for Quantifying the Robustness of Anomaly Detection Methods. In: 2nd Workshop on Evaluation and Experimental Design in Data Mining and Machine Learning @ ECML/PKDD (2020). [3] Kriegel, H.-P., Kröger, P., Schubert, E., Zimek, A.: Interpreting and unifying outlier scores. In: Proceedings of the 2011 SIAM International Conference on Data Mining (SDM), pp. 13–24 (2011) Technical details Experiments are tested Python 3.9.6. Provided scripts generate all synthetic data and results. We keep them in the repo for the sake of comparability and replicability ("outputs.zip" file). The file and folder structure is as follows: "compare_scores_group.py" is a Python script to extract new dynamic indices proposed in the paper. "generate_data.py" is a Python script to generate datasets used for evaluation. "latex_table.py" is a Python script to show results in a latex-table format. "merge_indices.py" is a Python script to merge accuracy and dynamic indices in the same table-structured summary. "metric_corr.py" is a Python script to calculate correlation estimations between indices. "outdet.py" is a Python script that runs outlier detection with different algorithms on diverse datasets. "perini_tests.py" is a Python script to run Perini's confidence and stability on all datasets and algorithms' performances. "scatterplots.py" is a Python script that generates scatter plots for comparing accuracy and dynamic performances. "README.md" provides explanations and step by step instructions for replication. "requirements.txt" contains references to required Python libraries and versions. "outputs.zip" contains all result tables, plots and synthetic data generated with the scripts. [data/real_data] contain CSV versions of the Wilt, Shuttle, Waveform and Cardiotocography datasets (inherited and adapted from the LMU repository) License The CC-BY license applies to all data generated with the "generated_data.py" script. All distributed code is under the GNU GPL license. For the "ExCeeD.py" and "stability.py" scripts, please consult and refer to the original sources provided above.

This product was developed as part of the project supported by the grant from and the National Oceanic and Atmospheric Administration’s Ocean Acidification Program under award NA18OAR0170430 to the Virginia Institute of Marine Science. The data product consists of water quality data for tidal 98 stations for 1984–2018. The source data used to generate this product were downloaded from the Chesapeake Bay Program’s (CBP) data hub. Out of the total of 255 monitoring stations in the Tidal Monitoring Program, we selected 98 with the long monitoring record (30 years or longer). The following variables were downloaded from the data hub at the native temporal and vertical resolution (between one and four cruises per month and approximately 10 depth levels sampled between 0 and 37 m) for 1984–2018: water temperature (T), salinity (S), pH, total alkalinity (TA), dissolved oxygen (DO) , and chlorophyll (Chl). All pH data prior to 1998 were removed because of the data quality concerns (Herrmann et al., 2020). Briefly, we found a dramatic difference in long-term trends between stations measured by institutions in the state of Virginia and stations measured by the state of Maryland, particularly from late spring to early fall. The boundary between the station groups runs east–west within the mesohaline portion of the bay, where the Potomac River estuary intersects the mainstem bay. The boundary separates strong negative linear trends to the south (Virginia stations) from neutral and weakly positive linear trends to the north (Maryland stations). For all variables, data entries marked with CBP’s “Problem” and “Qualifier” flags were removed. Additionally, all variables were scanned for extreme outliers: for each variable, data from all stations, depths, and times were combined into a single composite sample for which the 75th and 25th percentiles (i.e., the upper and lower quantiles) and the interquartile range (the difference between the upper and lower quantiles) were calculated. Extreme outliers were defined as the values falling outside of a certain number (censoring criterion) of interquartile ranges from the upper and lower quantiles.

The FST-heterozygosity outlier approach has been a popular method for identifying loci under balancing and positive selection since Beaumont and Nichols first proposed it in 1996 and recommended its use for studies sampling a large number of independent populations (at least 10). Since then, their program FDIST2 and a user-friendly program optimized for large datasets, LOSITAN, have been used widely in the population genetics literature, often without the requisite number of samples. We observed empirical datasets whose distributions could not be reconciled with the confidence intervals generated by the null coalescent island model. Here, we use forward-in-time simulations to investigate circumstances under which the FST-heterozygosity outlier approach performs poorly for next-generation single-nucleotide polymorphism (SNP) datasets. Our results show that samples involving few independent populations, particularly when migration rates are low, result in distributions of the FST-heterozy...

Outliers widely occur in big-data applications and may severely affect statistical estimation and inference. In this article, a framework of outlier-resistant estimation is introduced to robustify an arbitrarily given loss function. It has a close connection to the method of trimming and includes explicit outlyingness parameters for all samples, which in turn facilitates computation, theory, and parameter tuning. To tackle the issues of nonconvexity and nonsmoothness, we develop scalable algorithms with implementation ease and guaranteed fast convergence. In particular, a new technique is proposed to alleviate the requirement on the starting point such that on regular datasets, the number of data resamplings can be substantially reduced. Based on combined statistical and computational treatments, we are able to perform nonasymptotic analysis beyond M-estimation. The obtained resistant estimators, though not necessarily globally or even locally optimal, enjoy minimax rate optimality in both low dimensions and high dimensions. Experiments in regression, classification, and neural networks show excellent performance of the proposed methodology at the occurrence of gross outliers. Supplementary materials for this article are available online.

Three datasets are chosen from the UCI machine learning repository in this study, which have been extensively adopted in data-driven researches, including Australian and Japanese datasets (Asuncion & Newman, 2007), and Polish bankruptcy dataset (Zięba et al., 2016). The three datasets contain different numbers of samples and features. Each sample in a credit dataset can be classified into good credit or bad credit. The size of Australian credit dataset is 690, with 307 samples in good credit and 383 in bad, and its feature dimension is 14, with 6 numerical and 8 categorical features. The size of Japanese credit dataset is 690, with 307 samples in good credit and 383 in bad, and its feature dimension is 15, with 6 numerical and 9 categorical features. Similarly, there are 7027 samples in Polish bankruptcy dataset, with 6756 samples in good credit and 271 in bad, and its 64 input features are numerical. All the dimensions of the input features of the three datasets listed in Table 1 do not include the class labels.

Over the years there have been a number of different computational methods that allow for the identification of outliers. Methods for robust estimation are known in the set of M-estimates methods (derived from the method of Maximum Likelihood Estimation) or in the set of R-estimation methods (robust estimation based on the application of some rank test). There are also algorithms that are not classified in any of these groups but these methods are also resistant to gross errors, for example, in M-split estimation. Another proposal, which can be used to detect outliers in the process of transformation of coordinates, where the coordinates of some points may be affected by gross errors, can be a method called RANSAC algorithm (Random Sample and Consensus). The authors present a study that was performed in the process of 2D transformation parameter estimation using RANSAC algorithm to detect points that have coordinates with outliers. The calculations were performed in three scenarios on the real geodetic network. Selected coordinates were burdened with simulated values of errors to confirm the efficiency of the proposed method.

Gene expression data have been presented as non-normalized (2-Ct*109) in all but the last two rows; this allows for the back-calculation of the raw threshold cycle (Ct) values so that the typical range of expression of each gene can be more easily assessed by interested individuals. The sample number fraction following the island name represents the number of outliers over the total number of samples for which a Mahalanobis distance could be calculated (rather than the number of samples analyzed from that site). Values representing aberrant levels for a particular response variable (i.e., that contributed to the heat map score) have been highlighted in bold. When there was a statistically significant difference (student’s t-test, p

Comparison by week of the first detected influenza-negative ILI time series outlier and the first reported COVID-19 case and peak by country.

Copy number variations (CNVs) are one of the main sources of variability in the human genome. Many CNVs are associated with various diseases including cardiovascular disease. In addition to hybridization-based methods, next-generation sequencing (NGS) technologies are increasingly used for CNV discovery. However, respective computational methods applicable to NGS data are still limited. We developed a novel CNV calling method based on outlier detection applicable to small cohorts, which is of particular interest for the discovery of individual CNVs within families, de novo CNVs in trios and/or small cohorts of specific phenotypes like rare diseases. Approximately 7,000 rare diseases are currently known, which collectively affect ∼6% of the population. For our method, we applied the Dixon’s Q test to detect outliers and used a Hidden Markov Model for their assessment. The method can be used for data obtained by exome and targeted resequencing. We evaluated our outlier- based method in comparison to the CNV calling tool CoNIFER using eight HapMap exome samples and subsequently applied both methods to targeted resequencing data of patients with Tetralogy of Fallot (TOF), the most common cyanotic congenital heart disease. In both the HapMap samples and the TOF cases, our method is superior to CoNIFER, such that it identifies more true positive CNVs. Called CNVs in TOF cases were validated by qPCR and HapMap CNVs were confirmed with available array-CGH data. In the TOF patients, we found four copy number gains affecting three genes, of which two are important regulators of heart development (NOTCH1, ISL1) and one is located in a region associated with cardiac malformations (PRODH at 22q11). In summary, we present a novel CNV calling method based on outlier detection, which will be of particular interest for the analysis of de novo or individual CNVs in trios or cohorts up to 30 individuals, respectively.