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Description:

pythresh 0.3.7

Deployment, Stats, & License

PyThresh is a comprehensive and scalable Python toolkit for
thresholding outlier detection likelihood scores in
univariate/multivariate data. It has been written to work in tandem with
PyOD and has similar syntax and data structures. However, it is not
limited to this single library. PyThresh is meant to threshold
likelihood scores generated by an outlier detector. It thresholds these
likelihood scores and replaces the need to set a contamination level or
have the user guess the amount of outliers that may exist in the dataset
beforehand. These non-parametric methods were written to reduce the
user’s input/guess work and rather rely on statistics instead to
threshold outlier likelihood scores. For thresholding to be applied
correctly, the outlier detection likelihood scores must follow this
rule: the higher the score, the higher the probability that it is an
outlier in the dataset. All threshold functions return a binary array
where inliers and outliers are represented by a 0 and 1 respectively.
PyThresh includes more than 30 thresholding algorithms. These algorithms
range from using simple statistical analysis like the Z-score to more
complex mathematical methods that involve graph theory and topology.

Documentation & Citing
Visit PyThresh Docs for full
documentation or see below for a quickstart installation and usage
example.
To cite this work you can visit PyThresh Citation

Outlier Detection Thresholding with 7 Lines of Code:
# train the KNN detector
from pyod.models.knn import KNN
from pythresh.thresholds.filter import FILTER

clf = KNN()
clf.fit(X_train)

# get outlier scores
decision_scores = clf.decision_scores_ # raw outlier scores on the train data

# get outlier labels
thres = FILTER()
labels = thres.eval(decision_scores)
or using multiple outlier detection score sets
# train multiple detectors
from pyod.models.knn import KNN
from pyod.models.pca import PCA
from pyod.models.iforest import IForest
from pythresh.thresholds.filter import FILTER

clfs = [KNN(), IForest(), PCA()]

# get outlier scores for each detector
scores = [clf.fit(X_train).decision_scores_ for clf in clfs]

scores = np.vstack(scores).T

# get outlier labels
thres = FILTER()
labels = thres.eval(scores)

Installation
It is recommended to use pip or conda for installation:
pip install pythresh # normal install
pip install --upgrade pythresh # or update if needed
conda install -c conda-forge pythresh
Alternatively, you can get the version with the latest updates by
cloning the repo and run setup.py file:
git clone https://github.com/KulikDM/pythresh.git
cd pythresh
pip install .
Or with pip:
pip install https://github.com/KulikDM/pythresh/archive/main.zip
Required Dependencies:

matplotlib
numpy>=1.13
pyod
scipy>=1.3.1
scikit_learn>=0.20.0

Optional Dependencies:

pyclustering (used in the CLUST thresholder)
ruptures (used in the CPD thresholder)
scikit-lego (used in the META thresholder)
joblib>=0.14.1 (used in the META thresholder and RANK)
pandas (used in the META thresholder)
torch (used in the VAE thresholder)
tqdm (used in the VAE thresholder)
xgboost>=2.0.0 (used in the RANK)

API Cheatsheet

eval(score): evaluate a single outlier or multiple outlier
detection likelihood score sets.

Key Attributes of threshold:

thresh_: Return the threshold value that separates inliers from
outliers. Outliers are considered all values above this threshold
value. Note the threshold value has been derived from likelihood
scores normalized between 0 and 1.
confidence_interval_: Return the lower and upper confidence
interval of the contamination level. Only applies to the COMB
thresholder
dscores_: 1D array of the TruncatedSVD decomposed decision scores
if multiple outlier detector score sets are passed
mixture_: fitted mixture model class of the selected model used
for thresholding. Only applies to MIXMOD. Attributes include:
components, weights, params. Functions include: fit, loglikelihood,
pdf, and posterior.

External Feature Cases
Towards Data Science: Thresholding Outlier Detection Scores with
PyThresh
Towards Data Science: When Outliers are Significant: Weighted
Linear Regression
ArXiv: Estimating the Contamination Factor’s Distribution in
Unsupervised Anomaly Detection.

Available Thresholding Algorithms

Abbr
Description
References
Documentation

AUCP
Area Under Curve Percentage
[1]
pythresh.thresholds.aucp module

BOOT
Bootstrapping
[2]
pythresh.thresholds.boot module

CHAU
Chauvenet’s Criterion
[3]
pythresh.thresholds.chau module

CLF
Trained Linear Classifier
[4]
pythresh.thresholds.clf module

CLUST
Clustering Based
[5]
pythresh.thresholds.clust module

CPD
Change Point Detection
[6]
pythresh.thresholds.cpd module

DECOMP
Decomposition
[7]
pythresh.thresholds.decomp module

DSN
Distance Shift from Normal
[8]
pythresh.thresholds.dsn module

EB
Elliptical Boundary
[9]
pythresh.thresholds.eb module

FGD
Fixed Gradient Descent
[10]
pythresh.thresholds.fgd module

FILTER
Filtering Based
[11]
pythresh.thresholds.filter module

FWFM
Full Width at Full Minimum
[12]
pythresh.thresholds.fwfm module

GAMGMM
Bayesian Gamma GMM
[13]
pythresh.thresholds.gamgmm module

GESD
Generalized Extreme Studentized Deviate
[14]
pythresh.thresholds.gesd module

HIST
Histogram Based
[15]
pythresh.thresholds.hist module

IQR
Inter-Quartile Region
[16]
pythresh.thresholds.iqr module

KARCH
Karcher mean (Riemannian Center of Mass)
[17]
pythresh.thresholds.karch module

MAD
Median Absolute Deviation
[18]
pythresh.thresholds.mad module

MCST
Monte Carlo Shapiro Tests
[19]
pythresh.thresholds.mcst module

META
Meta-model Trained Classifier
[20]
pythresh.thresholds.meta module

MIXMOD
Normal & Non-Normal Mixture Models
[21]
pythresh.thresholds.mixmod module

MOLL
Friedrichs’ Mollifier
[22]
[23]
pythresh.thresholds.moll module

MTT
Modified Thompson Tau Test
[24]
pythresh.thresholds.mtt module

OCSVM
One-Class Support Vector Machine
[25]
pythresh.thresholds.ocsvm module

QMCD
Quasi-Monte Carlo Discrepancy
[26]
pythresh.thresholds.qmcd module

REGR
Regression Based
[27]
pythresh.thresholds.regr module

VAE
Variational Autoencoder
[28]
pythresh.thresholds.vae module

WIND
Topological Winding Number
[29]
pythresh.thresholds.wind module

YJ
Yeo-Johnson Transformation
[30]
pythresh.thresholds.yj module

ZSCORE
Z-score
[31]
pythresh.thresholds.zscore module

COMB
Thresholder Combination
None
pythresh.thresholds.comb module

Implementations, Benchmarks, & Utilities
The comparison among implemented models and general implementation
is made available below
Additional benchmarking has been
done on all the thresholders and it was found that the MIXMOD
thresholder performed best while the CLF thresholder provided the
smallest uncertainty about its mean and is the most robust (best least
accurate prediction). However, for interpretability and general
performance the MIXMOD, FILTER, and META thresholders are good
fits.
Further utilities are available for assisting in the selection of the
most optimal outlier detection and thresholding methods ranking as well as
determining the confidence with regards to the selected thresholding
method thresholding confidence

For Jupyter Notebooks, please navigate to notebooks.
A quick look at all the thresholders performance can be found at
“/notebooks/Compare All Models.ipynb”

Contributing
Anyone is welcome to contribute to PyThresh:

Please share your ideas and ask questions by opening an issue.
To contribute, first check the Issue list for the “help wanted” tag
and comment on the one that you are interested in. The issue will
then be assigned to you.
If the bug, feature, or documentation change is novel (not in the
Issue list), you can either log a new issue or create a pull request
for the new changes.
To start, fork the main branch and add your
improvement/modification/fix.
To make sure the code has the same style and standard, please refer
to qmcd.py for example.
Create a pull request to the main branch and follow the pull
request template PR template
Please make sure that all code changes are accompanied with proper
new/updated test functions. Automatic tests will be triggered. Before
the pull request can be merged, make sure that all the tests pass.

References
Please Note not all references’ exact methods have been employed in
PyThresh. Rather, the references serve to demonstrate the validity of
the threshold types available in PyThresh.

[1]
A Robust AUC Maximization Framework With Simultaneous Outlier Detection
and Feature Selection for Positive-Unlabeled Classification

[2]
An evaluation of bootstrap methods for outlier detection in least
squares regression

[3]
Chauvenet’s Test in the Classical Theory of Errors

[4]
Linear Models for Outlier Detection

[5]
Cluster Analysis for Outlier Detection

[6]
Changepoint Detection in the Presence of Outliers

[7]
Influence functions and outlier detection under the common principal
components model: A robust approach

[8]
Fast and Exact Outlier Detection in Metric Spaces: A Proximity
Graph-based Approach

[9]
Elliptical Insights: Understanding Statistical Methods through
Elliptical Geometry

[10]
Iterative gradient descent for outlier detection

[11]
Filtering Approaches for Dealing with Noise in Anomaly Detection

[12]
Sparse Auto-Regressive: Robust Estimation of AR Parameters

[13]
Estimating the Contamination Factor’s Distribution in Unsupervised
Anomaly Detection

[14]
An adjusted Grubbs’ and generalized extreme studentized deviation

[15]
Effective Histogram Thresholding Techniques for Natural Images Using
Segmentation

[16]
A new non-parametric detector of univariate outliers for distributions
with unbounded support

[17]
Riemannian center of mass and mollifier smoothing

[18]
Periodicity Detection of Outlier Sequences Using Constraint Based
Pattern Tree with MAD

[19]
Testing normality in the presence of outliers

[20]
Automating Outlier Detection via Meta-Learning

[21]
Application of Mixture Models to Threshold Anomaly Scores

[22]
Riemannian center of mass and mollifier smoothing

[23]
Using the mollifier method to characterize datasets and models: The
case of the Universal Soil Loss Equation

[24]
Towards a More Reliable Interpretation of Machine Learning Outputs for
Safety-Critical Systems using Feature Importance Fusion

[25]
Rule extraction in unsupervised anomaly detection for model
explainability: Application to OneClass SVM

[26]
Deterministic and quasi-random sampling of optimized Gaussian mixture
distributions for vibronic Monte Carlo

[27]
Linear Models for Outlier Detection

[28]
Likelihood Regret: An Out-of-Distribution Detection Score For
Variational Auto-encoder

[29]
Robust Inside-Outside Segmentation Using Generalized Winding Numbers

[30]
Transforming variables to central normality

[31]
Multiple outlier detection tests for parametric models