Drift
mercury.monitoring.drift
auto_encoder_drift_detector
AutoEncoderDriftDetector(p_val=0.05, bootstrap_samples=30, bootstrap_sample_size=10000, autoencoder_kwargs=None, custom_reconstruction_error='mse', fitted_models=None, reference_errors=None)
This class uses several autoencoders for testing whether the joint distributions of two datasets are the same. In order to do this, it makes bootstrap samples from a source dataset (X_src), trains an autoencoder on each one of them (using training/test splits) and it stores the distribution of reconstruction errors (i.e. the error distribution reconstructing the source dataset). The default reconstruction error is the MSE, although you can specify your own.
Then, when target data is available (X_target), it calculates the error distribution on the new environment and compares it with the one obtained on X_src by using a MannWithneyU statistical test under the null hypothesis (H0) that no drift exists (that is, the two error samples come from the same distribution).
Parameters:
Name  Type  Description  Default 

p_val 
float

Significance level for rejecting the null hypothesis. Default value is 0.05. 
0.05

bootstrap_samples 
int

How many bootstrap samples to make 
30

bootstrap_sample_size 
int

The size of each bootstrap sample. 
10000

autoencoder_kwargs 
dict

Dictionary with arguments for training the internal 
None

custom_reconstruction_error 
callable or string

Custom function for measuring reconstruction quality. This is only used for the
drift calculation, not for training the autoencoders (use autoencoder_kwargs for that). This
can be a string in (mse, rmse, mae), meaning (Mean Squared Error, Root Mean Squared Error,
Mean Absolute Loss error). Alternatively, you can also provide a custom function with the form

'mse'

fitted_models 
list

List with trained autoencoders (tf.keras.Model). Use it only if you want to "reload" an already trained detector. 
None

reference_errors 
List[float]

List with the errors obtained at the time of training the detector. Use it only if you want to "reload" an already trained detector. 
None

Example
>>> from mercury.monitoring.drift.auto_encoder_drift_detector import AutoEncoderDriftDetector
# Create example datasets
>>> X_src = np.array([np.random.normal(0, 1, 1000), np.random.normal(0, 1, 1000)]).T
>>> X_target = np.array([np.random.normal(0, 1, 500) + 2, np.random.normal(0, 1, 500)]).T
# Train the detector on the source dataset
>>> drift_detector = AutoEncoderDriftDetector()
>>> drift_detector = drift_detector.fit(X_src)
# Use the detector for checking whether drift exists on X_target
>>> drift_detector.calculate_drift(X_target)
"{'pval': 7.645836962858183e06, 'drift': True}"
Source code in mercury/monitoring/drift/auto_encoder_drift_detector.py
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is_fitted: bool
property
Whether the detector has been fitted and it's ready for calculating drift
calculate_drift(X, return_errors=False)
Checks whether drift exists on a given dataset using X_src as reference:
Parameters:
Name  Type  Description  Default 

X 
np.ndarray

the target dataset. 
required 
return_errors 
bool

Whether to include the reconstruction errors in the result. 
False

Returns:
Type  Description 

dict

Dictionary containing the result of the test and, optionally, the reference 
dict

and target reconstruction errors. 
Source code in mercury/monitoring/drift/auto_encoder_drift_detector.py
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fit(X_src)
Trains the detector using a source (reference) dataset.
Parameters:
Name  Type  Description  Default 

X_src 
np.ndarray

the reference dataset. 
required 
Returns:
Type  Description 

AutoEncoderDriftDetector

the detector itself. 
Source code in mercury/monitoring/drift/auto_encoder_drift_detector.py
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base
BaseBatchDriftDetector(X_src=None, X_target=None, distr_src=None, distr_target=None, features=None, correction='bonferroni', p_val=0.05)
Bases: ABC
Base class for batch drift detection.
The class can be extended to create a method for batch drift detection over a source dataset X_src
and target
dataset X_target
, or a source dataset distributions distr_src
and a target dataset distributions distr_target
The main method to implement is the calculate_drift()
method.
Source code in mercury/monitoring/drift/base.py
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calculate_drift()
abstractmethod
Method to implement in extended classes
Source code in mercury/monitoring/drift/base.py
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get_drifted_features(return_as_indices=False)
Gets the features that are considered to have drift. The method calculate_drift
needs to be called first.
The parameter return_as_indices
controls whether to return the features as indices or names.
Parameters:
Name  Type  Description  Default 

return_as_indices 
boolean

whether to return the features as indices or names. 
False

Returns:
Type  Description 

list

features with drift. 
Source code in mercury/monitoring/drift/base.py
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plot_distribution_drifted_features(figsize=(8, 4), kde=True, stat='density', common_bins=True, common_norm=False, **kwargs)
Plots the distributions of the features that are considered to have drift. The method calculate_drift
needs to be called first.
Parameters:
Name  Type  Description  Default 

figsize 
tuple

figsize to use if 
(8, 4)

kde 
bool

whether to show the smoothed distribution. Default is True 
True

stat 
str

Aggregate statistic to compute in each bin. By default is 'density'. Valid values can be checked in seaborn documentation 
'density'

common_bins 
bool

If True, use the same bins for the target and source dataset. By default is True 
True

common_norm 
bool

If True and using a normalized statistic, the normalization will apply over the full dataset (src and target). Otherwise, the normalization is applied to each set independently. Default is False. 
False

kwargs 
Extra key arguments that can be passed to seaborn 
{}

Source code in mercury/monitoring/drift/base.py
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plot_distribution_feature(idx_feature=None, name_feature=None, ax=None, figsize=(8, 4), kde=True, stat='density', common_bins=True, common_norm=False, **kwargs)
Plots the distribution of a given feature for the source and the target datasets.
The feature can be indicated by the index using the idx_feature
parameter, or by the name using the
name_feature
parameter (only possible if attribute features
was specified.
Parameters:
Name  Type  Description  Default 

idx_feature 
int

index of the feature 
None

name_feature 
string

name of the feature 
None

ax 
matplotlib.axes._subplots.AxesSubplot

Axes object on which the data will be plotted. If not specified it creates one. 
None

figsize 
tuple

figsize to use if 
(8, 4)

kde 
bool

whether to show the smoothed distribution. Default is True 
True

stat 
str

Aggregate statistic to compute in each bin. By default is 'density'. Valid values can be checked in seaborn documentation 
'density'

common_bins 
bool

If True, use the same bins for the target and source dataset. By default is True 
True

common_norm 
bool

If True and using a normalized statistic, the normalization will apply over the full dataset (src and target). Otherwise, the normalization is applied to each set independently. Default is False. 
False

kwargs 
Extra key arguments that can be passed to seaborn 
{}

Returns:
Type  Description 

The axes 
Source code in mercury/monitoring/drift/base.py
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plot_feature_drift_scores(top_k=None, ax=None, figsize=(8, 4))
Plots a summary of the scores for each feature. The meaning of the score depends on the subclass that is used.
Parameters:
Name  Type  Description  Default 

top_k 
int

If specified, plots only the top_k features with higher scores. 
None

ax 
matplotlib.axes._subplots.AxesSubplot

Axes object on which the data will be plotted. If not specified it creates one. 
None

figsize 
tuple

Size of the plotted figure 
(8, 4)

Source code in mercury/monitoring/drift/base.py
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plot_histograms_drifted_features(figsize=(8, 4))
Plots the histograms of the features that are considered to have drift. The method calculate_drift
needs to be called first.
Parameters:
Name  Type  Description  Default 

figsize 
tuple

figsize to use if 
(8, 4)

Source code in mercury/monitoring/drift/base.py
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plot_histograms_feature(idx_feature=None, name_feature=None, figsize=(8, 4))
Plots the histograms of a given feature for the source and the target distributions.
The feature can be indicated by the index using the idx_feature
parameter, or by the name using the
name_feature
parameter (only possible if attribute features
was specified.
Parameters:
Name  Type  Description  Default 

idx_feature 
int

index of the feature 
None

name_feature 
string

name of the feature 
None

figsize 
tuple

figsize to use if 
(8, 4)

Returns:
Type  Description 

The axes 
Source code in mercury/monitoring/drift/base.py
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chi2_drift_detector
Chi2Drift(distr_src=None, distr_target=None, features=None, correction='bonferroni', p_val=0.05)
Bases: BaseBatchDriftDetector
The Chi2Drift class allows us to detect drift in the source dataset distributions distr_src
and the
target dataset distributions distr_target
by performing a chisquare test of independence of variables in a
contingency table for each feature. It does it separately for each feature, calculating the statistic and the
pvalue. The source and target distributions are specified when creating the object. Then, the method
calculate_drift()
is used to obtain a dict of metrics.
Parameters:
Name  Type  Description  Default 

distr_src 
list of np.arrays

The source dataset distributions. It's a list of np.arrays, where each np.array represents the counts of
each bin for that feature. The features and its bins must be in the same order than the 
None

distr_target 
list of np.arrays

The target dataset distributions. It's a list of np.arrays, where each np.array represents the counts of
each bin for that feature. The features and its bins must be in the same order than the 
None

features 
list

The name of the features of 
None

p_val 
float

Threshold to be used with the pvalue obtained to decide if there is drift or not (affects

0.05

correction 
string

Since multiple tests are performed, this parameter controls whether to perform a correction of the pvalue
or not (affects 
'bonferroni'

Example
>>> from mercury.monitoring.drift.chi2_drift_detector import Chi2Drift
# Create example distributions
>>> histograms_src = [np.array([5, 5, 5]), np.array([3, 6, 9])]
>>> histograms_target = [np.array([4, 1, 8]), np.array([20, 3, 2])]
# Calculate drift
>>> drift_detector = Chi2Drift(
... distr_src=histograms_src, distr_target=histograms_target, features=["f1", "f2"],
... correction="bonferroni", p_val=0.01)
>>> drift_metrics = drift_detector.calculate_drift()
# Print the metrics
>>> print("Drift Score: ", drift_metrics["score"])
>>> print("Is drift detected? ", drift_metrics["drift_detected"])
# Plot feature drift scores
>>> ax = drift_detector.plot_feature_drift_scores(top_k=7)
# Get drifted features
>>> print(drift_detector.get_drifted_features())
# Plot histograms of drifted features
>>> drift_detector.plot_histograms_drifted_features()
Source code in mercury/monitoring/drift/chi2_drift_detector.py
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calculate_drift()
Computes drift by performing a chisquare test of independence between the source dataset distributions
distr_src
and the target dataset distributions distr_target
. It performs the test individually for each
feature and obtains the pvalues and the value of the statistic for each.
The returned dictionary contains the next metrics:
 p_vals: np.array of the pvalues returned by the Chi2 test for each feature.
 scores: np.array of the chi2 statistics for each feature.
 score: average of all the scores.
 drift_detected: final decision if drift is detected. If any of the pvalues of the features is lower than
the threshold, then this is set to 1. Otherwise is 0. This will depend on the specified
p_val
andcorrection
values.  threshold: final threshold applied to decide if drift is detected. It depends on the specified
p_val
andcorrection
values.
Returns:
Type  Description 

dict

Dictionary with the drift metrics as specified. 
Source code in mercury/monitoring/drift/chi2_drift_detector.py
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density_drift_detector
DensityDriftDetector(embedding_dim=2, vae=None, encoder=None, decoder=None)
This detector calculates the "probability" of a particular sample of being an anomaly (or presenting drift) with respect to a source reference dataset.
This detector works using a VAE for building embeddings of the input data. Then, with those source embeddings, the density is estimated in such a way that zones in the embeddings space with lots of samples have high density whereas zones with low density represent "less" probable samples.
After having trained the detector it can be used for checking whether a particular (new) sample is an anomaly.
Parameters:
Name  Type  Description  Default 

embedding_dim 
int

embedding dimensionality for the VAE (if no 
2

vae 
tf.keras.Model

Optional VAE architecture 
None

encoder 
tf.keras.Model

encoder part from 
None

decoder 
tf.keras.Model

decoder part from 
None

Example
>>> from mercury.monitoring.drift.density_drift_detector import DensityDriftDetector
>>> detector = DensityDriftDetector().fit(X_source)
Source code in mercury/monitoring/drift/density_drift_detector.py
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explain(x, ref_point=None)
Explains what features have to change in a certain sample (or batch of samples)
x so it becomes a ref_point
in the embedding space. You can use this mehod when
you have "anomalies" and what to check what feeatures need to change for the point
to be an inlier.
If ref_point
is None, the considered reference point will be the point in the
embedding space with highest density (i.e. the most normal one).
The returned explanation will be an array with dim(explanation) = dim(x) in which each item points the direction and amount each feature needs to change (also known as delta).
Parameters:
Name  Type  Description  Default 

x 
np.ndarray

datapoint (or batch of datapoints) to explain 
required 
ref_point 
Optional[np.ndarray]

Reference point coords in the embedding space 
None

Returns:
Type  Description 

np.ndarray

numpy array(s) with explanation(s) per item. 
Source code in mercury/monitoring/drift/density_drift_detector.py
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fit(source, epochs=None, batch_size=128)
Fits the model
Parameters:
Name  Type  Description  Default 

source 
Union[np.ndarray, pd.DataFrame]

Reference dataset 
required 
epochs 
int

Number of epochs to train the model. If None, early stopping will be used. 
None

batch_size 
int

batch_size 
128

Returns:
Type  Description 

self, detector trained 
Source code in mercury/monitoring/drift/density_drift_detector.py
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predict(X)
Predicts the "probability" of each sample in X being an inlier. That is, its similarity to the reference points seen during training.
Parameters:
Name  Type  Description  Default 

X 
np.ndarray

dataset 
required 
Returns:
Type  Description 

np.ndarray

numpy array with densities 
Source code in mercury/monitoring/drift/density_drift_detector.py
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predict_embeddings(target)
Gets the embeddings predicted by the VAE's encoder.
Parameters:
Name  Type  Description  Default 

target 
dataset 
required 
Returns:
Type  Description 

np.ndarray

numpy array with embeddings 
Source code in mercury/monitoring/drift/density_drift_detector.py
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domain_classifier_drift_detector
DomainClassifierDrift(X_src=None, X_target=None, features=None, p_val=0.05, test_size=0.3, n_runs=10, alpha=0.025, **kwargs)
Bases: BaseBatchDriftDetector
This class is a drift detector that allows us to train a classifier (Random Forest) to distinguish between a
source dataset X_src
and a target dataset X_target
. The source and target datasets are specified when creating
the object together with other available parameters. Then the method calculate_drift()
is used to obtain a dict
of metrics.
Parameters:
Name  Type  Description  Default 

X_src 
np.array

The source dataset. 
None

X_target 
np.array

The target dataset. 
None

features 
list

The name of the features of 
None

p_val 
float

Threshold to be used with the pvalue obtained to decide if there is drift or not (affects

0.05

test_size 
float

When training the domain classifier, this parameter indicates the size of the test set of the domain
classifier. Since the metric 
0.3

n_runs 
int

This is the number of times that the domain classifier is trained with different splits. The returned metrics correspond to the averages of different runs. A higher number of runs will produce more accurate metrics, but it will be computationally more expensive. 
10

alpha 
float

This parameter impacts directly to the false drift detection rate. Concretely, it specifies how much better the AUC of the domain classifier has to be than 0.5 (as a random classifier) to consider that successfully distinguishes samples from the source dataset and target dataset. Increasing the value will be more conservative when detecting drift, so it will lower the false positive detection rate. However, higher values also can miss true drift detection. Default value is 0.025 which in general a good tradeoff. 
0.025

**kwargs 
The rest of the parameters will be used in the Random forest trained as domain classifier. If not specified, then the default parameters will be used. 
{}

Example
>>> from mercury.monitoring.drift.domain_classifier_drift import DomainClassifierDrift
# Create example datasets
>>> X_src = np.array([np.random.normal(0, 1, 1000), np.random.normal(0, 1, 1000)]).T
>>> X_target = np.array([np.random.normal(0, 1, 500) + 2, np.random.normal(0, 1, 500)]).T
# Calculate drift
>>> drift_detector = DomainClassifierDrift(
... X_src, X_target, features=["f1", "f2"], p_val=0.01, test_size=0.3, n_runs=10)
>>> drift_metrics = drift_detector.calculate_drift()
# Print the metrics
>>> print("Drift Score: ", drift_metrics["score"])
>>> print("p_val: ", drift_metrics["p_val"])
>>> print("Is drift detected? ", drift_metrics["drift_detected"])
# Get drift scores per feature
>>> drift_detector.plot_feature_drift_scores(figsize=(8,4))
Source code in mercury/monitoring/drift/domain_classifier_drift_detector.py
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calculate_drift(return_drift_score_target=False)
Calculates the drift metrics. The returned drift metrics are in a dictionary with the next keys:
 drift_detected: indicates if drift is detected or not, comparing the indicated
p_val
and the obtained pvalue. The obtained pvalue is based on a binomial test that takes into account the number of times that the AUC of the domain classifier was higher than random guesses.  drift_score: this is the average AUC obtained by the domain classifier over the different runs.
If the parameter return_drift_score_target
is True, then it also returns a dataframe with a drift score for
each sample in the target dataset. This score is the predicted probability by the domain classifier and can
help to detect the drifted samples.
Parameters:
Name  Type  Description  Default 

return_drift_score_target 
boolean

Indicates if additionally return a dataframe with a drift score for each sample in the target dataset 
False

Returns:
Type  Description 

dict

Dictionary with the drift metrics. If parameter 
returns a dataframe with the drift scores for the target dataset. 
Source code in mercury/monitoring/drift/domain_classifier_drift_detector.py
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drift_simulation
BatchDriftGenerator(X, schema=None)
This is a simulator for applying synthetic perturbations to a given dataset, so real life drift situations can be generated.
It allows generating several typical driftlike perturbations. In particular, it has the
following ones implemented
1) Shift drift: Each one of the numerical features will be shifted by an amount N. With this,
you will be able to simulate situations where a particular feature increases of decreases.
2) Recodification drift: This operations simulates the situation where a particular feature
changes its codification (due to some change in a data ingestion pipeline). For example, imagine
a feature codified as [A, B, C] and, for some reason, category "C" becomes "A" and vice versa.
3) Missing value drift: Artificially increases the percentage of NaNs on a given feature or
list of features.
4) Hyperplane rotation drift: This method operates by modifying a set of features at once but
attempting to preserve the relationships they have. In other terms, it tries to change the
joint distribution of N continuous variables at once.
5) Outliers drift: This method artificially introduces outliers in the specified columns. You
can use one of the existing methods to inject outliers or create your own method. Check the
method documentation for outliers_drift
for further documentation
Parameters:
Name  Type  Description  Default 

X 
Union[pd.DataFrame, np.ndarray]

Dataset features 
required 
names_categorical 
An optional list with the names of the categorical variables. If given, 
required 
Source code in mercury/monitoring/drift/drift_simulation.py
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__get_rotation_matrix(n, deg)
Returns a rotation matrix for a R^n space.
Parameters:
Name  Type  Description  Default 

n 
int

Dimensionality of the space 
required 
deg 
float

amount of rotation to be applied. In degrees. 
required 
Returns:
Type  Description 

np.ndarray

nxn dimensional rotation matrix 
Source code in mercury/monitoring/drift/drift_simulation.py
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__remap_categorical(df, colname)
Randomly shuffles the categories of a particular column
Source code in mercury/monitoring/drift/drift_simulation.py
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hyperplane_rotation_drift(cols=None, force=10.0)
Adds drift to several features at once by rotating them.
Parameters:
Name  Type  Description  Default 

cols 
List[str]

columns which will be jointly rotated. 
None

force 
float

rotation amount in degrees (0 or 360 = no transformation) 
10.0

Returns:
Type  Description 

BatchDriftGenerator

An updated version of the simulator. 
Source code in mercury/monitoring/drift/drift_simulation.py
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missing_val_drift(cols=None, percent=0.1)
Randomly injects NaN values in a column.
Parameters:
Name  Type  Description  Default 

cols 
List[str]

Columns where this operation will be performed 
None

percent 
Union[float, List[float]]

Percentage of values which will become Null values. 
0.1

Returns:
Type  Description 

BatchDriftGenerator

An updated version of the simulator. 
Source code in mercury/monitoring/drift/drift_simulation.py
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outliers_drift(cols=None, method='percentile', method_params=None)
Injects outliers in cols
using the method specified in method
. Parameters of the method can
be specified using method_params
.
Parameters:
Name  Type  Description  Default 

cols 
List[str]

List of columns names to generate outliers. 
None

method 
Union[str, Callable]

string of the method to generate to use or custom function to generate outliers. If
using string, the current available method are 'percentile' and 'value'. If using 'percentile'
values in the dataframe are replaced by a percentile of that column. The percentile to use is
specified in key 'percentile' in 
'percentile'

method_params 
dict

dictionary containing the parameters to use in 
None

Returns:
Type  Description 

BatchDriftGenerator

An updated version of the simulator. 
Source code in mercury/monitoring/drift/drift_simulation.py
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recodification_drift(cols=None)
Adds drift by randomly remapping the categories of cols. For example, if you have a column with domain: ["A", "B", "C"], then, this operation would swap all the "A" with "C" (and vice versa).
Note the swaps are random. The same remapping will not be repeated.
Parameters:
Name  Type  Description  Default 

cols 
List[str]

List of columns names to be recoded 
None

Returns:
Type  Description 

BatchDriftGenerator

An updated version of the simulator. 
Source code in mercury/monitoring/drift/drift_simulation.py
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scale_drift(cols=None, mean=1, sd=0.05, iqr=None)
Adds drift to one or several features by multiplying then by some random factor (normally close to 1).
Parameters:
Name  Type  Description  Default 

cols 
List[str]

List of columns names where the operation will be performed 
None

mean 
The mean value of the random scale (if iqr is not given). Default is 1. 
1


sd 
The standard deviation of the random scale (if iqr is not given). Default is 0.05. 
0.05


iqr 
An alternative way to define the random scale is by giving the interquartile range as a list of 2 elements. E.g. [1, 1.2] 
None

Returns:
Type  Description 

BatchDriftGenerator

An updated version of the simulator. 
Source code in mercury/monitoring/drift/drift_simulation.py
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shift_drift(cols=None, force=5.0, noise=0.0)
Adds drift to one or several features by adding or substracting a force
quantity. You could also add random noise to these shifts via the noise
parameter. The shifted amount will follow a gaussian distribution with mean
force
and std noise
.
Parameters:
Name  Type  Description  Default 

cols 
List[str]

List of columns names where the operation will be performed 
None

force 
Amount shift each column will receive 
5.0


noise 
Amount of standard deviation the shift of each column will receive. 
0.0

Returns:
Type  Description 

BatchDriftGenerator

An updated version of the simulator. 
Source code in mercury/monitoring/drift/drift_simulation.py
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histogram_distance_drift_detector
HistogramDistanceDrift(distr_src=None, distr_target=None, features=None, correction=None, p_val=None, n_permutations=50, distance_metric='hellinger')
Bases: BaseBatchDriftDetector
The HistogramDistanceDrift class allows us to detect drift in the source dataset distributions distr_src
and the
target dataset distributions distr_target
by calculating distances between the distributions. For each feature,
the distance between its distributions in distr_src
and distr_target
is calculated. The distance function to
use is indicated by the distance_metric
parameter. For each feature, a pvalue is also calculated. This is
calculated by doing a permutation test, where data from distr_src
and distr_target
are put together and sampled
to calculate a new simulated distance n_permutations
times. The pvalue then is obtained by computing
the fraction of simulated distances equal or greater than the observed distance. The source and target distributions
are specified when creating the object. Then, the method calculate_drift()
is used to obtain a dict of metrics.
Parameters:
Name  Type  Description  Default 

distr_src 
list of np.arrays

The source dataset distributions. It's a list of np.arrays, where each np.array represents the counts of
each bin for that feature. The features and its bins must be in the same order than the 
None

distr_target 
list of np.arrays

The target dataset distributions. It's a list of np.arrays, where each np.array represents the counts of
each bin for that feature. The features and its bins must be in the same order than the 
None

features 
list

The name of the features of 
None

distance_metric 
string

The distance metric to use. Available metrics are "hellinger", "jeffreys" or "psi". Default value is "hellinger" 
'hellinger'

p_val 
float

Threshold to be used with the pvalue obtained to decide if there is drift or not (affects

None

correction 
string

Since multiple tests are performed, this parameter controls whether to perform a correction of the pvalue
or not (affects 
None

n_permutations 
int

The number of permutations to perform to calculate the pvalue. A higher number will calculate a more accurate pvalue, but it will be computationally more expensive. Default value is 50 
50

Example
>>> from mercury.monitoring.drift.histogram_distance_drift_detector import HistogramDistanceDrift
# Create example distributions
>>> histograms_src = [np.array([5, 5, 5]), np.array([3, 6, 9])]
>>> histograms_target = [np.array([4, 1, 8]), np.array([20, 3, 2])]
# Calculate drift
>>> drift_detector = HistogramDistanceDrift(
... distr_src=histograms_src, distr_target=histograms_target, features=["f1", "f2"],
... distance_metric="hellinger", correction="bonferroni", p_val=0.01, n_permutations=100)
>>> drift_metrics = drift_detector.calculate_drift()
# Print the metrics
>>> print("Drift Score: ", drift_metrics["score"])
>>> print("Is drift detected? ", drift_metrics["drift_detected"])
# Plot feature drift scores
>>> ax = drift_detector.plot_feature_drift_scores(top_k=7)
# Get drifted features
>>> print(drift_detector.get_drifted_features())
# Plot histograms of drifted features
>>> drift_detector.plot_histograms_drifted_features()
Source code in mercury/monitoring/drift/histogram_distance_drift_detector.py
69 70 71 72 73 74 75 76 77 

calculate_drift()
Computes drift by calculating histogrambased distances between the source dataset distributions distr_src
and the target dataset distributions distr_target
. It calculates the distance individually for each feature
and obtains the pvalues and distance for each.
The returned dictionary contains the next metrics:
 p_vals: np.array of the pvalues returned by the permutation test for each feature.
 scores: np.array of the distances for each feature.
 score: average of all the distances.
 drift_detected: final decision if drift is detected. If any of the pvalues of the features is lower than
the threshold, then this is set to 1. Otherwise is 0. This will depend on the specified
p_val
andcorrection
values.  threshold: final threshold applied to decide if drift is detected. It depends on the specified
p_val
andcorrection
values.
Returns:
Type  Description 

dict

Dictionary with the drift metrics as specified. 
Source code in mercury/monitoring/drift/histogram_distance_drift_detector.py
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ks_drift_detector
KSDrift(X_src=None, X_target=None, features=None, correction='bonferroni', p_val=0.05)
Bases: BaseBatchDriftDetector
This class is a drift detector that allows us to detect drift in a source dataset X_src
and a target dataset
X_target
by calculating the KolmogorovSmirnov (KS) statistic. For each feature in the datasets, a
KolmogorovSmirnov test is performed, which calculates the distance between the feature using the samples of each
dataset. A pvalue is also obtained when performing the tests, which are used to decide if exists drift in the
datasets. The source and target datasets are specified when creating the object together with other available
parameters. Then the method calculate_drift()
is used to obtain a dict of metrics.
Parameters:
Name  Type  Description  Default 

X_src 
np.array

The source dataset. 
None

X_target 
np.array

The target dataset. 
None

features 
list

The name of the features of 
None

p_val 
float

Threshold to be used with the pvalue obtained to decide if there is drift or not (affects

0.05

correction 
string

Since multiple tests are performed, this parameter controls whether to perform a correction of the pvalue
or not (affects 
'bonferroni'

Example
>>> from mercury.monitoring.drift.ks_drift_detector import KSDrift
# Create example datasets
>>> X_src = np.array([np.random.normal(0, 1, 1000), np.random.normal(0, 1, 1000)]).T
>>> X_target = np.array([np.random.normal(0, 1, 500) + 2, np.random.normal(0, 1, 500)]).T
# Calculate drift
>>> drift_detector = KSDrift(X_src, X_target, features=["f1", "f2"], p_val=0.01, correction="bonferroni")
>>> drift_metrics = drift_detector.calculate_drift()
# Print the metrics
>>> print("Drift Score: ", drift_metrics["score"])
>>> print("Is drift detected? ", drift_metrics["drift_detected"])
# Plot feature drift scoress
>>> ax = drift_detector.plot_feature_drift_scores(top_k=7)
# Get drifted features
>>> print(drift_detector.get_drifted_features())
# Plot distributions of drifted features
>>> drift_detector.plot_distribution_drifted_features()
Source code in mercury/monitoring/drift/ks_drift_detector.py
56 57 

calculate_drift()
Computes Drift using the KolmogorovSmirnov KS Test, which calculates the largest difference of the cumulative density functions of two variables. It performs the test individually for each feature and obtains the pvalues and the statistics for each feature. The returned dictionary contains the next metrics:
 p_vals (np.array): the pvalues returned by the KS test for each feature.
 scores (np.array): the distances (ks statistic) return by the KS test for each feature.
 score: average of all the distances.
 drift_detected: final decision if drift is detected. If any of the pvalues of the features is lower than
the threshold, then this is set to 1. Otherwise is 0. This will depend on the specified
p_val
andcorrection
values.  threshold: final threshold applied to decide if drift is detected. It depends on the specified
p_val
andcorrection
values.
Returns:
Type  Description 

dict

Dictionary with the drift metrics as specified. 
Source code in mercury/monitoring/drift/ks_drift_detector.py
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metrics
bootstrap_eval_drift(y_true_src=None, y_pred_src=None, y_true_target=None, y_pred_target=None, eval_fn=None, resample_size_src=None, resample_size_target=None, num_resamples=50, drift_detector=None)
This function performs resampling with replacement for a source set and a target set to obtain
a distribution of some evaluation metric for both sets. Then, applies a drift detector to calculate
the drift of the metric between the source and target sets. More concretely, first performs resampling
with replacement in the arrays y_true_src
and y_pred_src
and calculates a metric using the
eval_fn
function in order to obtain a metric for each resample. Thus, we obtain a distribution of a
metric for the source set. Next, it performs the same procedure with the arrays y_true_target
and
y_pred_target
, which gives a distribution of the metric for the target dataset. Finally, applies
a drift detector (KSDrift if not specified) in order to calculate the drift between the source and
target obtained distributions.
Parameters:
Name  Type  Description  Default 

y_true_src 
np.array

array which will be the first argument when calling 
None

y_pred_src 
np.array

array which will be the second argument when calling 
None

y_true_target 
np.array

array which will the first argument when calling 
None

y_pred_target 
np.array

array which will be the second argument when calling 
None

eval_fn 
Callable

function that must return a float. For the source dataset, receives a resamples
of 
None

resample_size_src 
int

size of each resample for the source dataset. If None, length of the source. 
None

resample_size_target 
int

size of each resample for the target dataset. If None, length of the target. 
None

num_resamples 
int

number of resamples 
50

drift_detector 
drift detector to use. If None it will create a KSDrift object 
None

Returns:
Name  Type  Description 

drift_metrics 
dict

dictionary with the obtained drift metrics 
drift_detector 
BaseBatchDriftDetector

drift detector object used to calculate drift 
dist_src 
np.array

obtained metrics distribution for the source dataset 
dist_target 
np.array

obtained metrics distribution for the target dataset 
Example
>>> y_true_src = np.array([0,0,0,0,0,1,1,1,1,1])
>>> y_pred_src = np.array([0,0,0,0,1,0,1,1,1,1])
>>> y_true_target = np.array([0,0,0,0,0,1,1,1,1,1])
>>> y_pred_target = np.array([0,1,1,1,1,0,0,0,0,1])
>>> def eval_acc(y_true, y_pred):
... return np.sum(y_true == y_pred) / y_true.shape[0]
>>> drift_metrics, drift_detector, dist_src, dist_target = bootstrap_eval_drift(
... y_true_src=y_true_src, y_pred_src=y_pred_src, y_true_target=y_true_target, y_pred_target=y_pred_target,
... resample_size_src=8, resample_size_target=8, num_resamples=1000,
... eval_fn=eval_acc, drift_detector=None
... )
>>> drift_metrics["drift_detected]
True
>>> drift_metrics["score"]
0.943
Source code in mercury/monitoring/drift/metrics.py
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hellinger_distance(p, q, normalize=True)
Computes Hellinger distance between two histograms as specified in this paper: http://users.rowan.edu/~polikar/RESEARCH/PUBLICATIONS/cidue11.pdf Both histograms are represented by numpy arrays with the same number of dimensions, where each dimension represents the counts for that particular bin. It is assumed that the bin edges are the same.
Parameters:
Name  Type  Description  Default 

p 
np.array

First histogram. Each dimension represents one bin and bin edges are assumed to be the same as in q. 
required 
q 
np.array

Second histogram. Each dimension represents one bin and bin edges are assumed to be the same as in p. 
required 
normalize 
bool

Whether to normalize the histograms. If True the proportions of each bin are calculated first and then the distance is calculated with the proportions 
True

Returns 
(float): float representing the Hellinger distance 
required 
Source code in mercury/monitoring/drift/metrics.py
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jeffreys_divergence(p, q, normalize=True)
Computes Jeffreys divergence between two histograms as specified in this paper: https://www.cs.cmu.edu/~efros/courses/LBMV07/Papers/rubnerjcviu00.pdf Both histograms are represented by numpy arrays with the same number of dimensions, where each dimension represents the counts for that particular bin. It is assumed that the bin edges are the same.
Parameters:
Name  Type  Description  Default 

p 
np.array

First histogram. Each dimension represents one bin and bin edges are assumed to be the same as in q. 
required 
q 
np.array

Second histogram. Each dimension represents one bin and bin edges are assumed to be the same as in p. 
required 
normalize 
bool

Whether to normalize the histograms. If True the proportions of each bin are calculated first and then the distance is calculated with the proportions 
True

Returns 
(float): float representing the hellinger distance 
required 
Source code in mercury/monitoring/drift/metrics.py
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psi(p, q, normalize=True, eps=0.0001)
Calculates the Population Stability Index (PSI). The metric helps to measure the stability between two population samples. It assumes that the two population samples have already been splitted in bins, so the histograms are the input to this function.
Parameters:
Name  Type  Description  Default 

p 
np.array

First histogram. Each dimension represents one bin and bin edges are assumed to be the same as in q. 
required 
q 
np.array

Second histogram. Each dimension represents one bin and bin edges are assumed to be the same as in p. 
required 
normalize 
bool

Whether to normalize the histograms. If True the proportions of each bin are calculated first and then the distance is calculated with the proportions 
True

Returns:
Type  Description 

float

float representing the PSI 
Example
>>> a = np.array([12, 11, 14, 12, 12, 10, 12, 6, 6, 5])
>>> b = np.array([11, 11, 12, 13, 11, 11, 13, 5, 7, 6])
>>> psi = psi(a, b)
Source code in mercury/monitoring/drift/metrics.py
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