# Data Drift Detection

## What is data drift and why is it important?

Take a machine learning model that uses some multidimensional input data $$\mathbf{X}$$ and makes predictions $$y$$.

The model has been trained on some data distribution $$P(\mathbf{X})$$. There is data drift when the production data comes from a different distribution $$P(\mathbf{X'}) \neq P(\mathbf{X})$$.

A machine learning model operating on an input distribution different from the one it has been trained on will probably underperform. It is therefore crucial to detect data drift, in a timely manner, when a model is in production. By further investigating the characteristics of the observed drift, the data scientists operating the model can potentially estimate the impact of the drift on the model’s performance.

There is also a special case of data drift called label shift. In this case, the outcome distributions between the training and production data are different, meaning $$P(y') \neq P(y)$$. However, the relationship between the population characteristics and a specific outcome does not change, namely $$P(\mathbf{X'}|y') = P(\mathbf{X}|y)$$.

It is important to note that data drift is not the only change that can happen when there is a machine learning model in production. Another important change is concept drift, where the relationship between the model inputs and the target changes. In this case we have: $$P(y'|\mathbf{X'}) \neq P(y|\mathbf{X})$$. In production it can happen that a model experiences data drift and concept drift simultaneously.

## Data Partitions

In order to detect data drift NannyML needs two datasets. The reference partition and the analysis partition.

### Reference Partition

The reference partition’s purpose is to establish a baseline of expectations for the machine learning model being monitored. The model inputs, model outputs and the performance results of the monitored model are needed in the reference partition and are assumed to be stable and acceptable.

The reference dataset can be a reference (or benchmark) period when the monitored model has been in production and its performance results were satisfactory. Alternatively, it can be the test set used when evaluating the monitored model before deploying it to production. The reference dataset cannot be the training set used to fit the model.

### Analysis Partition

The analysis partition is where NannyML analyzes the data drift and performance characteristics of the monitored model and compares them to the reference partition. The analysis partition will usually consist of the latest production data up to a desired point in the past, which needs to be after the point where the reference partition ends. The analysis partition is not required to have ground truth and associated performance results available.

NannyML when performing drift analysis compares each Data Chunk of the analysis partition with the reference data. NannyML will flag any meaningful changes data distributions as data drift.

NannyML uses statistics to issue an Alert. It establishes an expected baseline from the reference data and when the drift results for a chunk are unlikely, given the expectations from the baseline, then it issues a drift alert. Given this statistical approach, there can be cases where the alert is a false positive. However when reviewing the data drift visualizations they can be easily spotted and discarded. An example of that will be presented later.

## Detecting drift in model inputs

Let’s start by loading some synthetic data provided by the NannyML package.

>>> import nannyml as nml
>>> import pandas as pd
>>> reference, analysis, analysis_target = nml.load_synthetic_sample()


distance_from_office

salary_range

gas_price_per_litre

public_transportation_cost

wfh_prev_workday

workday

tenure

identifier

work_home_actual

timestamp

y_pred_proba

partition

0

5.96225

40K - 60K €

2.11948

8.56806

False

Friday

0.212653

0

1

2014-05-09 22:27:20

0.99

reference

1

0.535872

40K - 60K €

2.3572

5.42538

True

Tuesday

4.92755

1

0

2014-05-09 22:59:32

0.07

reference

2

1.96952

40K - 60K €

2.36685

8.24716

False

Monday

0.520817

2

1

2014-05-09 23:48:25

1

reference

3

2.53041

20K - 20K €

2.31872

7.94425

False

Tuesday

0.453649

3

1

2014-05-10 01:12:09

0.98

reference

4

2.25364

60K+ €

2.22127

8.88448

True

Thursday

5.69526

4

1

2014-05-10 02:21:34

0.99

reference

### Univariate drift detection

NannyML’s Univariate approach for data drift looks at each variable individually and conducts statistical tests comparing the chunks created from the data provided with the reference dataset. NannyML uses the KS Test for continuous features and the 2 sample Chi squared test for categorical features. Both tests provide a statistic where they measure the observed drift and a p-value that shows how likely we are to get the observed sample under the assumption that there was no drift. If the p-value is less than 0.05 NannyML considers the result unlikely and issues an alert for the associated chunk and feature.

The UnivariateStatisticalDriftCalculator class implements the functionality needed for Univariate Drift Detection. An example using it can be seen below:

>>> # Let's initialize the object that will perform the Univariate Drift calculations
>>> # Let's use a chunk size of 5000 data points to create our drift statistics
>>> # NannyML compares drift versus the full reference dataset.
>>> univariate_calculator.fit(reference_data=reference)
>>> # let's see drift statistics for all available data
>>> data = pd.concat([reference, analysis], ignore_index=True)
>>> univariate_results = univariate_calculator.calculate(data=data)
>>> # let's view a small subset of our results:
>>> # We use the data property of the results class to view the relevant data.
>>> univariate_results.data.iloc[:5, :9]


key

start_index

end_index

start_date

end_date

partition

wfh_prev_workday_chi2

wfh_prev_workday_p_value

5

[25000:29999]

25000

29999

2016-01-08 00:00:00

2016-05-09 23:59:59

reference

3.61457

0.057

False

6

[30000:34999]

30000

34999

2016-05-09 00:00:00

2016-09-04 23:59:59

reference

0.0757052

0.783

False

7

[35000:39999]

35000

39999

2016-09-04 00:00:00

2017-01-03 23:59:59

reference

0.414606

0.52

False

8

[40000:44999]

40000

44999

2017-01-03 00:00:00

2017-05-03 23:59:59

reference

0.0126564

0.91

False

9

[45000:49999]

45000

49999

2017-05-03 00:00:00

2017-08-31 23:59:59

reference

2.20383

0.138

False

>>> univariate_results.data.iloc[-5:, :9]


key

start_index

end_index

start_date

end_date

partition

wfh_prev_workday_chi2

wfh_prev_workday_p_value

15

[75000:79999]

75000

79999

2019-04-30 00:00:00

2019-09-01 23:59:59

analysis

1179.9

0

True

16

[80000:84999]

80000

84999

2019-09-01 00:00:00

2019-12-31 23:59:59

analysis

1162.99

0

True

17

[85000:89999]

85000

89999

2019-12-31 00:00:00

2020-04-30 23:59:59

analysis

1170.49

0

True

18

[90000:94999]

90000

94999

2020-04-30 00:00:00

2020-09-01 23:59:59

analysis

1023.35

0

True

19

[95000:99999]

95000

99999

2020-09-01 00:00:00

2021-01-01 23:59:59

analysis

1227.54

0

True

NannyML returns a dataframe with 3 columns for each feature. The first column contains the corresponding test statistic. The second column contains the corresponding p-value and the third column says whether there is a drift alert for that feature and the relevant chunk.

NannyML can also visualize those results with the following code:

>>> # let's plot drift results for all model inputs
...     figure = univariate_results.plot(kind='feature_drift', metric='statistic', feature_label=feature.label)
...     figure.show()


NannyML also shows details about the distributions of continuous variables and stacked bar charts for categorical variables. It does so with the following code:

>>> # let's plot distribution drift results for continuous model inputs
...     figure = univariate_results.plot(
...         kind='feature_distribution',
...         feature_label=feature.label
...     )
...     figure.show()

>>> # let's plot distribution drift results for categorical model inputs
...     figure = univariate_results.plot(
...         kind='feature_distribution',
...         feature_label=feature.label
...     )
...     figure.show()


NannyML highlights the areas with possible data drift. Here, the tenure feature has two alerts that are false positives, from a model monitoring point of view. That is so because the measure of the drift, as shown by the KS d-statistic is very low. This is in conrast to the alerts for the public_transportation_cost for example, where the KS d-statistc grows significantly. The features distance_from_office, salary_range, public_transportation_cost, wfh_prev_workday have been rightly identified as exhibiting drift.

NannyML can rank features according to how many alerts they have had within the data analyzed for data drift. NannyML allows for the option to view the ranking of all the model inputs or just the ones that have drifted. NannyML provides a dataframe with the resulting ranking of features using the code below:

>>> ranker = nml.Ranker.by('alert_count')
>>> ranked_features


feature

rank

0

wfh_prev_workday

5

1

1

salary_range

5

2

2

distance_from_office

5

3

3

public_transportation_cost

5

4

4

tenure

2

5

5

workday

0

6

6

gas_price_per_litre

0

7

### Multivariate drift detection

The univariate approach to data drift detection is simple and interpretable but has a few significant downsides. Multidimensional data can have complex structures whose change may not be visible by just viewing the distributions of each feature.

NannyML uses Data Reconstruction with PCA to detect such changes. For a detailed explanation of the method see Data Reconstruction with PCA Deep Dive. The method returns a single number, Reconstruction Error. The changes in this value reflect a change in the structure of the model inputs. NannyML monitors the reconstruction error over time for the monitored model and raises an alert if the values get outside the range observed in the reference partition.

The DataReconstructionDriftCalculator module implements this functionality. An example of us using it can be seen below:

>>> # Let's initialize the object that will perform Data Reconstruction with PCA
>>> # Let's use a chunk size of 5000 data points to create our drift statistics
>>> # NannyML compares drift versus the full reference dataset.
>>> rcerror_calculator.fit(reference_data=reference)
>>> # let's see RC error statistics for all available data
>>> rcerror_results = rcerror_calculator.calculate(data=data)


An important detail is that Data Reconstruction with PCA Deep Dive cannot process missing values, therefore they need to be imputed. The default Imputation implemented by NannyML imputes the most frequent value for categorical features and the mean for continuous features. It takes place if the relevant optional arguments are not specified. If needed they can be specified with an instannce of SimpleImputer class in which cases NannyML will perform the imputation as instructed. An example where custom imputation strategies are used can be seen below:

>>> from sklearn.impute import SimpleImputer
>>>
>>> # Let's initialize the object that will perform Data Reconstruction with PCA
>>> rcerror_calculator = nml.DataReconstructionDriftCalculator(
>>>     chunk_size=5000,
>>>     imputer_categorical=SimpleImputer(strategy='constant', fill_value='missing'),
>>>     imputer_continuous=SimpleImputer(strategy='median')
>>> )
>>> # NannyML compares drift versus the full reference dataset.
>>> rcerror_calculator.fit(reference_data=reference)
>>> # let's see RC error statistics for all available data
>>> rcerror_results = rcerror_calculator.calculate(data=data)


Because our synthetic dataset does not have missing values, the results are the same in both cases:

>>> # We use the data property of the results class to view the relevant data.
>>> rcerror_results.data


key

start_index

end_index

start_date

end_date

partition

reconstruction_error

lower_threshold

upper_threshold

0

[0:4999]

0

4999

2014-05-09 00:00:00

2014-09-09 23:59:59

reference

1.12096

1.09658

1.13801

False

1

[5000:9999]

5000

9999

2014-09-09 00:00:00

2015-01-09 23:59:59

reference

1.11807

1.09658

1.13801

False

2

[10000:14999]

10000

14999

2015-01-09 00:00:00

2015-05-09 23:59:59

reference

1.11724

1.09658

1.13801

False

3

[15000:19999]

15000

19999

2015-05-09 00:00:00

2015-09-07 23:59:59

reference

1.12551

1.09658

1.13801

False

4

[20000:24999]

20000

24999

2015-09-07 00:00:00

2016-01-08 23:59:59

reference

1.10945

1.09658

1.13801

False

5

[25000:29999]

25000

29999

2016-01-08 00:00:00

2016-05-09 23:59:59

reference

1.12276

1.09658

1.13801

False

6

[30000:34999]

30000

34999

2016-05-09 00:00:00

2016-09-04 23:59:59

reference

1.10714

1.09658

1.13801

False

7

[35000:39999]

35000

39999

2016-09-04 00:00:00

2017-01-03 23:59:59

reference

1.12713

1.09658

1.13801

False

8

[40000:44999]

40000

44999

2017-01-03 00:00:00

2017-05-03 23:59:59

reference

1.11424

1.09658

1.13801

False

9

[45000:49999]

45000

49999

2017-05-03 00:00:00

2017-08-31 23:59:59

reference

1.11045

1.09658

1.13801

False

10

[50000:54999]

50000

54999

2017-08-31 00:00:00

2018-01-02 23:59:59

analysis

1.11854

1.09658

1.13801

False

11

[55000:59999]

55000

59999

2018-01-02 00:00:00

2018-05-01 23:59:59

analysis

1.11504

1.09658

1.13801

False

12

[60000:64999]

60000

64999

2018-05-01 00:00:00

2018-09-01 23:59:59

analysis

1.12546

1.09658

1.13801

False

13

[65000:69999]

65000

69999

2018-09-01 00:00:00

2018-12-31 23:59:59

analysis

1.12845

1.09658

1.13801

False

14

[70000:74999]

70000

74999

2018-12-31 00:00:00

2019-04-30 23:59:59

analysis

1.12289

1.09658

1.13801

False

15

[75000:79999]

75000

79999

2019-04-30 00:00:00

2019-09-01 23:59:59

analysis

1.22839

1.09658

1.13801

True

16

[80000:84999]

80000

84999

2019-09-01 00:00:00

2019-12-31 23:59:59

analysis

1.22003

1.09658

1.13801

True

17

[85000:89999]

85000

89999

2019-12-31 00:00:00

2020-04-30 23:59:59

analysis

1.23739

1.09658

1.13801

True

18

[90000:94999]

90000

94999

2020-04-30 00:00:00

2020-09-01 23:59:59

analysis

1.20605

1.09658

1.13801

True

19

[95000:99999]

95000

99999

2020-09-01 00:00:00

2021-01-01 23:59:59

analysis

1.24258

1.09658

1.13801

True

NannyML can also visualize multivariate drift results with the following code:

>>> figure = rcerror_results.plot(kind='drift')
>>> figure.show()


The multivariate drift results provide a consice summary of where data drift is happening in our input data.

## Drift detection for model outputs

NannyML also detects data drift in the Model Outputs. It uses the same univariate methodology as for a continuous feature. The results are in our previously created univariate_results object. We can visualize them with:

>>> figure = univariate_results.plot(kind='prediction_drift', metric='statistic')
>>> figure.show()


NannyML can also show how the distributions of the model predictions evolved over time:

>>> figure = univariate_results.plot(kind='prediction_distribution', metric='statistic')
>>> figure.show()


Looking at the results we see that we have a false alert on the first chunk of the analysis data. Similar to the tenure variable this is a false alert because the drift measured by the KS d-statistic is very low. This can happen when the statistical tests consider significant a small change in the distribtion of a variable in the chunks.

## Drift detection for model targets

NannyML uses TargetDistributionCalculator in order to monitor drift in Target distribution. It can calculate the mean occurance of positive events as well as the chi-squared statistic, from the 2 sample Chi Squared test, of the target values for each chunk.

In order to calculate target drift, the target values must be available. Let’s manually add the target data to the analysis data first.

Note

The Target Drift detection process can handle missing target values across all partitions.

>>> data = pd.concat([reference, analysis.set_index('identifier').join(analysis_target.set_index('identifier'), on='identifier', rsuffix='_r')], ignore_index=True).reset_index(drop=True)


distance_from_office

salary_range

gas_price_per_litre

public_transportation_cost

wfh_prev_workday

workday

tenure

identifier

work_home_actual

timestamp

y_pred_proba

partition

y_pred

50000

0.527691

0 - 20K €

1.8

8.96072

False

Tuesday

4.22463

nan

1

2017-08-31 04:20:00

0.99

analysis

1

50001

8.48513

20K - 20K €

2.22207

8.76879

False

Friday

4.9631

nan

1

2017-08-31 05:16:16

0.98

analysis

1

50002

2.07388

40K - 60K €

2.31008

8.64998

True

Friday

4.58895

nan

1

2017-08-31 05:56:44

0.98

analysis

1

Now that the data is in place we’ll create a new TargetDistributionCalculator and fit it to the reference data using the fit() method.

>>> target_distribution_calculator = nml.TargetDistributionCalculator(model_metadata=metadata, chunk_size=5000)
>>> target_distribution_calculator.fit(reference_data=reference)


After fitting the calculator is ready to use. We calculate the target distribution by calling the calculate() method, providing our previously assembled dat as an argument.

>>> target_distribution = target_distribution_calculator.calculate(data)


key

start_index

end_index

start_date

end_date

partition

targets_missing_rate

metric_target_drift

statistical_target_drift

p_value

thresholds

significant

0

[0:4999]

0

4999

2014-05-09 22:27:20

2014-09-09 08:18:27

reference

0

0.4944

0.467363

0.494203

0.05

False

False

1

[5000:9999]

5000

9999

2014-09-09 09:13:35

2015-01-09 00:02:51

reference

0

0.493

0.76111

0.382981

0.05

False

False

2

[10000:14999]

10000

14999

2015-01-09 00:04:43

2015-05-09 15:54:26

reference

0

0.505

0.512656

0.473991

0.05

False

False

The results can be easily plotted by using the plot() method.

>>> fig = target_distribution.plot(kind='distribution', distribution='metric')
>>> fig.show()


Note that a dashed line, instead of a solid line, will be used for chunks that have missing target values.

>>> fig = target_distribution.plot(kind='distribution', distribution='statistical')
>>> fig.show()