# Multivariate Data Drift Detection

## Why Perform Multivariate Drift Detection

Multivariate data drift detection addresses the shortcomings of univariate data detection methods. It provides one summary number reducing the risk of false alerts, and detects more subtle changes in the data structure that cannot be detected with univariate approaches.

## Just The Code

```>>> import nannyml as nml
>>> from IPython.display import display

>>> # Define feature columns
>>> feature_column_names = [
...     col for col in reference.columns if col not in [
...         'timestamp', 'y_pred_proba', 'period', 'y_pred', 'work_home_actual', 'identifier'
...     ]]

>>> calc = nml.DataReconstructionDriftCalculator(
...     column_names=feature_column_names,
...     timestamp_column_name='timestamp',
...     chunk_size=5000
>>> )
>>> calc.fit(reference)
>>> results = calc.calculate(analysis)

>>> display(results.filter(period='analysis').to_df())

>>> display(results.filter(period='reference').to_df())

>>> figure = results.plot(plot_reference=True)
>>> figure.show()
```

## Walkthrough

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, measuring the Reconstruction Error. The changes in this value reflect a change in the structure of the model inputs.

NannyML calculates the reconstruction error over time for the monitored model, and raises an alert if the values get outside of a range defined by the variance in the reference data period.

In order to monitor a model, NannyML needs to learn about it from a reference dataset. Then it can monitor the data that is subject to actual analysis, provided as the analysis dataset. You can read more about this in our section on data periods

Let’s start by loading some synthetic data provided by the NannyML package, and setting it up as our reference and analysis dataframes. This synthetic data is for a binary classification model, but multi-class classification can be handled in the same way.

```>>> import nannyml as nml
>>> from IPython.display import display

```

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

period

y_pred

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

1

0.535872

40K - 60K €

2.3572

5.42538

True

Tuesday

4.92755

1

0

2014-05-09 22:59:32

0.07

reference

0

2

1.96952

40K - 60K €

2.36685

8.24716

False

Monday

0.520817

2

1

2014-05-09 23:48:25

1

reference

1

3

2.53041

20K - 40K €

2.31872

7.94425

False

Tuesday

0.453649

3

1

2014-05-10 01:12:09

0.98

reference

1

4

2.25364

60K+ €

2.22127

8.88448

True

Thursday

5.69526

4

1

2014-05-10 02:21:34

0.99

reference

1

The `DataReconstructionDriftCalculator` module implements this functionality. We need to instantiate it with appropriate parameters - the column names of the features that we want to run drift detection on, and the timestamp column name. The features can be passed in as a simple list of strings. Alternatively we can create a list by excluding the columns in the dataframe that are not features, and pass them into the argument.

Next the `fit()` method needs to be called on the reference data where results will be based off. Then the `calculate()` method will calculate the multivariate drift results on the data provided to it.

```>>> # Define feature columns
>>> feature_column_names = [
...     col for col in reference.columns if col not in [
...         'timestamp', 'y_pred_proba', 'period', 'y_pred', 'work_home_actual', 'identifier'
...     ]]

>>> calc = nml.DataReconstructionDriftCalculator(
...     column_names=feature_column_names,
...     timestamp_column_name='timestamp',
...     chunk_size=5000
>>> )
>>> calc.fit(reference)
>>> results = calc.calculate(analysis)
```

Any missing values in our data need to be imputed. The default Imputation implemented by NannyML imputes the most frequent value for categorical features and the mean for continuous features. These defaults can be overridden with an instance 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.

```>>> # Define feature columns
>>> feature_column_names = [
...     col for col in reference.columns if col not in [
...         'timestamp', 'y_pred_proba', 'period', 'y_pred', 'work_home_actual', 'identifier'
...     ]]

>>> from sklearn.impute import SimpleImputer

>>> calc = nml.DataReconstructionDriftCalculator(
...     column_names=feature_column_names,
...     timestamp_column_name='timestamp',
...     chunk_size=5000,
...     imputer_categorical=SimpleImputer(strategy='constant', fill_value='missing'),
...     imputer_continuous=SimpleImputer(strategy='median')
>>> )
>>> calc.fit(reference)
>>> results = calc.calculate(analysis)
```

Because our synthetic dataset does not have missing values, the results are the same in both cases. We can see these results of the data provided to the `calculate()` method as a dataframe.

```>>> display(results.filter(period='analysis').to_df())
```

(‘chunk’, ‘key’)

(‘chunk’, ‘chunk_index’)

(‘chunk’, ‘start_index’)

(‘chunk’, ‘end_index’)

(‘chunk’, ‘start_date’)

(‘chunk’, ‘end_date’)

(‘chunk’, ‘period’)

(‘reconstruction_error’, ‘sampling_error’)

(‘reconstruction_error’, ‘value’)

(‘reconstruction_error’, ‘upper_confidence_boundary’)

(‘reconstruction_error’, ‘lower_confidence_boundary’)

(‘reconstruction_error’, ‘upper_threshold’)

(‘reconstruction_error’, ‘lower_threshold’)

0

[0:4999]

0

0

4999

2017-08-31 04:20:00

2018-01-02 00:45:44

analysis

0.0069621

1.11854

1.13942

1.09765

1.09658

1.13801

False

1

[5000:9999]

1

5000

9999

2018-01-02 01:13:11

2018-05-01 13:10:10

analysis

0.0069621

1.11504

1.13593

1.09416

1.09658

1.13801

False

2

[10000:14999]

2

10000

14999

2018-05-01 14:25:25

2018-09-01 15:40:40

analysis

0.0069621

1.12546

1.14635

1.10457

1.09658

1.13801

False

3

[15000:19999]

3

15000

19999

2018-09-01 16:19:07

2018-12-31 10:11:21

analysis

0.0069621

1.12845

1.14934

1.10757

1.09658

1.13801

False

4

[20000:24999]

4

20000

24999

2018-12-31 10:38:45

2019-04-30 11:01:30

analysis

0.0069621

1.12289

1.14378

1.10201

1.09658

1.13801

False

5

[25000:29999]

5

25000

29999

2019-04-30 11:02:00

2019-09-01 00:24:27

analysis

0.0069621

1.22839

1.24928

1.20751

1.09658

1.13801

True

6

[30000:34999]

6

30000

34999

2019-09-01 00:28:54

2019-12-31 09:09:12

analysis

0.0069621

1.22003

1.24091

1.19914

1.09658

1.13801

True

7

[35000:39999]

7

35000

39999

2019-12-31 10:07:15

2020-04-30 11:46:53

analysis

0.0069621

1.23739

1.25828

1.21651

1.09658

1.13801

True

8

[40000:44999]

8

40000

44999

2020-04-30 12:04:32

2020-09-01 02:46:02

analysis

0.0069621

1.20605

1.22694

1.18517

1.09658

1.13801

True

9

[45000:49999]

9

45000

49999

2020-09-01 02:46:13

2021-01-01 04:29:32

analysis

0.0069621

1.24258

1.26347

1.22169

1.09658

1.13801

True

The drift results from the reference data are accessible from the properties of the results object:

```>>> display(results.filter(period='reference').to_df())
```

(‘chunk’, ‘key’)

(‘chunk’, ‘chunk_index’)

(‘chunk’, ‘start_index’)

(‘chunk’, ‘end_index’)

(‘chunk’, ‘start_date’)

(‘chunk’, ‘end_date’)

(‘chunk’, ‘period’)

(‘reconstruction_error’, ‘sampling_error’)

(‘reconstruction_error’, ‘value’)

(‘reconstruction_error’, ‘upper_confidence_boundary’)

(‘reconstruction_error’, ‘lower_confidence_boundary’)

(‘reconstruction_error’, ‘upper_threshold’)

(‘reconstruction_error’, ‘lower_threshold’)

0

[0:4999]

0

0

4999

2014-05-09 22:27:20

2014-09-09 08:18:27

reference

0.0069621

1.12096

1.14185

1.10007

1.09658

1.13801

False

1

[5000:9999]

1

5000

9999

2014-09-09 09:13:35

2015-01-09 00:02:51

reference

0.0069621

1.11807

1.13896

1.09718

1.09658

1.13801

False

2

[10000:14999]

2

10000

14999

2015-01-09 00:04:43

2015-05-09 15:54:26

reference

0.0069621

1.11724

1.13812

1.09635

1.09658

1.13801

False

3

[15000:19999]

3

15000

19999

2015-05-09 16:02:08

2015-09-07 07:14:37

reference

0.0069621

1.12551

1.1464

1.10463

1.09658

1.13801

False

4

[20000:24999]

4

20000

24999

2015-09-07 07:27:47

2016-01-08 16:02:05

reference

0.0069621

1.10945

1.13033

1.08856

1.09658

1.13801

False

5

[25000:29999]

5

25000

29999

2016-01-08 17:22:00

2016-05-09 11:09:39

reference

0.0069621

1.12276

1.14365

1.10187

1.09658

1.13801

False

6

[30000:34999]

6

30000

34999

2016-05-09 11:19:36

2016-09-04 03:30:35

reference

0.0069621

1.10714

1.12802

1.08625

1.09658

1.13801

False

7

[35000:39999]

7

35000

39999

2016-09-04 04:09:35

2017-01-03 18:48:21

reference

0.0069621

1.12713

1.14802

1.10625

1.09658

1.13801

False

8

[40000:44999]

8

40000

44999

2017-01-03 19:00:51

2017-05-03 02:34:24

reference

0.0069621

1.11424

1.13512

1.09335

1.09658

1.13801

False

9

[45000:49999]

9

45000

49999

2017-05-03 02:49:38

2017-08-31 03:10:29

reference

0.0069621

1.11045

1.13134

1.08956

1.09658

1.13801

False

NannyML can also visualize the multivariate drift results in a plot. Our plot contains several key elements.

• The purple step plot shows the reconstruction error in each chunk of the analysis period. Thick squared point markers indicate the middle of these chunks.

• The low-saturated purple area around the reconstruction error indicates the sampling error.

• The red horizontal dashed lines show upper and lower thresholds for alerting purposes.

• If the reconstruction error crosses the upper or lower threshold an alert is raised which is indicated with a red, low-saturated background across the whole width of the relevant chunk. This is additionally indicated by a red, diamond-shaped point marker in the middle of the chunk.

```>>> figure = results.plot(plot_reference=True)
>>> figure.show()
```

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

## Insights

Using this method of detecting drift we can identify changes that we may not have seen using solely univariate methods.

## What Next

After reviewing the results we may want to look at the drift results of individual features to see what changed in the model’s feature’s individually.

The Performance Estimation functionality can be used to estimate the impact of the observed changes.

For more information on how multivariate drift detection works the Data Reconstruction with PCA explanation page gives more details.