Estimating Confusion Matrix Elements for Binary Classification

This tutorial explains how to use NannyML to estimate the confusion matrix for binary classification models in the absence of target data. To find out how CBPE estimates performance, read the explanation of Confidence-based Performance Estimation.

Note

The following example uses timestamps. These are optional but have an impact on the way data is chunked and results are plotted. You can read more about them in the data requirements.

Just The Code

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

>>> estimator = nml.CBPE(
...     y_pred_proba='y_pred_proba',
...     y_pred='y_pred',
...     y_true='repaid',
...     timestamp_column_name='timestamp',
...     metrics=['confusion_matrix'],
...     chunk_size=5000,
...     problem_type='classification_binary',
...     normalize_confusion_matrix="all",
>>> )

>>> estimator.fit(reference_df)

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

>>> metric_fig = results.plot()
>>> metric_fig.show()
```

Walkthrough

For simplicity this guide is based on a synthetic dataset included in the library, where the monitored model predicts whether a customer will repay a loan to buy a car. Check out Car Loan Dataset to learn more about this dataset.

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.

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

```

id

car_value

salary_range

debt_to_income_ratio

loan_length

repaid_loan_on_prev_car

size_of_downpayment

driver_tenure

repaid

timestamp

y_pred_proba

y_pred

0

0

39811

40K - 60K €

0.63295

19

False

40%

0.212653

1

2018-01-01 00:00:00.000

0.99

1

1

1

12679

40K - 60K €

0.718627

7

True

10%

4.92755

0

2018-01-01 00:08:43.152

0.07

0

2

2

19847

40K - 60K €

0.721724

17

False

0%

0.520817

1

2018-01-01 00:17:26.304

1

1

Next we create the Confidence-based Performance Estimation (`CBPE`) estimator. To initialize an estimator that estimates the confusion_matrix, we specify the following parameters:

• y_pred_proba: the name of the column in the reference data that contains the predicted probabilities.

• y_pred: the name of the column in the reference data that contains the predicted classes.

• y_true: the name of the column in the reference data that contains the true classes.

• timestamp_column_name (Optional): the name of the column in the reference data that contains timestamps.

• metrics: a list of metrics to estimate. In this example we will estimate the `confusion_matrix` metric.

• chunk_size (Optional): the number of observations in each chunk of data used to estimate performance. For more information about chunking configurations check out the chunking tutorial.

• problem_type: the type of problem being monitored. In this example we will monitor a binary classification problem.

• normalize_confusion_matrix (Optional): how to normalize the confusion matrix. The normalization options are:

• None : returns counts for each cell

• “true” : normalize over the true class of observations.

• “pred” : normalize over the predicted class of observations

• “all” : normalize over all observations

Note

Since we are estimating the confusion matrix, the count values in each cell of the confusion matrix are estimates. We normalize the estimates just as if they were true counts. This means that when we normalize over the true class, the estimates in each row will sum to 1. When we normalize over the predicted class, the estimates in each column will sum to 1. When we normalize over all observations, the estimates in the entire matrix will sum to 1.

```>>> estimator = nml.CBPE(
...     y_pred_proba='y_pred_proba',
...     y_pred='y_pred',
...     y_true='repaid',
...     timestamp_column_name='timestamp',
...     metrics=['confusion_matrix'],
...     chunk_size=5000,
...     problem_type='classification_binary',
...     normalize_confusion_matrix="all",
>>> )
```

The `CBPE` estimator is then fitted using the `fit()` method on the `reference` data.

```>>> estimator.fit(reference_df)
```

The fitted `estimator` can be used to estimate performance on other data, for which performance cannot be calculated. Typically, this would be used on the latest production data where target is missing. In our example this is the `analysis_df` data.

NannyML can then output a dataframe that contains all the results. Let’s have a look at the results for analysis period only.

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

chunk
key
chunk_index
start_index
end_index
start_date
end_date
period
true_positive
value
sampling_error
realized
upper_confidence_boundary
lower_confidence_boundary
upper_threshold
lower_threshold
true_negative
value
sampling_error
realized
upper_confidence_boundary
lower_confidence_boundary
upper_threshold
lower_threshold
false_positive
value
sampling_error
realized
upper_confidence_boundary
lower_confidence_boundary
upper_threshold
lower_threshold
false_negative
value
sampling_error
realized
upper_confidence_boundary
lower_confidence_boundary
upper_threshold
lower_threshold

0

[0:4999]

0

0

4999

2018-10-30 18:00:00

2018-11-30 00:27:16.848000

analysis

0.481766

0.00705286

nan

0.502925

0.460608

0.478879

0.449401

True

0.460026

0.00706512

nan

0.481221

0.43883

0.494119

0.464881

True

0.0212337

0.00202397

nan

0.0273056

0.0151617

0.025818

0.016022

False

0.0369745

0.00261473

nan

0.0448186

0.0291303

0.0416915

0.0291885

False

1

[5000:9999]

1

5000

9999

2018-11-30 00:36:00

2018-12-30 07:03:16.848000

analysis

0.454646

0.00705286

nan

0.475804

0.433487

0.478879

0.449401

False

0.488676

0.00706512

nan

0.509871

0.46748

0.494119

0.464881

False

0.0199543

0.00202397

nan

0.0260262

0.0138824

0.025818

0.016022

False

0.0367245

0.00261473

nan

0.0445687

0.0288803

0.0416915

0.0291885

False

2

[10000:14999]

2

10000

14999

2018-12-30 07:12:00

2019-01-29 13:39:16.848000

analysis

0.455756

0.00705286

nan

0.476914

0.434597

0.478879

0.449401

False

0.489736

0.00706512

nan

0.510931

0.46854

0.494119

0.464881

False

0.0198442

0.00202397

nan

0.0259161

0.0137723

0.025818

0.016022

False

0.0346643

0.00261473

nan

0.0425084

0.0268201

0.0416915

0.0291885

False

3

[15000:19999]

3

15000

19999

2019-01-29 13:48:00

2019-02-28 20:15:16.848000

analysis

0.457828

0.00705286

nan

0.478987

0.43667

0.478879

0.449401

False

0.486988

0.00706512

nan

0.508183

0.465793

0.494119

0.464881

False

0.0205719

0.00202397

nan

0.0266438

0.0145

0.025818

0.016022

False

0.0346121

0.00261473

nan

0.0424563

0.0267679

0.0416915

0.0291885

False

4

[20000:24999]

4

20000

24999

2019-02-28 20:24:00

2019-03-31 02:51:16.848000

analysis

0.468372

0.00705286

nan

0.489531

0.447213

0.478879

0.449401

False

0.476273

0.00706512

nan

0.497468

0.455078

0.494119

0.464881

False

0.020428

0.00202397

nan

0.0264999

0.014356

0.025818

0.016022

False

0.034927

0.00261473

nan

0.0427712

0.0270829

0.0416915

0.0291885

False

5

[25000:29999]

5

25000

29999

2019-03-31 03:00:00

2019-04-30 09:27:16.848000

analysis

0.461246

0.00705286

nan

0.482404

0.440087

0.478879

0.449401

False

0.449469

0.00706512

nan

0.470664

0.428273

0.494119

0.464881

True

0.0287544

0.00202397

nan

0.0348263

0.0226825

0.025818

0.016022

True

0.0605314

0.00261473

nan

0.0683756

0.0526873

0.0416915

0.0291885

True

6

[30000:34999]

6

30000

34999

2019-04-30 09:36:00

2019-05-30 16:03:16.848000

analysis

0.459067

0.00705286

nan

0.480225

0.437908

0.478879

0.449401

False

0.452083

0.00706512

nan

0.473278

0.430888

0.494119

0.464881

True

0.0283335

0.00202397

nan

0.0344054

0.0222616

0.025818

0.016022

True

0.060517

0.00261473

nan

0.0683612

0.0526729

0.0416915

0.0291885

True

7

[35000:39999]

7

35000

39999

2019-05-30 16:12:00

2019-06-29 22:39:16.848000

analysis

0.458246

0.00705286

nan

0.479404

0.437087

0.478879

0.449401

False

0.452947

0.00706512

nan

0.474142

0.431752

0.494119

0.464881

True

0.0295542

0.00202397

nan

0.0356261

0.0234823

0.025818

0.016022

True

0.0592531

0.00261473

nan

0.0670972

0.0514089

0.0416915

0.0291885

True

8

[40000:44999]

8

40000

44999

2019-06-29 22:48:00

2019-07-30 05:15:16.848000

analysis

0.453561

0.00705286

nan

0.47472

0.432403

0.478879

0.449401

False

0.460828

0.00706512

nan

0.482024

0.439633

0.494119

0.464881

True

0.0272388

0.00202397

nan

0.0333107

0.0211669

0.025818

0.016022

True

0.0583718

0.00261473

nan

0.066216

0.0505277

0.0416915

0.0291885

True

9

[45000:49999]

9

45000

49999

2019-07-30 05:24:00

2019-08-29 11:51:16.848000

analysis

0.473578

0.00705286

nan

0.494737

0.45242

0.478879

0.449401

False

0.438153

0.00706512

nan

0.459349

0.416958

0.494119

0.464881

True

0.0296219

0.00202397

nan

0.0356938

0.02355

0.025818

0.016022

True

0.0586468

0.00261473

nan

0.066491

0.0508026

0.0416915

0.0291885

True

Apart from chunk-related data, the results data have the following columns for each metric that was estimated:

• value - the estimate of a metric for a specific chunk.

• sampling_error - the estimate of the Sampling Error.

• realized - when target values are available for a chunk, the realized performance metric will also be calculated and included within the results.

• upper_confidence_boundary and lower_confidence_boundary - These values show the confidence band of the relevant metric and are equal to estimated value +/- 3 times the estimated sampling error.

• upper_threshold and lower_threshold - crossing these thresholds will raise an alert on significant performance change. The thresholds are calculated based on the actual performance of the monitored model on chunks in the reference partition. The thresholds are 3 standard deviations away from the mean performance calculated on chunks. The thresholds are calculated during fit phase.

• alert - flag indicating potentially significant performance change. `True` if estimated performance crosses upper or lower threshold.

These results can be also plotted. Our plot contains several key elements.

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

• The low-saturated purple area around the estimated performance in the analysis period corresponds to the confidence band which is calculated as the estimated performance +/- 3 times the estimated Sampling Error.

• The gray vertical line splits the reference and analysis periods.

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

• The red diamond-shaped point markers in the middle of a chunk indicate that an alert has been raised. Alerts are caused by the estimated performance crossing the upper or lower threshold.

```>>> metric_fig = results.plot()
>>> metric_fig.show()
```

Additional information such as the chunk index range and chunk date range (if timestamps were provided) is shown in the hover for each chunk (these are interactive plots, though only static views are included here).

Insights

After reviewing the performance estimation results, we should be able to see any indications of performance change that NannyML has detected based upon the model’s inputs and outputs alone.

What’s next

The Data Drift functionality can help us to understand whether data drift is causing the performance problem. When the target values become available we can compared realized and estimated confusion matrix results.