Calculating Confusion Matrix Elements for Multiclass Classification

This tutorial explains how to use NannyML to calculate the confusion matrix for multiclass classification models.

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

>>> reference_df, analysis_df, analysis_target_df = nml.load_synthetic_multiclass_classification_dataset()

>>> analysis_df = analysis_df.merge(analysis_target_df, left_index=True, right_index=True)

>>> display(reference_df.head(3))

>>> calc = nml.PerformanceCalculator(
...     y_pred_proba={
...         'prepaid_card': 'y_pred_proba_prepaid_card',
...         'highstreet_card': 'y_pred_proba_highstreet_card',
...         'upmarket_card': 'y_pred_proba_upmarket_card'
...     },
...     y_pred='y_pred',
...     y_true='y_true',
...     timestamp_column_name='timestamp',
...     problem_type='classification_multiclass',
...     metrics=['confusion_matrix'],
...     normalize_confusion_matrix='all',
...     chunk_size=6000)

>>> calc.fit(reference_df)

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

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

>>> figure = results.plot()
>>> figure.show()

Walkthrough

For simplicity this guide is based on a synthetic dataset where the monitored model predicts which type of credit card product new customers should be assigned to. Check out Credit Card 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.

The analysis_targets dataframe contains the target results of the analysis period. This is kept separate in the synthetic data because it is not used during performance estimation. But it is required to calculate performance, so the first thing we need to in this case is set up the right data in the right dataframes.

The analysis target values are joined on the analysis frame by their index. Your dataset may already contain the target column, so you may skip this join.

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

>>> reference_df, analysis_df, analysis_target_df = nml.load_synthetic_multiclass_classification_dataset()

>>> analysis_df = analysis_df.merge(analysis_target_df, left_index=True, right_index=True)

>>> display(reference_df.head(3))

	id	acq_channel	app_behavioral_score	requested_credit_limit	app_channel	credit_bureau_score	stated_income	is_customer	timestamp	y_pred_proba_prepaid_card	y_pred_proba_highstreet_card	y_pred_proba_upmarket_card	y_pred	y_true
0	0	Partner3	1.80823	350	web	309	15000	True	2020-05-02 02:01:30	0.97	0.03	0	prepaid_card	prepaid_card
1	1	Partner2	4.38257	500	mobile	418	23000	True	2020-05-02 02:03:33	0.87	0.13	0	prepaid_card	prepaid_card
2	2	Partner2	-0.787575	400	web	507	24000	False	2020-05-02 02:04:49	0.47	0.35	0.18	prepaid_card	upmarket_card

Next a PerformanceCalculator is created using the following:

• 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.

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

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

• 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

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

• thresholds (Optional): the thresholds used to calculate the alert flag. For more information about thresholds, check out the thresholds tutorial.

>>> calc = nml.PerformanceCalculator(
...     y_pred_proba={
...         'prepaid_card': 'y_pred_proba_prepaid_card',
...         'highstreet_card': 'y_pred_proba_highstreet_card',
...         'upmarket_card': 'y_pred_proba_upmarket_card'
...     },
...     y_pred='y_pred',
...     y_true='y_true',
...     timestamp_column_name='timestamp',
...     problem_type='classification_multiclass',
...     metrics=['confusion_matrix'],
...     normalize_confusion_matrix='all',
...     chunk_size=6000)

The new PerformanceCalculator is fitted using the fit() method on the reference data.

>>> calc.fit(reference_df)

The fitted PerformanceCalculator can then be used to calculate realized performance metrics on all data which has target values available with the calculate() method. NannyML can output a dataframe that contains all the results of the analysis data.

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

	chunk key	chunk_index	start_index	end_index	start_date	end_date	period	targets_missing_rate	true_highstreet_card_pred_highstreet_card sampling_error	value	upper_threshold	lower_threshold	alert	true_highstreet_card_pred_prepaid_card sampling_error	value	upper_threshold	lower_threshold	alert	true_highstreet_card_pred_upmarket_card sampling_error	value	upper_threshold	lower_threshold	alert	true_prepaid_card_pred_highstreet_card sampling_error	value	upper_threshold	lower_threshold	alert	true_prepaid_card_pred_prepaid_card sampling_error	value	upper_threshold	lower_threshold	alert	true_prepaid_card_pred_upmarket_card sampling_error	value	upper_threshold	lower_threshold	alert	true_upmarket_card_pred_highstreet_card sampling_error	value	upper_threshold	lower_threshold	alert	true_upmarket_card_pred_prepaid_card sampling_error	value	upper_threshold	lower_threshold	alert	true_upmarket_card_pred_upmarket_card sampling_error	value	upper_threshold	lower_threshold	alert
0	[0:5999]	0	0	5999	2020-09-01 03:10:01	2020-09-13 16:15:10	analysis	0	0.00555482	0.242833	0.262292	0.228341	False	0.00265159	0.0458333	0.0486211	0.0396456	False	0.00262565	0.0416667	0.0470817	0.039385	False	0.00267108	0.0456667	0.0526699	0.0369635	False	0.00562464	0.26	0.265912	0.243455	False	0.00239047	0.034	0.0421872	0.0289128	False	0.00254241	0.0408333	0.046008	0.0348254	False	0.00248954	0.0408333	0.0441763	0.0331904	False	0.00561357	0.248333	0.270106	0.236227	False
1	[6000:11999]	1	6000	11999	2020-09-13 16:15:32	2020-09-25 19:48:42	analysis	0	0.00555482	0.256	0.262292	0.228341	False	0.00265159	0.0435	0.0486211	0.0396456	False	0.00262565	0.0395	0.0470817	0.039385	False	0.00267108	0.0395	0.0526699	0.0369635	False	0.00562464	0.253	0.265912	0.243455	False	0.00239047	0.0335	0.0421872	0.0289128	False	0.00254241	0.042	0.046008	0.0348254	False	0.00248954	0.039	0.0441763	0.0331904	False	0.00561357	0.254	0.270106	0.236227	False
2	[12000:17999]	2	12000	17999	2020-09-25 19:50:04	2020-10-08 02:53:47	analysis	0	0.00555482	0.241833	0.262292	0.228341	False	0.00265159	0.0416667	0.0486211	0.0396456	False	0.00262565	0.0431667	0.0470817	0.039385	False	0.00267108	0.044	0.0526699	0.0369635	False	0.00562464	0.2595	0.265912	0.243455	False	0.00239047	0.0333333	0.0421872	0.0289128	False	0.00254241	0.0418333	0.046008	0.0348254	False	0.00248954	0.0373333	0.0441763	0.0331904	False	0.00561357	0.257333	0.270106	0.236227	False
3	[18000:23999]	3	18000	23999	2020-10-08 02:57:34	2020-10-20 15:48:19	analysis	0	0.00555482	0.241667	0.262292	0.228341	False	0.00265159	0.0413333	0.0486211	0.0396456	False	0.00262565	0.0418333	0.0470817	0.039385	False	0.00267108	0.0395	0.0526699	0.0369635	False	0.00562464	0.262833	0.265912	0.243455	False	0.00239047	0.041	0.0421872	0.0289128	False	0.00254241	0.0436667	0.046008	0.0348254	False	0.00248954	0.0335	0.0441763	0.0331904	False	0.00561357	0.254667	0.270106	0.236227	False
4	[24000:29999]	4	24000	29999	2020-10-20 15:49:06	2020-11-01 22:04:40	analysis	0	0.00555482	0.248	0.262292	0.228341	False	0.00265159	0.04	0.0486211	0.0396456	False	0.00262565	0.0461667	0.0470817	0.039385	False	0.00267108	0.045	0.0526699	0.0369635	False	0.00562464	0.248833	0.265912	0.243455	False	0.00239047	0.0323333	0.0421872	0.0289128	False	0.00254241	0.0403333	0.046008	0.0348254	False	0.00248954	0.0381667	0.0441763	0.0331904	False	0.00561357	0.261167	0.270106	0.236227	False
5	[30000:35999]	5	30000	35999	2020-11-01 22:04:59	2020-11-14 03:55:33	analysis	0	0.00555482	0.220333	0.262292	0.228341	True	0.00265159	0.0701667	0.0486211	0.0396456	True	0.00262565	0.055	0.0470817	0.039385	True	0.00267108	0.0898333	0.0526699	0.0369635	True	0.00562464	0.146333	0.265912	0.243455	True	0.00239047	0.0746667	0.0421872	0.0289128	True	0.00254241	0.0875	0.046008	0.0348254	True	0.00248954	0.062	0.0441763	0.0331904	True	0.00561357	0.194167	0.270106	0.236227	True
6	[36000:41999]	6	36000	41999	2020-11-14 03:55:49	2020-11-26 09:19:06	analysis	0	0.00555482	0.224333	0.262292	0.228341	True	0.00265159	0.0673333	0.0486211	0.0396456	True	0.00262565	0.053	0.0470817	0.039385	True	0.00267108	0.0991667	0.0526699	0.0369635	True	0.00562464	0.151333	0.265912	0.243455	True	0.00239047	0.0698333	0.0421872	0.0289128	True	0.00254241	0.0846667	0.046008	0.0348254	True	0.00248954	0.0636667	0.0441763	0.0331904	True	0.00561357	0.186667	0.270106	0.236227	True
7	[42000:47999]	7	42000	47999	2020-11-26 09:19:22	2020-12-08 14:33:56	analysis	0	0.00555482	0.232833	0.262292	0.228341	False	0.00265159	0.066	0.0486211	0.0396456	True	0.00262565	0.0503333	0.0470817	0.039385	True	0.00267108	0.0916667	0.0526699	0.0369635	True	0.00562464	0.145833	0.265912	0.243455	True	0.00239047	0.0693333	0.0421872	0.0289128	True	0.00254241	0.0891667	0.046008	0.0348254	True	0.00248954	0.0636667	0.0441763	0.0331904	True	0.00561357	0.191167	0.270106	0.236227	True
8	[48000:53999]	8	48000	53999	2020-12-08 14:34:25	2020-12-20 18:30:30	analysis	0	0.00555482	0.2255	0.262292	0.228341	True	0.00265159	0.0686667	0.0486211	0.0396456	True	0.00262565	0.052	0.0470817	0.039385	True	0.00267108	0.0898333	0.0526699	0.0369635	True	0.00562464	0.148	0.265912	0.243455	True	0.00239047	0.0733333	0.0421872	0.0289128	True	0.00254241	0.0855	0.046008	0.0348254	True	0.00248954	0.0628333	0.0441763	0.0331904	True	0.00561357	0.194333	0.270106	0.236227	True
9	[54000:59999]	9	54000	59999	2020-12-20 18:31:09	2021-01-01 22:57:55	analysis	0	0.00555482	0.225667	0.262292	0.228341	True	0.00265159	0.065	0.0486211	0.0396456	True	0.00262565	0.0543333	0.0470817	0.039385	True	0.00267108	0.0946667	0.0526699	0.0369635	True	0.00562464	0.144833	0.265912	0.243455	True	0.00239047	0.0726667	0.0421872	0.0289128	True	0.00254241	0.0855	0.046008	0.0348254	True	0.00248954	0.0618333	0.0441763	0.0331904	True	0.00561357	0.1955	0.270106	0.236227	True

The results from the reference data are also available.

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

	chunk key	chunk_index	start_index	end_index	start_date	end_date	period	targets_missing_rate	true_highstreet_card_pred_highstreet_card sampling_error	value	upper_threshold	lower_threshold	alert	true_highstreet_card_pred_prepaid_card sampling_error	value	upper_threshold	lower_threshold	alert	true_highstreet_card_pred_upmarket_card sampling_error	value	upper_threshold	lower_threshold	alert	true_prepaid_card_pred_highstreet_card sampling_error	value	upper_threshold	lower_threshold	alert	true_prepaid_card_pred_prepaid_card sampling_error	value	upper_threshold	lower_threshold	alert	true_prepaid_card_pred_upmarket_card sampling_error	value	upper_threshold	lower_threshold	alert	true_upmarket_card_pred_highstreet_card sampling_error	value	upper_threshold	lower_threshold	alert	true_upmarket_card_pred_prepaid_card sampling_error	value	upper_threshold	lower_threshold	alert	true_upmarket_card_pred_upmarket_card sampling_error	value	upper_threshold	lower_threshold	alert
0	[0:5999]	0	0	5999	2020-05-02 02:01:30	2020-05-14 12:25:35	reference	0	0.00555482	0.244	0.262292	0.228341	False	0.00265159	0.0453333	0.0486211	0.0396456	False	0.00262565	0.0435	0.0470817	0.039385	False	0.00267108	0.05	0.0526699	0.0369635	False	0.00562464	0.2535	0.265912	0.243455	False	0.00239047	0.0346667	0.0421872	0.0289128	False	0.00254241	0.0366667	0.046008	0.0348254	False	0.00248954	0.0393333	0.0441763	0.0331904	False	0.00561357	0.253	0.270106	0.236227	False
1	[6000:11999]	1	6000	11999	2020-05-14 12:29:25	2020-05-26 18:27:42	reference	0	0.00555482	0.253833	0.262292	0.228341	False	0.00265159	0.0458333	0.0486211	0.0396456	False	0.00262565	0.042	0.0470817	0.039385	False	0.00267108	0.0473333	0.0526699	0.0369635	False	0.00562464	0.25	0.265912	0.243455	False	0.00239047	0.0363333	0.0421872	0.0289128	False	0.00254241	0.0408333	0.046008	0.0348254	False	0.00248954	0.0366667	0.0441763	0.0331904	False	0.00561357	0.247167	0.270106	0.236227	False
2	[12000:17999]	2	12000	17999	2020-05-26 18:31:06	2020-06-07 19:55:45	reference	0	0.00555482	0.246333	0.262292	0.228341	False	0.00265159	0.041	0.0486211	0.0396456	False	0.00262565	0.0428333	0.0470817	0.039385	False	0.00267108	0.0455	0.0526699	0.0369635	False	0.00562464	0.2555	0.265912	0.243455	False	0.00239047	0.0303333	0.0421872	0.0289128	False	0.00254241	0.0423333	0.046008	0.0348254	False	0.00248954	0.0408333	0.0441763	0.0331904	False	0.00561357	0.255333	0.270106	0.236227	False
3	[18000:23999]	3	18000	23999	2020-06-07 19:58:39	2020-06-19 19:42:20	reference	0	0.00555482	0.2455	0.262292	0.228341	False	0.00265159	0.0426667	0.0486211	0.0396456	False	0.00262565	0.0426667	0.0470817	0.039385	False	0.00267108	0.0448333	0.0526699	0.0369635	False	0.00562464	0.258167	0.265912	0.243455	False	0.00239047	0.0345	0.0421872	0.0289128	False	0.00254241	0.0435	0.046008	0.0348254	False	0.00248954	0.0415	0.0441763	0.0331904	False	0.00561357	0.246667	0.270106	0.236227	False
4	[24000:29999]	4	24000	29999	2020-06-19 19:44:14	2020-07-02 01:58:05	reference	0	0.00555482	0.242	0.262292	0.228341	False	0.00265159	0.0435	0.0486211	0.0396456	False	0.00262565	0.0421667	0.0470817	0.039385	False	0.00267108	0.0403333	0.0526699	0.0369635	False	0.00562464	0.256833	0.265912	0.243455	False	0.00239047	0.0346667	0.0421872	0.0289128	False	0.00254241	0.0415	0.046008	0.0348254	False	0.00248954	0.0385	0.0441763	0.0331904	False	0.00561357	0.2605	0.270106	0.236227	False
5	[30000:35999]	5	30000	35999	2020-07-02 02:06:56	2020-07-14 08:14:04	reference	0	0.00555482	0.242833	0.262292	0.228341	False	0.00265159	0.0461667	0.0486211	0.0396456	False	0.00262565	0.044	0.0470817	0.039385	False	0.00267108	0.0455	0.0526699	0.0369635	False	0.00562464	0.253667	0.265912	0.243455	False	0.00239047	0.0353333	0.0421872	0.0289128	False	0.00254241	0.0401667	0.046008	0.0348254	False	0.00248954	0.0401667	0.0441763	0.0331904	False	0.00561357	0.252167	0.270106	0.236227	False
6	[36000:41999]	6	36000	41999	2020-07-14 08:14:08	2020-07-26 12:55:42	reference	0	0.00555482	0.247333	0.262292	0.228341	False	0.00265159	0.0446667	0.0486211	0.0396456	False	0.00262565	0.0463333	0.0470817	0.039385	False	0.00267108	0.0428333	0.0526699	0.0369635	False	0.00562464	0.261167	0.265912	0.243455	False	0.00239047	0.0366667	0.0421872	0.0289128	False	0.00254241	0.0411667	0.046008	0.0348254	False	0.00248954	0.0355	0.0441763	0.0331904	False	0.00561357	0.244333	0.270106	0.236227	False
7	[42000:47999]	7	42000	47999	2020-07-26 12:57:37	2020-08-07 16:32:15	reference	0	0.00555482	0.255667	0.262292	0.228341	False	0.00265159	0.0443333	0.0486211	0.0396456	False	0.00262565	0.0431667	0.0470817	0.039385	False	0.00267108	0.0441667	0.0526699	0.0369635	False	0.00562464	0.2475	0.265912	0.243455	False	0.00239047	0.0373333	0.0421872	0.0289128	False	0.00254241	0.0383333	0.046008	0.0348254	False	0.00248954	0.0368333	0.0441763	0.0331904	False	0.00561357	0.252667	0.270106	0.236227	False
8	[48000:53999]	8	48000	53999	2020-08-07 16:33:44	2020-08-20 00:06:08	reference	0	0.00555482	0.236333	0.262292	0.228341	False	0.00265159	0.0446667	0.0486211	0.0396456	False	0.00262565	0.044	0.0470817	0.039385	False	0.00267108	0.0458333	0.0526699	0.0369635	False	0.00562464	0.253833	0.265912	0.243455	False	0.00239047	0.0391667	0.0421872	0.0289128	False	0.00254241	0.0393333	0.046008	0.0348254	False	0.00248954	0.0393333	0.0441763	0.0331904	False	0.00561357	0.2575	0.270106	0.236227	False
9	[54000:59999]	9	54000	59999	2020-08-20 00:07:58	2020-09-01 03:03:23	reference	0	0.00555482	0.239333	0.262292	0.228341	False	0.00265159	0.0431667	0.0486211	0.0396456	False	0.00262565	0.0416667	0.0470817	0.039385	False	0.00267108	0.0418333	0.0526699	0.0369635	False	0.00562464	0.256667	0.265912	0.243455	False	0.00239047	0.0365	0.0421872	0.0289128	False	0.00254241	0.0403333	0.046008	0.0348254	False	0.00248954	0.0381667	0.0441763	0.0331904	False	0.00561357	0.262333	0.270106	0.236227	False

Apart from chunk and period-related columns, the results data have a set of columns for each calculated metric.

• targets_missing_rate - The fraction of missing target data.

• value - the realized metric value for a specific chunk.

• sampling_error - the estimate of the 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. They are calculated during fit phase.

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

The results can be plotted for visual inspection. Our plot contains several key elements.

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

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

• 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 performance crossing the upper or lower threshold.

>>> figure = results.plot()
>>> figure.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 calculation results, we should be able to clearly see how the model is performing against the targets, according to whatever metrics we wish to track.

What’s Next

If we decide further investigation is needed, the Data Drift functionality can help us to see what feature changes may be contributing to any performance changes.

It is also wise to check whether the model’s performance is satisfactory according to business requirements. This is an ad-hoc investigation that is not covered by NannyML.