# Single Table Metrics¶

In this section we will show you which metrics exist for single table datasets and how to use them.

Let us start by loading some demo data that we will use to explore the different metrics that exist.

```
In [1]: from sdv.metrics.demos import load_single_table_demo
In [2]: real_data, synthetic_data, metadata = load_single_table_demo()
```

This will return us three objects:

The `real_data`

, which is the single table `student_placements`

demo dataset:

```
In [3]: real_data
Out[3]:
student_id gender second_perc high_perc high_spec degree_perc ... mba_perc salary placed start_date end_date duration
0 17264 M 67.00 91.00 Commerce 58.00 ... 58.80 27000.0 True 2020-07-23 2020-10-12 3.0
1 17265 M 79.33 78.33 Science 77.48 ... 66.28 20000.0 True 2020-01-11 2020-04-09 3.0
2 17266 M 65.00 68.00 Arts 64.00 ... 57.80 25000.0 True 2020-01-26 2020-07-13 6.0
3 17267 M 56.00 52.00 Science 52.00 ... 59.43 NaN False NaT NaT NaN
4 17268 M 85.80 73.60 Commerce 73.30 ... 55.50 42500.0 True 2020-07-04 2020-09-27 3.0
.. ... ... ... ... ... ... ... ... ... ... ... ... ...
210 17474 M 80.60 82.00 Commerce 77.60 ... 74.49 40000.0 True 2020-07-27 2020-10-20 3.0
211 17475 M 58.00 60.00 Science 72.00 ... 53.62 27500.0 True 2020-01-23 2020-08-04 6.0
212 17476 M 67.00 67.00 Commerce 73.00 ... 69.72 29500.0 True 2020-01-25 2020-08-05 6.0
213 17477 F 74.00 66.00 Commerce 58.00 ... 60.23 20400.0 True 2020-01-19 2020-04-20 3.0
214 17478 M 62.00 58.00 Science 53.00 ... 60.22 NaN False NaT NaT NaN
.
[215 rows x 17 columns]
```

The `synthetic_data`

, which is a clone of the `real_data`

which has been generated
by the `CTGAN`

tabular model.

```
In [4]: synthetic_data
Out[4]:
student_id gender second_perc high_perc high_spec degree_perc ... mba_perc salary placed start_date end_date duration
0 0 F 41.361060 85.425072 Commerce 74.972674 ... 57.291083 NaN True 2020-02-11 2020-08-02 3.0
1 1 M 63.720169 99.059033 Commerce 62.769650 ... 79.068319 NaN False NaT NaT NaN
2 2 M 58.473884 89.241528 Science 83.066328 ... 77.042950 26727.0 True 2020-02-13 2020-05-27 3.0
3 3 F 77.232204 100.523788 Commerce 61.010445 ... 68.132991 22058.0 True 2020-09-24 2020-11-07 3.0
4 4 F 54.067830 109.611537 Commerce 72.846753 ... 66.363138 NaN False NaT NaT NaN
.. ... ... ... ... ... ... ... ... ... ... ... ... ...
210 210 M 58.981597 97.809826 Commerce 73.548889 ... 61.981631 NaN False NaT NaT NaN
211 211 M 42.643139 75.259843 Commerce 72.478613 ... 55.746391 NaN False NaT NaT NaN
212 212 M 58.202031 103.876132 Commerce 81.088376 ... 58.117902 28772.0 True 2020-01-23 2021-02-26 6.0
213 213 M 53.939037 70.498207 Commerce 65.284175 ... 53.206451 25441.0 True 2020-06-13 2020-06-14 6.0
214 214 M 35.696869 100.655357 Commerce 58.946189 ... 48.470545 NaN False NaT NaT NaN
.
[215 rows x 17 columns]
```

And a `metadata`

, which is the `dict`

representation of the `student_placements`

metadata.

```
In [5]: metadata
Out[5]:
{'fields': {'start_date': {'type': 'datetime', 'format': '%Y-%m-%d'},
'end_date': {'type': 'datetime', 'format': '%Y-%m-%d'},
'salary': {'type': 'numerical', 'subtype': 'integer'},
'duration': {'type': 'categorical'},
'student_id': {'type': 'id', 'subtype': 'integer'},
'high_perc': {'type': 'numerical', 'subtype': 'float'},
'high_spec': {'type': 'categorical'},
'mba_spec': {'type': 'categorical'},
'second_perc': {'type': 'numerical', 'subtype': 'float'},
'gender': {'type': 'categorical'},
'degree_perc': {'type': 'numerical', 'subtype': 'float'},
'placed': {'type': 'boolean'},
'experience_years': {'type': 'numerical', 'subtype': 'float'},
'employability_perc': {'type': 'numerical', 'subtype': 'float'},
'mba_perc': {'type': 'numerical', 'subtype': 'float'},
'work_experience': {'type': 'boolean'},
'degree_type': {'type': 'categorical'}},
'constraints': [],
'model_kwargs': {},
'name': None,
'primary_key': 'student_id',
'sequence_index': None,
'entity_columns': [],
'context_columns': []}
```

These three elements, or their corresponding equivalents, are all you will need to
run most of the *Single Table Metrics* on your own *Synthetic Dataset*.

## Single Table Metric Families¶

The *Single Table Metrics* are grouped in multiple families:

**Statistical Metrics**: These are metrics that compare the tables by running different statistical tests on them. Some of them work by comparing multiple columns at once, while other compare the different individual columns separately and later on return an aggregated result.**Likelihood Metrics**: These metrics attempt to fit a probabilistic model to the real data and later on evaluate the likelihood of the synthetic data on it.**Detection Metrics**: These metrics try to train a Machine Learning Classifier that learns to distinguish the real data from the synthetic data, and report a score of how successful this classifier is.**Machine Learning Efficacy Metrics**: These metrics train a Machine Learning model on your synthetic data and later on evaluate the model performance on the real data. Since these metrics need to evaluate the performance of a Machine Learning model on the dataset, they work only on datasets that represent a Machine Learning problem.**Privacy Metrics**: These metrics fit an adversial attacker model on the synthetic data and then evaluate its accuracy (or probability of making the correct attack) on the real data.

### Statistical Metrics¶

The metrics of this family compare the tables by running different types of statistical tests on them.

In the most simple scenario, these metrics compare individual columns from the real table with the corresponding column from the synthetic table, and at the end report the average outcome from the test.

Such metrics are:

`sdv.metrics.tabular.KSComplement`

: This metric uses the two-sample Kolmogorov–Smirnov test to compare the distributions of continuous columns using the empirical CDF. The output for each column is 1 minus the KS Test D statistic, which indicates the maximum distance between the expected CDF and the observed CDF values.`sdv.metrics.tabular.CSTest`

: This metric uses the Chi-Squared test to compare the distributions of two discrete columns. The output for each column is the CSTest p-value, which indicates the probability of the two columns having been sampled from the same distribution.

Let us execute these two metrics on the loaded data:

```
In [6]: from sdv.metrics.tabular import CSTest, KSComplement
In [7]: CSTest.compute(real_data, synthetic_data)
Out[7]: 0.8078084931103922
In [8]: KSComplement.compute(real_data, synthetic_data)
Out[8]: 0.6372093023255814
```

In each case, the statistical test will be executed on all the compatible column (so, categorical
or boolean columns for `CSTest`

and numerical columns for `KSComplement`

), and report the average
score obtained.

Note

If your table does not contain any column of the compatible type, the output of
either metric will be `nan`

.

We can also compute the metrics by calling the `sdv.evaluate`

function passing either the
metric classes or their names:

```
In [9]: from sdv.evaluation import evaluate
In [10]: evaluate(synthetic_data, real_data, metrics=['CSTest', 'KSComplement'], aggregate=False)
Out[10]:
metric name raw_score normalized_score min_value max_value goal
0 CSTest Chi-Squared 0.807808 0.807808 0.0 1.0 MAXIMIZE
1 KSComplement Inverted Kolmogorov-Smirnov D statistic 0.637209 0.637209 0.0 1.0 MAXIMIZE
```

### Likelihood Metrics¶

The metrics of this family compare the tables by fitting the real data to a probabilistic model and afterwards compute the likelihood of the synthetic data belonging to the learned distribution.

Such metrics are:

`sdv.metrics.tabular.BNLikelihood`

: This metric fits a BayesianNetwork to the real data and then evaluates the average likelihood of the rows from the synthetic data on it.`sdv.metrics.tabular.BNLogLikelihood`

: This metric fits a BayesianNetwork to the real data and then evaluates the average log likelihood of the rows from the synthetic data on it.`sdv.metrics.tabular.GMLogLikelihood`

: This metric fits multiple GaussianMixture models to the real data and then evaluates the average log likelihood of the synthetic data on them.

Note

These metrics do not accept missing data, so we will replace all the missing values with a 0 before executing them.

Let us execute these metrics on the loaded data:

```
In [11]: from sdv.metrics.tabular import BNLikelihood, BNLogLikelihood, GMLogLikelihood
In [12]: BNLikelihood.compute(real_data.fillna(0), synthetic_data.fillna(0))
Out[12]: 0.004311090583670755
In [13]: BNLogLikelihood.compute(real_data.fillna(0), synthetic_data.fillna(0))
Out[13]: -14.62132601319649
In [14]: GMLogLikelihood.compute(real_data.fillna(0), synthetic_data.fillna(0))
Out[14]: -35024.711762921426
```

Our metrics can also be returned as values between 0 and 1 instead of likelihood scores. To do so, simply use the normalize method, as in the example below:

```
In [15]: raw_score = BNLogLikelihood.compute(real_data.fillna(0), synthetic_data.fillna(0))
In [16]: BNLogLikelihood.normalize(raw_score)
Out[15]: 4.467234949793966e-07
```

Note

All of our metrics support the normalize method, but since the majority of them already return values between 0 and 1 usually normalize simply returns the raw score.

### Detection Metrics¶

The metrics of this family evaluate how hard it is to distinguish the synthetic data from the real data by using a Machine Learning model. To do this, the metrics will shuffle the real data and synthetic data together with flags indicating whether the data is real or synthetic, and then cross validate a Machine Learning model that tries to predict this flag. The output of the metrics will be the 1 minus the average ROC AUC score across all the cross validation splits.

Such metrics are:

`sdv.metrics.tabular.LogisticDetection`

: Detection metric based on a`LogisticRegression`

classifier from`scikit-learn`

.`sdv.metrics.tabular.SVCDetection`

: Detection metric based on a`SVC`

classifier from`scikit-learn`

.

Let us execute these metrics on the loaded data:

```
In [16]: from sdv.metrics.tabular import LogisticDetection, SVCDetection
In [17]: LogisticDetection.compute(real_data, synthetic_data)
Out[17]: 0.0
In [18]: SVCDetection.compute(real_data, synthetic_data)
Out[18]: 0.0009056395989102128
```

### Machine Learning Efficacy Metrics¶

This family of metrics will evaluate whether it is possible to replace the real data with synthetic data in order to solve a Machine Learning Problem by learning a Machine Learning model on the synthetic data and then evaluating the score which it obtains when evaluated on the real data.

Note

Since this metrics will be evaluated by trying to solve a Machine Learning problem, they can only be used on datasets that contain a target column that needs or can be predicted using the rest of the data, and the scores obtained by the metrics will be inversely proportional to how hard that Machine Problem is.

The metrics on this family are organized by Machine Learning problem type and model.

Binary Classification Metrics:

`BinaryDecisionTreeClassifier`

`BinaryAdaBoostClassifier`

`BinaryLogisticRegression`

`BinaryMLPClassifier`

Multiclass Classification Metrics:

`MulticlassDecisionTreeClassifier`

`MulticlassMLPClassifier`

Regression Metrics:

`LinearRegression`

`MLPRegressor`

In order to run these metrics we will need to select a column from our dataset which we will use as the target for the prediction problem. For example, in the demo dataset there are multiple columns that can be used as possible targets for a Machine Learning problem:

`work_experience`

and`placed`

can be used for binary classification problems.`high_spec`

,`degree_type`

,`mba_spec`

and`duration`

can be used for multiclass classification problems.`second_perc`

,`high_perc`

,`degree_perc`

,`experience_years`

,`employability_perc`

,`mba_perc`

and`salary`

can be used for regression problems.

Let’s select the `mba_spect`

column as the target for our problem and let the Machine Learning
Efficacy Metric attempt to predict it using the rest of the columns.

```
In [19]: from sdv.metrics.tabular import MulticlassDecisionTreeClassifier
In [20]: MulticlassDecisionTreeClassifier.compute(real_data, synthetic_data, target='mba_spec')
Out[20]: 0.5581012959477294
```

Notice that the value returned by the metric does not only depend on how good our synthetic data is, but also on how hard the Machine Learning problem that we are trying to solve is. For reference, we may want to compare this result with the one obtained when trying to make the prediction using real data as input. For this, we will need to split the data into train and test partitions and call the metric replacing the real data and synthetic data with the test and training data respectively.

```
In [21]: train = real_data.sample(int(len(real_data) * 0.75))
In [22]: test = real_data[~real_data.index.isin(train.index)]
In [23]: MulticlassDecisionTreeClassifier.compute(test, train, target='mba_spec')
Out[23]: 0.5703908682116914
```

Note

Apart from passing the `target`

variable as an argument, we can also store its
value inside the `metadata`

dict and pass it to the metric:

```
In [24]: metadata['target'] = 'mba_spec'
In [25]: MulticlassDecisionTreeClassifier.compute(real_data, synthetic_data, metadata)
Out[25]: 0.5767075571709829
```

### Privacy Metrics¶

This family of metrics measures the privacy of a synthetic dataset by positing the question: given the synthetic data, can an attacker predict sensitive attributes in the real dataset? These models accomplish this by fitting an adversarial attacker model on the synthetic data to predict sensitive attributes from “key” attributes and then evaluating its accuracy on the real data.

The metrics on this family are organized according to the data type they take as input:

Categorical metrics:

`sdv.metrics.tabular.CategoricalCAP`

`sdv.metrics.tabular.CategoricalZeroCAP`

`sdv.metrics.tabular.CategoricalGeneralizedCAP`

`sdv.metrics.tabular.CategoricalKNN`

`sdv.metrics.tabular.CategoricalNB`

`sdv.metrics.tabular.CategoricalRF`

`sdv.metrics.tabular.CategoricalEnsemble`

Numerical metrics:

`sdv.metrics.tabular.NumericalMLP`

`sdv.metrics.tabular.NumericalLR`

`sdv.metrics.tabular.NumericalSVR`

`sdv.metrics.tabular.NumericalRadiusNearestNeighbor`

In addition to the real and synthetic data, these metrics also require
two additional inputs, `sensitive_fields`

which is a list of columns
considered private and `key_fields`

which are the columns that will be
used to try to predict the sensitive ones.

Using the demo data set, one possible example is to use:

`salary`

as a sensitive column, which is the column we are measuring ahow private it is`second_perc`

,`mba_perc`

and`degree_perc`

as the key columns, which will be used by the adversarial attacker to predict the sensitive column

Notice that as all the involved columns are numerical, we need to apply
a numerical privacy metric. Conversely, if all of the columns are
categorical, we need to use a categorical privacy metric. Currently, the
privacy metrics do **not** support mixed data types.

Note

These metrics do not accept missing data, so we will replace all the missing values with a 0 before executing them.

```
In [26]: from sdv.metrics.tabular import NumericalLR
In [27]: NumericalLR.compute(
....: real_data,
....: synthetic_data,
....: key_fields=['second_perc', 'mba_perc', 'degree_perc'],
....: sensitive_fields=['salary']
....: )
....:
Out[27]: 0.09552544249953869
```

The output of this metric is between 0 and 1, where the closer the value is to 0, the less private it is.