GaussianCopula Model

In this guide we will go through a series of steps that will let you discover functionalities of the GaussianCopula model, including how to:

  • Create an instance of a GaussianCopula.

  • Fit the instance to your data.

  • Generate synthetic versions of your data.

  • Use GaussianCopula to anonymize PII information.

  • Customize the data transformations to improve the learning process.

  • Specify the column distributions to improve the output quality.

What is GaussianCopula?

The sdv.tabular.GaussianCopula model is based on copula funtions.

In mathematical terms, a copula is a distribution over the unit cube \({\displaystyle [0,1]^{d}}\) which is constructed from a multivariate normal distribution over \({\displaystyle \mathbb {R} ^{d}}\) by using the probability integral transform. Intuitively, a copula is a mathematical function that allows us to describe the joint distribution of multiple random variables by analyzing the dependencies between their marginal distributions.

Let’s now discover how to learn a dataset and later on generate synthetic data with the same format and statistical properties by using the GaussianCopula model.

Quick Usage

We will start by loading one of our demo datasets, the student_placements, which contains information about MBA students that applied for placements during the year 2020.

In [1]: from sdv.demo import load_tabular_demo

In [2]: data = load_tabular_demo('student_placements')

In [3]: data.head()
Out[3]: 
   student_id gender  second_perc  high_perc high_spec  degree_perc degree_type  work_experience  experience_years  employability_perc mba_spec  mba_perc   salary  placed start_date   end_date duration
0       17264      M        67.00      91.00  Commerce        58.00    Sci&Tech            False                 0                55.0   Mkt&HR     58.80  27000.0    True 2020-07-23 2020-10-12      3.0
1       17265      M        79.33      78.33   Science        77.48    Sci&Tech             True                 1                86.5  Mkt&Fin     66.28  20000.0    True 2020-01-11 2020-04-09      3.0
2       17266      M        65.00      68.00      Arts        64.00   Comm&Mgmt            False                 0                75.0  Mkt&Fin     57.80  25000.0    True 2020-01-26 2020-07-13      6.0
3       17267      M        56.00      52.00   Science        52.00    Sci&Tech            False                 0                66.0   Mkt&HR     59.43      NaN   False        NaT        NaT      NaN
4       17268      M        85.80      73.60  Commerce        73.30   Comm&Mgmt            False                 0                96.8  Mkt&Fin     55.50  42500.0    True 2020-07-04 2020-09-27      3.0

As you can see, this table contains information about students which includes, among other things:

  • Their id and gender

  • Their grades and specializations

  • Their work experience

  • The salary that they were offered

  • The duration and dates of their placement

You will notice that there is data with the following characteristics:

  • There are float, integer, boolean, categorical and datetime values.

  • There are some variables that have missing data. In particular, all the data related to the placement details is missing in the rows where the student was not placed.

Let us use the GaussianCopula to learn this data and then sample synthetic data about new students to see how well the model captures the characteristics indicated above. In order to do this you will need to:

  • Import the sdv.tabular.GaussianCopula class and create an instance of it.

  • Call its fit method passing our table.

  • Call its sample method indicating the number of synthetic rows that you want to generate.

In [4]: from sdv.tabular import GaussianCopula

In [5]: model = GaussianCopula()

In [6]: model.fit(data)

Note

Notice that the model fitting process took care of transforming the different fields using the appropriate Reversible Data Transforms to ensure that the data has a format that the GaussianMultivariate model can handle.

Generate synthetic data from the model

Once the modeling has finished you are ready to generate new synthetic data by calling the sample method from your model passing the number of rows that we want to generate.

In [7]: new_data = model.sample(200)

This will return a table identical to the one which the model was fitted on, but filled with new data which resembles the original one.

In [8]: new_data.head()
Out[8]: 
   student_id gender  second_perc  high_perc high_spec  degree_perc degree_type  work_experience  experience_years  employability_perc mba_spec   mba_perc        salary  placed start_date   end_date duration
0       17338      F    64.181235  66.544103  Commerce    66.336633   Comm&Mgmt            False                 0           53.809509  Mkt&Fin  67.563477  30224.542293    True 2020-02-12 2021-02-23     12.0
1       17370      F    48.523598  45.465191   Science    63.976260   Comm&Mgmt            False                 0           50.871384   Mkt&HR  50.461222           NaN   False        NaT        NaT      NaN
2       17325      M    66.210129  60.213549  Commerce    67.362243   Comm&Mgmt            False                 1           55.251668  Mkt&Fin  70.173525           NaN   False        NaT        NaT      NaN
3       17274      F    85.621139  66.028705   Science    69.764263      Others            False                 1           69.376680  Mkt&Fin  60.389233  26426.034043    True 2020-03-31 2020-06-12      3.0
4       17321      M    63.276089  65.915013  Commerce    65.964453   Comm&Mgmt            False                 0           59.184216   Mkt&HR  65.797136  25147.436510    True 2020-01-17 2020-04-17      3.0

Note

You can control the number of rows by specifying the number of samples in the model.sample(<num_rows>). To test, try model.sample(10000). Note that the original table only had ~200 rows.

Save and Load the model

In many scenarios it will be convenient to generate synthetic versions of your data directly in systems that do not have access to the original data source. For example, if you may want to generate testing data on the fly inside a testing environment that does not have access to your production database. In these scenarios, fitting the model with real data every time that you need to generate new data is feasible, so you will need to fit a model in your production environment, save the fitted model into a file, send this file to the testing environment and then load it there to be able to sample from it.

Let’s see how this process works.

Save and share the model

Once you have fitted the model, all you need to do is call its save method passing the name of the file in which you want to save the model. Note that the extension of the filename is not relevant, but we will be using the .pkl extension to highlight that the serialization protocol used is pickle.

In [9]: model.save('my_model.pkl')

This will have created a file called my_model.pkl in the same directory in which you are running SDV.

Important

If you inspect the generated file you will notice that its size is much smaller than the size of the data that you used to generate it. This is because the serialized model contains no information about the original data, other than the parameters it needs to generate synthetic versions of it. This means that you can safely share this my_model.pkl file without the risk of disclosing any of your real data!

Load the model and generate new data

The file you just generated can be sent over to the system where the synthetic data will be generated. Once it is there, you can load it using the GaussianCopula.load method, and then you are ready to sample new data from the loaded instance:

In [10]: loaded = GaussianCopula.load('my_model.pkl')

In [11]: new_data = loaded.sample(200)

Warning

Notice that the system where the model is loaded needs to also have sdv installed, otherwise it will not be able to load the model and use it.

Specifying the Primary Key of the table

One of the first things that you may have noticed when looking at the demo data is that there is a student_id column which acts as the primary key of the table, and which is supposed to have unique values. Indeed, if we look at the number of times that each value appears, we see that all of them appear at most once:

In [12]: data.student_id.value_counts().max()
Out[12]: 1

However, if we look at the synthetic data that we generated, we observe that there are some values that appear more than once:

In [13]: new_data[new_data.student_id == new_data.student_id.value_counts().index[0]]
Out[13]: 
     student_id gender  second_perc   high_perc high_spec  degree_perc degree_type  work_experience  experience_years  employability_perc mba_spec   mba_perc        salary  placed start_date   end_date duration
71        17315      M    82.520213   86.628848   Science    74.621151    Sci&Tech            False                 0           91.538255  Mkt&Fin  59.081347  31628.681218    True 2020-03-20 2020-10-07      3.0
108       17315      F    72.008366   75.612261  Commerce    67.094954   Comm&Mgmt            False                 2           71.607191  Mkt&Fin  71.618924           NaN   False        NaT        NaT      NaN
112       17315      F    60.232074   63.523101  Commerce    68.713908   Comm&Mgmt            False                 0           60.592540  Mkt&Fin  61.100692           NaN   False        NaT        NaT      3.0
137       17315      M    61.983224   46.097386  Commerce    52.845057    Sci&Tech            False                 0           81.741801   Mkt&HR  63.081250           NaN   False        NaT        NaT      NaN
145       17315      F    71.741651   71.222269  Commerce    65.997807   Comm&Mgmt            False                 0           73.270146   Mkt&HR  72.496757           NaN   False        NaT        NaT      NaN
176       17315      F    71.441818  115.723273  Commerce    77.766414   Comm&Mgmt            False                 1           76.516696  Mkt&Fin  69.796434  35710.590174    True 2020-02-06 2020-11-12     12.0

This happens because the model was not notified at any point about the fact that the student_id had to be unique, so when it generates new data it will provoke collisions sooner or later. In order to solve this, we can pass the argument primary_key to our model when we create it, indicating the name of the column that is the index of the table.

In [14]: model = GaussianCopula(
   ....:     primary_key='student_id'
   ....: )
   ....: 

In [15]: model.fit(data)

In [16]: new_data = model.sample(200)

In [17]: new_data.head()
Out[17]: 
   student_id gender  second_perc  high_perc high_spec  degree_perc degree_type  work_experience  experience_years  employability_perc mba_spec   mba_perc        salary  placed start_date   end_date duration
0           0      M    61.916813  67.128159  Commerce    62.174657   Comm&Mgmt            False                 0           80.625020  Mkt&Fin  63.140435  32761.012958    True 2020-02-11 2020-08-24     12.0
1           1      M    72.314817  84.230085  Commerce    67.307607   Comm&Mgmt            False                 1           86.392786  Mkt&Fin  71.948674  27656.562043    True 2020-02-04 2020-08-24      3.0
2           2      M    84.745332  71.180452   Science    71.889331    Sci&Tech            False                 0           54.779427  Mkt&Fin  70.355750           NaN   False        NaT        NaT      NaN
3           3      M    55.229688  57.048697  Commerce    49.239246   Comm&Mgmt            False                 1           62.714429   Mkt&HR  55.396712           NaN   False        NaT        NaT      NaN
4           4      F    48.038052  49.056623  Commerce    52.901254   Comm&Mgmt            False                 0           79.342439   Mkt&HR  53.274493           NaN   False        NaT        NaT      NaN

As a result, the model will learn that this column must be unique and generate a unique sequence of values for the column:

In [18]: new_data.student_id.value_counts().max()
Out[18]: 1

Anonymizing Personally Identifiable Information (PII)

There will be many cases where the data will contain Personally Identifiable Information which we cannot disclose. In these cases, we will want our Tabular Models to replace the information within these fields with fake, simulated data that looks similar to the real one but does not contain any of the original values.

Let’s load a new dataset that contains a PII field, the student_placements_pii demo, and try to generate synthetic versions of it that do not contain any of the PII fields.

Note

The student_placements_pii dataset is a modified version of the student_placements dataset with one new field, address, which contains PII information about the students. Notice that this additional address field has been simulated and does not correspond to data from the real users.

In [19]: data_pii = load_tabular_demo('student_placements_pii')

In [20]: data_pii.head()
Out[20]: 
   student_id                                            address gender  second_perc  high_perc high_spec  degree_perc degree_type  work_experience  experience_years  employability_perc mba_spec  mba_perc   salary  placed start_date   end_date duration
0       17264        70304 Baker Turnpike\nEricborough, MS 15086      M        67.00      91.00  Commerce        58.00    Sci&Tech            False                 0                55.0   Mkt&HR     58.80  27000.0    True 2020-07-23 2020-10-12      3.0
1       17265    805 Herrera Avenue Apt. 134\nMaryview, NJ 36510      M        79.33      78.33   Science        77.48    Sci&Tech             True                 1                86.5  Mkt&Fin     66.28  20000.0    True 2020-01-11 2020-04-09      3.0
2       17266        3702 Bradley Island\nNorth Victor, FL 12268      M        65.00      68.00      Arts        64.00   Comm&Mgmt            False                 0                75.0  Mkt&Fin     57.80  25000.0    True 2020-01-26 2020-07-13      6.0
3       17267                   Unit 0879 Box 3878\nDPO AP 42663      M        56.00      52.00   Science        52.00    Sci&Tech            False                 0                66.0   Mkt&HR     59.43      NaN   False        NaT        NaT      NaN
4       17268  96493 Kelly Canyon Apt. 145\nEast Steven, NC 3...      M        85.80      73.60  Commerce        73.30   Comm&Mgmt            False                 0                96.8  Mkt&Fin     55.50  42500.0    True 2020-07-04 2020-09-27      3.0

If we use our tabular model on this new data we will see how the synthetic data that it generates discloses the addresses from the real students:

In [21]: model = GaussianCopula(
   ....:     primary_key='student_id',
   ....: )
   ....: 

In [22]: model.fit(data_pii)

In [23]: new_data_pii = model.sample(200)

In [24]: new_data_pii.head()
Out[24]: 
   student_id                                            address gender  second_perc  high_perc high_spec  degree_perc degree_type  work_experience  experience_years  employability_perc mba_spec   mba_perc        salary  placed start_date   end_date duration
0           0                   Unit 3091 Box 7338\nDPO AP 23696      M    49.989625  37.268740   Science    55.228111    Sci&Tech            False                 1           77.571994   Mkt&HR  63.043014           NaN   False        NaT        NaT      NaN
1           1             39392 Dodson Club\nYoungberg, SC 75263      F    75.985240  66.897008   Science    77.166625    Sci&Tech            False                 1           76.142784  Mkt&Fin  65.388418  22550.807273    True 2020-01-17 2020-07-30      NaN
2           2            526 Patricia Parks\nMccoyport, DC 77793      M    44.575775  61.812223  Commerce    48.892362   Comm&Mgmt            False                 0           75.621465   Mkt&HR  50.130206           NaN   False        NaT        NaT      NaN
3           3        90563 Charles Road\nSouth Melinda, MA 00878      F    64.458887  67.186594  Commerce    75.001889   Comm&Mgmt            False                 0           59.264294  Mkt&Fin  61.248955           NaN   False        NaT        NaT      NaN
4           4  46861 Hanson Ridges Suite 587\nNorth Timstad, ...      M    79.381381  73.236458   Science    74.429158    Sci&Tech            False                 0           68.908282  Mkt&Fin  60.739729  28501.868703    True 2020-02-01 2020-07-23      3.0

More specifically, we can see how all the addresses that have been generated actually come from the original dataset:

In [25]: new_data_pii.address.isin(data_pii.address).sum()
Out[25]: 200

In order to solve this, we can pass an additional argument anonymize_fields to our model when we create the instance. This anonymize_fields argument will need to be a dictionary that contains:

  • The name of the field that we want to anonymize.

  • The category of the field that we want to use when we generate fake values for it.

The list complete list of possible categories can be seen in the Faker Providers page, and it contains a huge list of concepts such as:

  • name

  • address

  • country

  • city

  • ssn

  • credit_card_number

  • credit_card_expire

  • credit_card_security_code

  • email

  • telephone

In this case, since the field is an e-mail address, we will pass a dictionary indicating the category address

In [26]: model = GaussianCopula(
   ....:     primary_key='student_id',
   ....:     anonymize_fields={
   ....:         'address': 'address'
   ....:     }
   ....: )
   ....: 

In [27]: model.fit(data_pii)

As a result, we can see how the real address values have been replaced by other fake addresses:

In [28]: new_data_pii = model.sample(200)

In [29]: new_data_pii.head()
Out[29]: 
   student_id                                            address gender  second_perc  high_perc high_spec  degree_perc degree_type  work_experience  experience_years  employability_perc mba_spec   mba_perc        salary  placed start_date   end_date duration
0           0  3600 Cole Camp Suite 398\nNew Tinashire, MD 02387      M    50.614977  56.803428  Commerce    52.656126   Comm&Mgmt            False                 0           54.155383   Mkt&HR  64.019490           NaN   False        NaT        NaT      NaN
1           1                        USS Alexander\nFPO AE 95941      M    57.896030  63.404704  Commerce    58.939304   Comm&Mgmt            False                 0           84.119119   Mkt&HR  72.922585           NaN   False        NaT        NaT      NaN
2           2    1478 Darrell Forest Apt. 702\nRayfort, OR 68993      M    50.650849  74.550421  Commerce    67.508372   Comm&Mgmt            False                 1           81.554426  Mkt&Fin  60.903375  28837.902553    True 2020-01-26 2020-06-03      3.0
3           3                   Unit 2353 Box 1545\nDPO AE 19682      M    47.338609  59.746061  Commerce    55.873947   Comm&Mgmt            False                 1           63.006357   Mkt&HR  56.387225           NaN   False        NaT        NaT      NaN
4           4  15001 Alexander Knolls Apt. 083\nWest Gregoryv...      F    75.244101  80.523194   Science    67.900379   Comm&Mgmt            False                 0           96.751812  Mkt&Fin  67.930548  30092.464629    True 2020-04-29 2020-11-10      3.0

Which means that none of the original addresses can be found in the sampled data:

In [30]: data_pii.address.isin(new_data_pii.address).sum()
Out[30]: 0

Advanced Usage

Now that we have discovered the basics, let’s go over a few more advanced usage examples and see the different arguments that we can pass to our GaussianCopula Model in order to customize it to our needs.

How to set transforms to use?

One thing that you may have noticed when executing the previous steps is that the fitting process took much longer on the student_placements_pii dataset than it took on the previous version that did not contain the student address. This happens because the address field is interpreted as a categorical variable, which the GaussianCopula one-hot encoded generating 215 new columns that it had to learn afterwards.

This transformation, which in this case was very inefficient, happens because the Tabular Models apply Reversible Data Transforms under the hood to transform all the non-numerical variables, which the underlying models cannot handle, into numerical representations which they can properly work with. In the case of the GaussianCopula, the default transformation is a One-Hot encoding, which can work very well with variables that have a small number of different values, but which is very inefficient in cases where there is a large number of values.

For this reason, the Tabular Models have an additional argument called field_transformers that let you select which transformer to apply to each column. This field_transformers argument must be passed as a dict which contains the name of the fields for which we want to use a transformer different than the default, and the name of the transformer that we want to use.

Possible transformer names are:

  • integer: Uses a NumericalTransformer of dtype int.

  • float: Uses a NumericalTransformer of dtype float.

  • categorical: Uses a CategoricalTransformer without gaussian noise.

  • categorical_fuzzy: Uses a CategoricalTransformer adding gaussian noise.

  • one_hot_encoding: Uses a OneHotEncodingTransformer.

  • label_encoding: Uses a LabelEncodingTransformer.

  • boolean: Uses a BooleanTransformer.

  • datetime: Uses a DatetimeTransformer.

NOTE: For additional details about each one of the transformers, please visit RDT

Let’s now try to improve the previous fitting process by changing the transformer that we use for the address field to something other than the default. As an example, we will use the label_encoding transformer, which instead of generating one column for each possible value, it just replaces each value with a unique integer value.

In [31]: model = GaussianCopula(
   ....:     primary_key='student_id',
   ....:     anonymize_fields={
   ....:         'address': 'address'
   ....:     },
   ....:     field_transformers={
   ....:         'address': 'label_encoding'
   ....:     }
   ....: )
   ....: 

In [32]: model.fit(data_pii)

In [33]: new_data_pii = model.sample(200)

In [34]: new_data_pii.head()
Out[34]: 
   student_id                                            address gender  second_perc  high_perc high_spec  degree_perc degree_type  work_experience  experience_years  employability_perc mba_spec   mba_perc        salary  placed start_date   end_date duration
0           0              124 Cassandra Rest\nIanview, MA 80481      F    80.938672  70.652100  Commerce    70.486247   Comm&Mgmt            False                 0           52.297210   Mkt&HR  74.823515           NaN   False        NaT        NaT      NaN
1           1  617 Perry Shoal Suite 605\nLake Brendatown, NJ...      M    58.787360  47.928114  Commerce    65.202339   Comm&Mgmt            False                -1           63.889376  Mkt&Fin  62.842863           NaN   False        NaT        NaT      NaN
2           2           52821 Kenneth Inlet\nNew David, AZ 17442      M    69.681745  65.516798  Commerce    67.164067   Comm&Mgmt            False                 0           73.452358   Mkt&HR  58.690001           NaN   False        NaT        NaT      NaN
3           3                   PSC 7660, Box 0654\nAPO AE 60516      M    72.778515  70.696675   Science    54.180383    Sci&Tech            False                 0           76.134726  Mkt&Fin  59.180392  27491.293008    True 2020-04-15 2020-11-08      3.0
4           4   661 Hicks Cliffs Suite 523\nLake Laura, ID 17335      M    63.807890  72.174068  Commerce    66.568022   Comm&Mgmt            False                 0           67.332621   Mkt&HR  65.104357           NaN   False        NaT        NaT      3.0

Exploring the Probability Distributions

During the previous steps, every time we fitted the GaussianCopula it performed the following operations:

  1. Learn the format and data types of the passed data

  2. Transform the non-numerical and null data using Reversible Data Transforms to obtain a fully numerical representation of the data from which we can learn the probability distributions.

  3. Learn the probability distribution of each column from the table

  4. Transform the values of each numerical column by converting them to their marginal distribution CDF values and then applying an inverse CDF transformation of a standard normal on them.

  5. Learn the correlations of the newly generated random variables.

After this, when we used the model to generate new data for our table using the sample method, it did:

  1. Sample from a Multivariate Standard Normal distribution with the learned correlations.

  2. Revert the sampled values by computing their standard normal CDF and then applying the inverse CDF of their marginal distributions.

  3. Revert the RDT transformations to go back to the original data format.

As you can see, during these steps the Marginal Probability Distributions have a very important role, since the GaussianCopula had to learn and reproduce the individual distributions of each column in our table. We can explore the distributions which the GaussianCopula used to model each column using its get_distributions method:

In [35]: model = GaussianCopula(
   ....:     primary_key='student_id'
   ....: )
   ....: 

In [36]: model.fit(data)

In [37]: distributions = model.get_distributions()

This will return us a dict which contains the name of the distribution class used for each column:

In [38]: distributions
Out[38]: 
{'second_perc': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
 'high_perc': 'copulas.univariate.log_laplace.LogLaplace',
 'degree_perc': 'copulas.univariate.student_t.StudentTUnivariate',
 'work_experience': 'copulas.univariate.student_t.StudentTUnivariate',
 'experience_years': 'copulas.univariate.gaussian.GaussianUnivariate',
 'employability_perc': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
 'mba_perc': 'copulas.univariate.gamma.GammaUnivariate',
 'placed': 'copulas.univariate.gamma.GammaUnivariate',
 'gender#0': 'copulas.univariate.gaussian.GaussianUnivariate',
 'gender#1': 'copulas.univariate.gaussian.GaussianUnivariate',
 'high_spec#0': 'copulas.univariate.gaussian.GaussianUnivariate',
 'high_spec#1': 'copulas.univariate.gamma.GammaUnivariate',
 'high_spec#2': 'copulas.univariate.gaussian.GaussianUnivariate',
 'degree_type#0': 'copulas.univariate.student_t.StudentTUnivariate',
 'degree_type#1': 'copulas.univariate.gaussian.GaussianUnivariate',
 'degree_type#2': 'copulas.univariate.gaussian.GaussianUnivariate',
 'mba_spec#0': 'copulas.univariate.gamma.GammaUnivariate',
 'mba_spec#1': 'copulas.univariate.gaussian.GaussianUnivariate',
 'salary#0': 'copulas.univariate.gamma.GammaUnivariate',
 'salary#1': 'copulas.univariate.gaussian.GaussianUnivariate',
 'start_date#0': 'copulas.univariate.gamma.GammaUnivariate',
 'start_date#1': 'copulas.univariate.gaussian.GaussianUnivariate',
 'end_date#0': 'copulas.univariate.gamma.GammaUnivariate',
 'end_date#1': 'copulas.univariate.gaussian.GaussianUnivariate',
 'duration#0': 'copulas.univariate.gaussian.GaussianUnivariate',
 'duration#1': 'copulas.univariate.gaussian.GaussianUnivariate',
 'duration#2': 'copulas.univariate.student_t.StudentTUnivariate',
 'duration#3': 'copulas.univariate.gaussian.GaussianUnivariate'}

Note

In this list we will see multiple distributions for each one of the columns that we have in our data. This is because the RDT transformations used to encode the data numerically often use more than one column to represent each one of the input variables.

Let’s explore the individual distribution of one of the columns in our data to better understand how the GaussianCopula processed them and see if we can improve the results by manually specifying a different distribution. For example, let’s explore the experience_years column by looking at the frequency of its values within the original data:

In [39]: data.experience_years.value_counts()
Out[39]: 
0    141
1     65
2      8
3      1
Name: experience_years, dtype: int64

In [40]: data.experience_years.hist();
../../_images/experience_years_1.png

By observing the data we can see that the behavior of the values in this column is very similar to a Gamma or even some types of Beta distribution, where the majority of the values are 0 and the frequency decreases as the values increase.

Was the GaussianCopula able to capture this distribution on its own?

In [41]: distributions['experience_years']
Out[41]: 'copulas.univariate.gaussian.GaussianUnivariate'

It seems that it was not, as it rather thought that the behavior was closer to a Gaussian distribution. And, as a result, we can see how the generated values now contain negative values which are invalid for this column:

In [42]: new_data.experience_years.value_counts()
Out[42]: 
 0    103
 1     76
-1     15
 2      6
Name: experience_years, dtype: int64

In [43]: new_data.experience_years.hist();
../../_images/experience_years_2.png

Let’s see how we can improve this situation by passing the GaussianCopula the exact distribution that we want it to use for this column.

Setting distributions for individual variables

The GaussianCopula class offers the possibility to indicate which distribution to use for each one of the columns in the table, in order to solve situations like the one that we just described. In order to do this, we need to pass a field_distributions argument with dict that indicates the distribution that we want to use for each column.

Possible values for the distribution argument are:

  • univariate: Let copulas select the optimal univariate distribution. This may result in non-parametric models being used.

  • parametric: Let copulas select the optimal univariate distribution, but restrict the selection to parametric distributions only.

  • bounded: Let copulas select the optimal univariate distribution, but restrict the selection to bounded distributions only. This may result in non-parametric models being used.

  • semi_bounded: Let copulas select the optimal univariate distribution, but restrict the selection to semi-bounded distributions only. This may result in non-parametric models being used.

  • parametric_bounded: Let copulas select the optimal univariate distribution, but restrict the selection to parametric and bounded distributions only.

  • parametric_semi_bounded: Let copulas select the optimal univariate distribution, but restrict the selection to parametric and semi-bounded distributions only.

  • gaussian: Use a Gaussian distribution.

  • gamma: Use a Gamma distribution.

  • beta: Use a Beta distribution.

  • student_t: Use a Student T distribution.

  • gaussian_kde: Use a GaussianKDE distribution. This model is non-parametric, so using this will make get_parameters unusable.

  • truncated_gaussian: Use a Truncated Gaussian distribution.

Let’s see what happens if we make the GaussianCopula use the gamma distribution for our column.

In [44]: from sdv.tabular import GaussianCopula

In [45]: model = GaussianCopula(
   ....:     primary_key='student_id',
   ....:     field_distributions={
   ....:         'experience_years': 'gamma'
   ....:     }
   ....: )
   ....: 

In [46]: model.fit(data)

After this, we can see how the GaussianCopula used the indicated distribution for the experience_years column

In [47]: model.get_distributions()['experience_years']
Out[47]: 'copulas.univariate.gamma.GammaUnivariate'

And, as a result, we can see how the generated data now have a behavior which is closer to the original data and always stays within the valid values range.

In [48]: new_data = model.sample(len(data))

In [49]: new_data.experience_years.value_counts()
Out[49]: 
0    205
1     10
Name: experience_years, dtype: int64

In [50]: new_data.experience_years.hist();
../../_images/experience_years_3.png

Note

Even though there are situations like the one shown above where manually choosing a distribution seems to give better results, in most cases the GaussianCopula will be able to find the optimal distribution on its own, making this manual search of the marginal distributions necessary on very little occasions.

Conditional Sampling

As the name implies, conditional sampling allows us to sample from a conditional distribution using the GaussianCopula model, which means we can generate only values that satisfy certain conditions. These conditional values can be passed to the conditions parameter in the sample method either as a dataframe or a dictionary.

In case a dictionary is passed, the model will generate as many rows as requested, all of which will satisfy the specified conditions, such as gender = M.

In [51]: conditions = {
   ....:     'gender': 'M'
   ....: }
   ....: 

In [52]: model.sample(5, conditions=conditions)
Out[52]: 
   student_id gender  second_perc  high_perc high_spec  degree_perc degree_type  work_experience  experience_years  employability_perc mba_spec   mba_perc        salary  placed start_date   end_date duration
0           0      M    63.295295  63.587375  Commerce    73.258294   Comm&Mgmt            False                 0           91.682132   Mkt&HR  64.850285  30336.255313    True 2020-02-20 2020-10-24     12.0
1           1      M    57.657967  61.087111      Arts    61.488033   Comm&Mgmt            False                 0           94.272689  Mkt&Fin  56.310621  30258.385719    True 2020-01-02 2020-05-08     12.0
2           2      M    46.403341  65.246935  Commerce    58.392598   Comm&Mgmt            False                 0           61.366822   Mkt&HR  64.126831           NaN    True        NaT        NaT      NaN
3           3      M    62.923403  51.052695   Science    63.794126   Comm&Mgmt            False                 0           61.633155  Mkt&Fin  55.973583  28622.954816    True 2020-02-21 2020-09-17      3.0
4           4      M    77.239896  68.927081   Science    67.538680    Sci&Tech            False                 0           69.123058   Mkt&HR  72.049664           NaN   False        NaT        NaT      NaN

It’s also possible to condition on multiple columns, such as gender = M, 'experience_years': 0.

In [53]: conditions = {
   ....:     'gender': 'M',
   ....:     'experience_years': 0
   ....: }
   ....: 

In [54]: model.sample(5, conditions=conditions)
Out[54]: 
   student_id gender  second_perc  high_perc high_spec  degree_perc degree_type  work_experience  experience_years  employability_perc mba_spec   mba_perc        salary  placed start_date   end_date duration
0           0      M    71.161948  75.402258   Science    63.437086   Comm&Mgmt            False                 0           55.739497  Mkt&Fin  52.050836  20922.976136    True 2020-03-27 2020-05-16      3.0
1           1      M    47.145980  61.249953  Commerce    54.844547   Comm&Mgmt            False                 0           62.496271   Mkt&HR  50.735618           NaN   False        NaT        NaT      NaN
2           2      M    48.506886  67.449542   Science    59.979473    Sci&Tech            False                 0           91.643279   Mkt&HR  59.048889           NaN   False        NaT        NaT      NaN
3           3      M    55.449519  55.802401  Commerce    50.310803   Comm&Mgmt            False                 0           64.737907   Mkt&HR  54.455629           NaN   False        NaT        NaT      NaN
4           4      M    78.122196  68.900259  Commerce    57.200343   Comm&Mgmt            False                 0           58.558378   Mkt&HR  58.881269  28038.474493    True 2020-02-27 2020-06-30      3.0

The conditions can also be passed as a dataframe. In that case, the model will generate one sample for each row of the dataframe, sorted in the same order. Since the model already knows how many samples to generate, passing it as a parameter is unnecessary. For example, if we want to generate three samples where gender = M and three samples with gender = F, we can do the following:

In [55]: import pandas as pd

In [56]: conditions = pd.DataFrame({
   ....:     'gender': ['M', 'M', 'M', 'F', 'F', 'F'],
   ....: })
   ....: 

In [57]: model.sample(conditions=conditions)
Out[57]: 
   student_id gender  second_perc  high_perc high_spec  degree_perc degree_type  work_experience  experience_years  employability_perc mba_spec   mba_perc        salary  placed start_date   end_date duration
0           0      M    80.134595  69.859909   Science    76.212891    Sci&Tech            False                 0           53.264885  Mkt&Fin  61.919393  38969.192086    True 2020-04-19 2020-08-29      3.0
1           1      M    64.981426  55.521510  Commerce    52.105234   Comm&Mgmt            False                 0           65.160272  Mkt&Fin  52.819546  30704.551333    True 2020-01-14 2020-06-26      NaN
2           2      M    81.212292  73.891487  Commerce    73.536962   Comm&Mgmt            False                 0           59.618138   Mkt&HR  59.840363  30734.670347    True 2020-03-05 2020-05-22      3.0
3           3      F    84.667818  78.284323   Science    77.592989    Sci&Tech            False                 0           71.713380  Mkt&Fin  75.400906  43669.416542    True 2020-06-03 2020-12-08      3.0
4           4      F    70.416175  63.036813  Commerce    60.056603   Comm&Mgmt            False                 0           63.945596   Mkt&HR  55.896563  30365.260073    True 2020-02-09 2020-09-19      3.0
5           5      F    69.901600  71.897945   Science    60.322364   Comm&Mgmt            False                 0           60.756485   Mkt&HR  76.073450  27276.141378    True 2020-01-10 2020-06-09      NaN

GaussianCopula also supports conditioning on continuous values, as long as the values are within the range of seen numbers. For example, if all the values of the dataset are within 0 and 1, GaussianCopula will not be able to set this value to 1000.

In [58]: conditions = {
   ....:     'degree_perc': 70.0
   ....: }
   ....: 

In [59]: model.sample(5, conditions=conditions)
Out[59]: 
   student_id gender  second_perc  high_perc high_spec  degree_perc degree_type  work_experience  experience_years  employability_perc mba_spec   mba_perc        salary  placed start_date   end_date duration
0           0      M    70.854837  64.929051   Science         70.0   Comm&Mgmt            False                 0           59.094458  Mkt&Fin  54.968098  21128.085804    True 2020-01-20 2020-11-13     12.0
1           1      F    66.962165  62.908323  Commerce         70.0   Comm&Mgmt            False                 0           61.398723  Mkt&Fin  66.548545  28842.472844    True 2020-01-09 2020-04-15      NaN
2           2      M    64.743250  69.962120  Commerce         70.0   Comm&Mgmt            False                 0           80.570533   Mkt&HR  58.829075           NaN   False        NaT        NaT      NaN
3           3      F    64.726267  65.862592   Science         70.0   Comm&Mgmt            False                 0           77.714509   Mkt&HR  58.418535  20799.191219    True 2020-01-03 2020-01-26      3.0
4           4      F    68.228979  66.083443   Science         70.0   Comm&Mgmt            False                 0           73.511732   Mkt&HR  57.382507  23755.939815   False 2020-02-01 2020-10-20      NaN

Note

Currently, conditional sampling works through a rejection sampling process, where rows are sampled repeatedly until one that satisfies the conditions is found. In case you are running into a Could not get enough valid rows within x trials or simply wish to optimize the results, there are three parameters that can be fine-tuned: max_rows_multiplier, max_retries and float_rtol. More information about these parameters can be found in the API section.

How do I specify constraints?

If you look closely at the data you may notice that some properties were not completely captured by the model. For example, you may have seen that sometimes the model produces an experience_years number greater than 0 while also indicating that work_experience is False. These types of properties are what we call Constraints and can also be handled using SDV. For further details about them please visit the Handling Constraints guide.

Can I evaluate the Synthetic Data?

A very common question when someone starts using SDV to generate synthetic data is: “How good is the data that I just generated?”

In order to answer this question, SDV has a collection of metrics and tools that allow you to compare the real that you provided and the synthetic data that you generated using SDV or any other tool.

You can read more about this in the Synthetic Data Evaluation guide.