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 where 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 de 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       17282      F    54.057732  68.584176  Commerce    66.490451   Comm&Mgmt            False                 0           50.921242   Mkt&HR  69.645173           NaN   False        NaT        NaT      NaN
1       17308      M    67.345834  72.586157   Science    69.852494   Comm&Mgmt            False                 1           63.240320  Mkt&Fin  61.042446  36065.342006    True 2020-04-06 2020-09-06      NaN
2       17316      F    79.645312  66.519094  Commerce    63.982310   Comm&Mgmt            False                 0           69.576170  Mkt&Fin  64.060420           NaN   False        NaT        NaT      NaN
3       17458      M    69.426677  68.176061   Science    71.263378    Sci&Tech            False                 0           96.852504   Mkt&HR  72.088149           NaN   False        NaT        NaT      NaN
4       17434      F    58.184740  43.575439   Science    68.543089    Sci&Tech            False                 0           71.986625   Mkt&HR  63.674287  40305.683531    True 2020-06-06 2021-01-16      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 send 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 that 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
41        17336      M    42.442340  38.875348   Science    62.362595    Sci&Tech            False                 1           73.901829   Mkt&HR  66.479228           NaN   False        NaT        NaT      NaN
48        17336      M    42.299378  57.320233  Commerce    50.495833   Comm&Mgmt            False                 0           73.486839  Mkt&Fin  55.124839           NaN   False        NaT        NaT      NaN
144       17336      M    64.750529  68.084270  Commerce    66.823206   Comm&Mgmt            False                 0           70.767517  Mkt&Fin  58.308139  29738.979230    True 2020-01-02 2020-08-21     12.0
167       17336      M    69.040436  69.688228  Commerce    70.153060   Comm&Mgmt            False                 0           93.427932  Mkt&Fin  57.200612  24930.981477    True 2020-04-18 2020-11-15      3.0
180       17336      M    74.335722  72.712466  Commerce    69.578679   Comm&Mgmt            False                -1           78.716761  Mkt&Fin  70.772008           NaN   False        NaT        NaT      NaN

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      F    81.147206  69.025892  Commerce    74.218032   Comm&Mgmt            False                 1           71.225761  Mkt&Fin  58.916194  22824.855078    True 2020-02-01 2020-08-23      3.0
1           1      M    49.923980  59.706875  Commerce    60.548911   Comm&Mgmt            False                 1           88.759124  Mkt&Fin  59.054274           NaN   False        NaT        NaT      NaN
2           2      M    65.306580  88.280591  Commerce    69.508106   Comm&Mgmt            False                 0           62.705200  Mkt&Fin  68.960101           NaN   False        NaT        NaT      NaN
3           3      M    70.583023  82.024244  Commerce    85.222373   Comm&Mgmt            False                 1           81.973128  Mkt&Fin  64.900636  29767.513528    True 2020-01-04 2020-10-22     12.0
4           4      M    49.632334  56.080607  Commerce    55.207576   Comm&Mgmt            False                 0           86.446114  Mkt&Fin  56.117058           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      42261 Booth Shores\nNorth Pattyfurt, UT 01028      M    71.246565  81.676326   Science    70.151344   Comm&Mgmt            False                 0           78.030102  Mkt&Fin  61.328618  27185.552731    True 2020-01-05 2020-08-04     12.0
1           1  016 Jessica Brooks Suite 606\nPort Laura, PA 9...      F    55.329087  44.357159   Science    55.174708   Comm&Mgmt            False                -1           52.834434   Mkt&HR  59.582693           NaN   False        NaT        NaT      NaN
2           2  767 Katherine Turnpike Apt. 168\nPort Makaylav...      F    86.988671  61.968473  Commerce    65.013788    Sci&Tech            False                 0           83.678584   Mkt&HR  65.908388           NaN   False        NaT        NaT      3.0
3           3  69071 Andrew Center Suite 067\nDavisborough, M...      F    73.384796  64.571568  Commerce    80.573059    Sci&Tech            False                 1           77.199957  Mkt&Fin  64.441407  26602.610409    True 2020-02-21 2020-07-26      NaN
4           4  016 Jessica Brooks Suite 606\nPort Laura, PA 9...      M    80.287562  82.042609  Commerce    68.615201   Comm&Mgmt            False                 1           68.036013  Mkt&Fin  65.141865  33288.622911    True 2020-01-22 2020-07-24      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             81034 Clark Isle\nLeslieview, SC 11385      F    69.009869  62.909948   Science    65.927447    Sci&Tech            False                 0           53.818861   Mkt&HR  58.925324  25834.636389    True 2020-02-26 2021-01-08     12.0
1           1  755 Christopher Island Apt. 051\nJosephtown, H...      M    44.938365  51.124611  Commerce    55.666013   Comm&Mgmt            False                 0           60.504901  Mkt&Fin  51.082852           NaN   False        NaT        NaT     12.0
2           2   293 Wallace Crossing\nPort Natashastad, PA 15478      M    63.346698  68.669647  Commerce    75.192934   Comm&Mgmt            False                 0           73.947258   Mkt&HR  59.267727  24126.248914    True 2020-04-17 2020-10-10      3.0
3           3  6614 Martin Groves Apt. 468\nWest Ryanchester,...      F    63.915496  58.176032   Science    70.261259   Comm&Mgmt            False                 0           68.245102   Mkt&HR  60.844484           NaN   False        NaT        NaT      NaN
4           4    06507 Meyer Trail Apt. 906\nPort Sean, KS 59510      F    69.779434  65.120852  Commerce    64.328885   Comm&Mgmt            False                 1           56.639520  Mkt&Fin  61.525441  31928.197725    True 2020-01-01 2020-08-08     12.0

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 little 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  5173 Benjamin Mews Suite 195\nStevenport, OH 7...      M    66.774055  73.187702  Commerce    65.815417    Sci&Tech            False                 0           61.148303   Mkt&HR  76.226419           NaN   False        NaT        NaT      NaN
1           1  8465 Brandon Turnpike Apt. 676\nLake William, ...      M    60.285327  76.507468  Commerce    74.297326   Comm&Mgmt            False                 0           58.075833   Mkt&HR  58.173966  19736.455902    True 2020-04-22 2020-10-16      3.0
2           2  323 Valencia Stravenue Apt. 978\nScotttown, MO...      M    66.664759  62.057133  Commerce    81.243537   Comm&Mgmt            False                 0           77.968381  Mkt&Fin  67.182386  24385.924135    True 2020-01-08 2020-06-17     12.0
3           3               3339 David Mill\nMarkhaven, AL 47981      M    74.708049  58.479533   Science    75.715576   Comm&Mgmt            False                 0           84.146207  Mkt&Fin  54.099369  39936.419792    True 2020-01-17 2020-08-21      3.0
4           4            9492 Fisher Dam\nWest Coryton, PA 37004      M    59.876514  52.942172  Commerce    61.944679   Comm&Mgmt            False                 0           92.175229  Mkt&Fin  63.246135           NaN   False        NaT        NaT      NaN

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]: 
{'gender#0': 'copulas.univariate.gaussian.GaussianUnivariate',
 'gender#1': 'copulas.univariate.gaussian.GaussianUnivariate',
 'second_perc': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
 'high_perc': 'copulas.univariate.log_laplace.LogLaplace',
 'high_spec#0': 'copulas.univariate.gaussian.GaussianUnivariate',
 'high_spec#1': 'copulas.univariate.gamma.GammaUnivariate',
 'high_spec#2': 'copulas.univariate.gaussian.GaussianUnivariate',
 'degree_perc': 'copulas.univariate.student_t.StudentTUnivariate',
 'degree_type#0': 'copulas.univariate.student_t.StudentTUnivariate',
 'degree_type#1': 'copulas.univariate.gaussian.GaussianUnivariate',
 'degree_type#2': 'copulas.univariate.gaussian.GaussianUnivariate',
 'work_experience': 'copulas.univariate.student_t.StudentTUnivariate',
 'experience_years': 'copulas.univariate.gaussian.GaussianUnivariate',
 'employability_perc': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
 'mba_spec#0': 'copulas.univariate.gamma.GammaUnivariate',
 'mba_spec#1': 'copulas.univariate.gaussian.GaussianUnivariate',
 'mba_perc': 'copulas.univariate.gamma.GammaUnivariate',
 'salary#0': 'copulas.univariate.gamma.GammaUnivariate',
 'salary#1': 'copulas.univariate.gaussian.GaussianUnivariate',
 'placed': 'copulas.univariate.gamma.GammaUnivariate',
 '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 the 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    101
 1     82
-1      9
 2      8
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, now 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    193
1     21
2      1
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 show 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.

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 type 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.