# CopulaGAN Model¶

In this guide we will go through a series of steps that will let you
discover functionalities of the `CopulaGAN`

model, including how to:

Create an instance of

`CopulaGAN`

.Fit the instance to your data.

Generate synthetic versions of your data.

Use

`CopulaGAN`

to anonymize PII information.Specify the column distributions to improve the output quality.

Specify hyperparameters to improve the output quality.

## What is CopulaGAN?¶

The `sdv.tabular.CopulaGAN`

model is a variation of the CTGAN Model
which takes advantage of the CDF based transformation that the GaussianCopulas
apply to make the underlying CTGAN model task of learning the data easier.

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 `CopulaGAN`

class from SDV.

## 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.

Warning

In order to follow this guide you need to have `ctgan`

installed on
your system. If you have not done it yet, please install `ctgan`

now
by executing the command `pip install sdv`

in a terminal.

```
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 `CopulaGAN`

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.CopulaGAN`

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 CopulaGAN
In [5]: model = CopulaGAN()
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 underlying CTGANSynthesizer class 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. The number of rows (`num_rows`

)
is a required parameter.

```
In [7]: new_data = model.sample(num_rows=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 17410 M 89.27 91.42 Commerce 59.46 Comm&Mgmt False 0 84.98 Mkt&HR 60.99 94000.0 True 2020-03-07 2020-03-27 NaN
1 17477 M 57.98 59.17 Science 64.28 Comm&Mgmt True 0 92.25 Mkt&HR 76.18 30765.0 False 2020-02-29 2020-08-01 7.0
2 17447 M 48.00 94.36 Commerce 72.26 Comm&Mgmt False 0 83.32 Mkt&HR 62.78 NaN True 2020-06-30 2021-01-04 NaN
3 17469 F 65.22 93.88 Commerce 72.47 Comm&Mgmt False 2 90.76 Mkt&Fin 51.61 32504.0 True NaT NaT NaN
4 17472 M 87.00 85.04 Science 85.83 Comm&Mgmt True 0 76.50 Mkt&HR 68.94 NaN False 2020-01-24 NaT 8.0
```

Note

There are a number of other parameters in this method that you can use to
optimize the process of generating synthetic data. Use `output_file_path`

to directly write results to a CSV file, `batch_size`

to break up sampling
into smaller pieces & track their progress and `randomize_samples`

to
determine whether to generate the same synthetic data every time.
See the API section for more details.

### 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.

#### 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 `CopulaGAN.load`

method, and then you are ready to sample new
data from the loaded instance:

```
In [10]: loaded = CopulaGAN.load('my_model.pkl')
In [11]: new_data = loaded.sample(num_rows=200)
```

Warning

Notice that the system where the model is loaded needs to also have
`sdv`

and `ctgan`

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
63 17265 F 82.88 85.35 Commerce 74.84 Sci&Tech True 0 61.69 Mkt&HR 73.64 30665.0 False NaT 2020-11-26 NaN
69 17265 M 42.39 89.18 Commerce 64.89 Sci&Tech True 0 61.93 Mkt&Fin 71.85 31836.0 True NaT 2020-09-01 3.0
75 17265 M 80.41 83.13 Commerce 64.41 Sci&Tech False 0 80.70 Mkt&HR 67.78 28778.0 False NaT 2020-09-22 NaN
76 17265 F 84.32 86.02 Commerce 52.46 Comm&Mgmt False 0 85.15 Mkt&HR 71.75 31273.0 True NaT 2020-11-02 NaN
96 17265 M 48.22 97.70 Science 50.13 Comm&Mgmt True 0 85.52 Mkt&HR 66.85 NaN True NaT NaT 9.0
102 17265 M 42.90 71.33 Commerce 75.68 Comm&Mgmt True 2 96.12 Mkt&Fin 56.23 25105.0 False 2020-03-15 2020-09-14 7.0
148 17265 M 45.89 76.93 Science 82.45 Sci&Tech False 2 56.38 Mkt&Fin 75.07 28366.0 False NaT 2020-10-21 7.0
199 17265 F 48.19 92.68 Commerce 82.00 Sci&Tech False 2 97.76 Mkt&HR 64.91 27481.0 True NaT NaT 8.0
```

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 = CopulaGAN(
....: 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 72.44 68.30 Commerce 84.84 Comm&Mgmt True 0 79.07 Mkt&Fin 72.01 NaN True 2020-03-03 2020-09-20 3.0
1 1 M 61.55 52.37 Science 61.70 Comm&Mgmt True 1 64.18 Mkt&HR 55.44 NaN True NaT 2020-07-28 NaN
2 2 M 47.41 75.81 Science 76.63 Comm&Mgmt True 0 53.42 Mkt&Fin 69.07 NaN True NaT NaT 12.0
3 3 M 84.92 38.97 Commerce 86.20 Sci&Tech False 0 63.74 Mkt&Fin 73.18 NaN True NaT NaT 3.0
4 4 M 71.78 50.66 Commerce 58.58 Comm&Mgmt True 1 68.98 Mkt&Fin 69.26 21832.0 False 2020-04-05 NaT 7.0
```

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 = CopulaGAN(
....: 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 PSC 7593, Box 4710\nAPO AA 62043 M 58.76 77.32 Science 59.37 Others False 2 68.12 Mkt&HR 57.37 31208.0 True 2020-01-03 2020-09-01 4.0
1 1 82602 Wilcox Curve\nNew Angela, OR 84462 F 67.08 68.52 Arts 52.40 Comm&Mgmt True 0 85.43 Mkt&Fin 53.44 27981.0 True 2020-01-02 2020-11-15 NaN
2 2 081 Carrie Square Apt. 439\nJohnsontown, NM 66991 F 71.89 85.91 Commerce 82.08 Comm&Mgmt False 2 65.68 Mkt&Fin 51.50 NaN True 2020-02-27 NaT 5.0
3 3 1825 Miles Ridge Suite 106\nPort Stephanieland... F 52.54 61.52 Commerce 50.66 Comm&Mgmt False 0 84.32 Mkt&Fin 51.25 23731.0 True NaT 2020-10-12 5.0
4 4 96493 Kelly Canyon Apt. 145\nEast Steven, NC 3... F 69.25 72.47 Science 78.30 Sci&Tech False 2 59.87 Mkt&Fin 63.01 63205.0 True 2020-01-03 2020-08-05 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 address, we will pass a
dictionary indicating the category `address`

```
In [26]: model = CopulaGAN(
....: 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 that were not taken from the real data
that we learned.

```
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 49133 Michael Vista\nNew Nicoleview, IL 35362 F 68.41 85.56 Science 52.75 Sci&Tech True 0 51.90 Mkt&Fin 51.34 NaN True 2020-03-02 2020-08-20 NaN
1 1 4293 Lewis Valley\nPeterview, FL 95797 M 47.61 96.90 Science 50.16 Comm&Mgmt False 1 50.47 Mkt&HR 54.81 31351.0 False NaT NaT 3.0
2 2 7190 Kyle Village\nSouth Robertland, WA 68985 M 89.36 63.79 Science 69.53 Sci&Tech False 0 53.30 Mkt&Fin 76.66 29180.0 False 2020-04-02 2020-09-26 NaN
3 3 8898 Johnson Centers\nPort Michaelchester, MT ... M 70.52 51.72 Commerce 50.30 Comm&Mgmt True 2 81.42 Mkt&HR 64.88 NaN True NaT NaT 4.0
4 4 446 Sean Oval\nVictoriabury, PA 97366 M 48.81 96.05 Commerce 53.59 Sci&Tech False 1 50.83 Mkt&Fin 72.58 55092.0 False NaT 2020-12-14 NaN
```

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 `CopulaGAN`

Model in order to customize it to our needs.

### Exploring the Probability Distributions¶

During the previous steps, every time we fitted the `CopulaGAN`

it performed the following operations:

Learn the format and data types of the passed data

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.

Learn the probability distribution of each column from the table

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.

Fit a CTGAN model on the transformed data, which learns how each column is correlated to the others.

After this, when we used the model to generate new data for our table
using the `sample`

method, it did:

Sample rows from the CTGAN model.

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

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 `CopulaGAN`

had to learn and reproduce the individual distributions of each column
in our table. We can explore the distributions which the
`CopulaGAN`

used to model each column using its
`get_distributions`

method:

```
In [31]: model = CopulaGAN(
....: primary_key='student_id',
....: enforce_min_max_values=False
....: )
....:
In [32]: model.fit(data)
In [33]: distributions = model.get_distributions()
```

This will return us a `dict`

which contains the name of the
distribution class used for each column:

```
In [34]: distributions
Out[34]:
{'second_perc.value': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
'high_perc.value': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
'degree_perc.value': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
'work_experience.value': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
'experience_years.value': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
'employability_perc.value': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
'mba_perc.value': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
'salary.value': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
'placed.value': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
'start_date.value': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
'end_date.value': 'copulas.univariate.truncated_gaussian.TruncatedGaussian',
'duration.value': 'copulas.univariate.truncated_gaussian.TruncatedGaussian'}
```

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 `CopulaGAN`

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 [35]: data.experience_years.value_counts()
Out[35]:
0 141
1 65
2 8
3 1
Name: experience_years, dtype: int64
In [36]: data.experience_years.hist();
```

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 `CopulaGAN`

able to capture this distribution on its own?

```
In [37]: distributions['experience_years.value']
Out[37]: 'copulas.univariate.truncated_gaussian.TruncatedGaussian'
```

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 [38]: new_data.experience_years.value_counts()
Out[38]:
0 164
1 26
2 9
3 1
Name: experience_years, dtype: int64
In [39]: new_data.experience_years.hist();
```

Let’s see how we can improve this situation by passing the
`CopulaGAN`

the exact distribution that we want it to use for
this column.

### Setting distributions for indvidual variables¶

The `CopulaGAN`

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:

`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 `CopulaGAN`

use the
`gamma`

distribution for our column.

```
In [40]: model = CopulaGAN(
....: primary_key='student_id',
....: field_distributions={
....: 'experience_years': 'gamma'
....: },
....: enforce_min_max_values=False
....: )
....:
In [41]: model.fit(data)
```

After this, we can see how the `CopulaGAN`

used the indicated
distribution for the `experience_years`

column

```
In [42]: model.get_distributions()['experience_years.value']
Out[42]: '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 [43]: new_data = model.sample(len(data))
In [44]: new_data.experience_years.value_counts()
Out[44]:
0 196
1 12
2 6
4 1
Name: experience_years, dtype: int64
In [45]: new_data.experience_years.hist();
```

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
`CopulaGAN`

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 to modify the CopulaGAN Hyperparameters?¶

A part from the arguments explained above, `CopulaGAN`

has a number
of additional hyperparameters that control its learning behavior and can
impact on the performance of the model, both in terms of quality of the
generated data and computational time:

`epochs`

and`batch_size`

: these arguments control the number of iterations that the model will perform to optimize its parameters, as well as the number of samples used in each step. Its default values are`300`

and`500`

respectively, and`batch_size`

needs to always be a value which is multiple of`10`

.These hyperparameters have a very direct effect in time the training process lasts but also on the performance of the data, so for new datasets, you might want to start by setting a low value on both of them to see how long the training process takes on your data and later on increase the number to acceptable values in order to improve the performance.

`log_frequency`

: Whether to use log frequency of categorical levels in conditional sampling. It defaults to`True`

. This argument affects how the model processes the frequencies of the categorical values that are used to condition the rest of the values. In some cases, changing it to`False`

could lead to better performance.`embedding_dim`

(int): Size of the random sample passed to the Generator. Defaults to 128.`generator_dim`

(tuple or list of ints): Size of the output samples for each one of the Residuals. A Resiudal Layer will be created for each one of the values provided. Defaults to (256, 256).`discriminator_dim`

(tuple or list of ints): Size of the output samples for each one of the Discriminator Layers. A Linear Layer will be created for each one of the values provided. Defaults to (256, 256).`generator_lr`

(float): Learning rate for the generator. Defaults to 2e-4.`generator_decay`

(float): Generator weight decay for the Adam Optimizer. Defaults to 1e-6.`discriminator_lr`

(float): Learning rate for the discriminator. Defaults to 2e-4.`discriminator_decay`

(float): Discriminator weight decay for the Adam Optimizer. Defaults to 1e-6.`discriminator_steps`

(int): Number of discriminator updates to do for each generator update. From the WGAN paper: https://arxiv.org/abs/1701.07875. WGAN paper default is 5. Default used is 1 to match original CTGAN implementation.`verbose`

: Whether to print fit progress on stdout. Defaults to`False`

.

Warning

Notice that the value that you set on the `batch_size`

argument must always be a
multiple of `10`

!

As an example, we will try to fit the `CopulaGAN`

model slightly
increasing the number of epochs, reducing the `batch_size`

, adding one
additional layer to the models involved and using a smaller wright
decay.

Before we start, we will evaluate the quality of the previously
generated data using the `sdv.evaluation.evaluate`

function

```
In [46]: from sdv.evaluation import evaluate
In [47]: evaluate(new_data, data)
Out[47]: 0.7774445193564621
```

Afterwards, we create a new instance of the `CopulaGAN`

model with the
hyperparameter values that we want to use

```
In [48]: model = CopulaGAN(
....: primary_key='student_id',
....: epochs=500,
....: batch_size=100,
....: generator_dim=(256, 256, 256),
....: discriminator_dim=(256, 256, 256)
....: )
....:
```

And fit to our data.

```
In [49]: model.fit(data)
```

Finally, we are ready to generate new data and evaluate the results.

```
In [50]: new_data = model.sample(len(data))
In [51]: evaluate(new_data, data)
Out[51]: 0.7897384046786191
```

As we can see, in this case these modifications changed the obtained results slightly, but they did neither introduce dramatic changes in the performance.

### Conditional Sampling¶

As the name implies, conditional sampling allows us to sample from a conditional
distribution using the `CopulaGAN`

model, which means we can generate only values that
satisfy certain conditions. These conditional values can be passed to the `sample_conditions`

method as a list of `sdv.sampling.Condition`

objects or to the `sample_remaining_columns`

method
as a dataframe.

When specifying a `sdv.sampling.Condition`

object, we can pass in the desired conditions
as a dictionary, as well as specify the number of desired rows for that condition.

```
In [52]: from sdv.sampling import Condition
In [53]: condition = Condition({
....: 'gender': 'M'
....: }, num_rows=5)
....:
In [54]: model.sample_conditions(conditions=[condition])
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 1 M 78.70 83.45 Commerce 89.89 Comm&Mgmt True 0 94.28 Mkt&Fin 55.88 26584.0 True 2020-02-20 2020-12-13 3.0
1 2 M 88.35 97.63 Commerce 59.51 Comm&Mgmt False 0 73.01 Mkt&Fin 62.20 54350.0 True 2020-07-19 2020-09-17 3.0
2 3 M 60.19 60.96 Science 52.32 Comm&Mgmt False 0 86.30 Mkt&Fin 51.27 NaN True 2020-02-03 2020-04-08 6.0
3 4 M 88.86 88.88 Commerce 89.60 Comm&Mgmt True 2 97.68 Mkt&Fin 64.48 43884.0 True 2020-01-11 2020-11-30 3.0
4 0 M 64.11 59.36 Commerce 69.02 Comm&Mgmt False 0 63.61 Mkt&Fin 54.64 NaN False NaT NaT 3.0
```

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

.

```
In [55]: condition = Condition({
....: 'gender': 'M',
....: 'experience_years': 0
....: }, num_rows=5)
....:
In [56]: model.sample_conditions(conditions=[condition])
Out[56]:
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 89.10 97.61 Science 89.88 Comm&Mgmt False 0 79.59 Mkt&Fin 52.18 21224.0 True 2020-01-19 2020-12-01 3.0
1 4 M 42.61 70.29 Science 58.74 Others False 0 62.72 Mkt&Fin 51.60 NaN False NaT 2021-01-27 7.0
2 3 M 73.11 97.46 Science 51.18 Sci&Tech False 0 52.47 Mkt&HR 53.22 NaN True 2020-01-04 2020-06-18 9.0
3 5 M 46.54 65.18 Science 50.10 Comm&Mgmt False 0 92.45 Mkt&Fin 51.27 39298.0 True 2020-03-31 NaT 3.0
4 6 M 41.02 58.98 Science 51.37 Sci&Tech False 0 95.94 Mkt&HR 52.93 NaN True NaT NaT NaN
```

In the `sample_remaining_columns`

method, `conditions`

is
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 [57]: import pandas as pd
In [58]: conditions = pd.DataFrame({
....: 'gender': ['M', 'M', 'M', 'F', 'F', 'F'],
....: })
....:
In [59]: model.sample_remaining_columns(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 52.03 70.84 Commerce 62.09 Sci&Tech False 0 71.53 Mkt&Fin 53.93 32005.0 True 2020-03-29 2020-11-10 3.0
1 1 M 56.71 81.15 Science 50.97 Comm&Mgmt False 0 80.12 Mkt&Fin 71.63 66619.0 True NaT 2020-06-05 3.0
2 2 M 77.34 78.73 Science 86.64 Comm&Mgmt True 1 97.73 Mkt&Fin 51.97 31637.0 True 2020-01-09 2020-03-21 3.0
3 3 F 61.40 89.21 Science 59.59 Comm&Mgmt True 0 74.46 Mkt&HR 52.70 47971.0 False 2020-01-02 NaT 3.0
4 4 F 43.09 58.79 Commerce 52.41 Others False 0 57.44 Mkt&Fin 60.49 NaN True 2020-03-18 NaT 3.0
5 5 F 40.93 38.20 Commerce 50.46 Sci&Tech False 3 64.81 Mkt&HR 53.80 NaN False NaT NaT NaN
```

`CopulaGAN`

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, `CopulaGAN`

will not be able to set this value to 1000.

```
In [60]: condition = Condition({
....: 'degree_perc': 70.0
....: }, num_rows=5)
....:
In [61]: model.sample_conditions(conditions=[condition])
Out[61]:
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 41.17 57.37 Commerce 70.0 Others False 0 70.85 Mkt&Fin 52.84 NaN True NaT NaT 5.0
1 45 M 43.06 42.15 Science 70.0 Comm&Mgmt False 0 82.48 Mkt&HR 51.33 NaN False NaT NaT 3.0
2 28 M 84.27 97.59 Commerce 70.0 Comm&Mgmt False 1 97.96 Mkt&Fin 51.38 31524.0 True 2020-01-12 2020-06-23 8.0
3 4 F 75.51 97.52 Commerce 70.0 Sci&Tech True 0 97.84 Mkt&Fin 61.11 50561.0 True 2020-03-13 2020-08-15 3.0
4 19 M 43.79 73.01 Arts 70.0 Others False 0 77.58 Mkt&HR 51.26 NaN False NaT NaT 7.0
```

Note

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 not able to sample enough valid rows, try increasing `max_tries_per_batch`

.
More information about this parameter can be found in the API section

If you have many conditions that cannot easily be satisified, consider switching to the GaussianCopula model, which is able to handle conditional sampling more efficiently.

### 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 Constraints guide.

### Can I evaluate the Synthetic Data?¶

After creating synthetic data, you may be wondering how you can evaluate it against the original data. You can use the SDMetrics library to get more insights, generate reports and visualize the data. This library is automatically installed with SDV.

To get started, visit: https://docs.sdv.dev/sdmetrics/