# 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 17318 M 67.459231 65.363306 Commerce 69.221815 Sci&Tech False -1 88.318099 Mkt&Fin 55.142590 25312.729020 True 2020-03-19 2020-05-31 3.0
1 17336 M 57.673583 73.769039 Science 66.708695 Sci&Tech False 0 85.591060 Mkt&HR 64.612023 NaN False NaT NaT NaN
2 17354 M 71.681980 70.601270 Science 73.835648 Sci&Tech False 0 85.081901 Mkt&HR 57.454183 25266.125322 True 2020-01-10 2020-07-22 3.0
3 17275 F 69.000231 64.075265 Commerce 65.854598 Comm&Mgmt False 0 52.404010 Mkt&HR 63.436819 NaN False NaT NaT NaN
4 17409 F 69.481804 68.210630 Commerce 63.749937 Comm&Mgmt False 1 61.895119 Mkt&Fin 53.905013 NaN False NaT NaT NaN
```

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.

#### 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.student_id.value_counts().max()
Out[13]: 5
In [14]: new_data[new_data.student_id == new_data.student_id.value_counts().index[0]]
Out[14]:
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
16 17359 M 79.619434 66.226971 Science 67.986712 Sci&Tech False -1 85.443593 Mkt&HR 58.242021 26896.458429 True 2020-02-08 2020-07-31 3.0
115 17359 M 76.305570 65.143614 Arts 62.494661 Others False 1 69.815086 Mkt&HR 65.939695 33265.060575 True 2020-02-13 2020-08-12 3.0
183 17359 M 69.434039 87.307529 Commerce 62.730293 Comm&Mgmt False 1 95.291322 Mkt&Fin 53.575568 20896.410321 True 2020-01-07 2020-09-07 12.0
184 17359 M 68.640793 65.518870 Science 57.740421 Comm&Mgmt False 1 92.279683 Mkt&HR 56.329927 30311.819960 True 2020-06-20 2020-12-31 3.0
193 17359 M 80.749196 65.087871 Science 59.466241 Sci&Tech False -1 56.692914 Mkt&Fin 60.181241 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 [15]: model = GaussianCopula(
....: primary_key='student_id'
....: )
....:
In [16]: model.fit(data)
In [17]: new_data = model.sample(200)
```

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.head()
Out[18]:
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 65.769739 65.660682 Commerce 66.923137 Comm&Mgmt False 0 73.237954 Mkt&Fin 56.375117 NaN False NaT NaT NaN
1 1 M 79.045326 64.792590 Science 68.110822 Sci&Tech False 0 87.929210 Mkt&Fin 64.337442 38089.306364 True 2020-01-06 2020-07-01 3.0
2 2 M 87.970588 93.169796 Science 62.977060 Sci&Tech False 1 82.628143 Mkt&Fin 62.849870 27343.184263 True 2020-03-01 2020-07-03 3.0
3 3 F 59.705723 64.773057 Commerce 66.078467 Comm&Mgmt False 0 77.345172 Mkt&Fin 64.707108 NaN False NaT NaT NaN
4 4 M 66.405494 64.624800 Commerce 66.003635 Comm&Mgmt False 0 65.889526 Mkt&HR 52.926746 NaN False NaT NaT NaN
In [19]: new_data.student_id.value_counts().max()
Out[19]: 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 [20]: data_pii = load_tabular_demo('student_placements_pii')
In [21]: data_pii.head()
Out[21]:
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 [22]: model = GaussianCopula(
....: primary_key='student_id',
....: )
....:
In [23]: model.fit(data_pii)
In [24]: new_data_pii = model.sample(200)
In [25]: new_data_pii.head()
Out[25]:
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 51290 Escobar Place\nSouth Madison, WI 89087 F 85.872486 78.005584 Science 78.750209 Comm&Mgmt False 1 56.639883 Mkt&HR 66.232675 31977.260634 True 2020-01-18 2020-09-17 3.0
1 1 16569 Koch Throughway\nPort Christopher, NM 46073 F 41.609433 38.047520 Commerce 55.082567 Comm&Mgmt False 1 58.534410 Mkt&HR 60.243543 NaN False NaT NaT NaN
2 2 PSC 7593, Box 4710\nAPO AA 62043 F 58.873829 70.304011 Commerce 69.751384 Comm&Mgmt False 0 82.117047 Mkt&Fin 64.127385 19738.986121 False 2020-01-02 2020-09-05 NaN
3 3 01921 Jackson Gardens Apt. 637\nDanielberg, OH... M 52.992688 64.899634 Science 66.102530 Sci&Tech False 0 64.430379 Mkt&HR 52.806471 NaN False NaT NaT NaN
4 4 21119 Bailey Mall Apt. 215\nCameronbury, GA 31205 M 42.013406 53.713977 Commerce 58.294853 Comm&Mgmt False 1 65.756823 Mkt&HR 55.173724 NaN False NaT NaT NaN
In [26]: new_data_pii.address.isin(data_pii.address).sum()
Out[26]: 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 [27]: model = GaussianCopula(
....: primary_key='student_id',
....: anonymize_fields={
....: 'address': 'address'
....: }
....: )
....:
In [28]: 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 [29]: new_data_pii = model.sample(200)
In [30]: new_data_pii.head()
Out[30]:
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 20574 Clark Loop\nLambside, VA 69537 M 80.681042 67.758259 Science 63.728880 Comm&Mgmt False 0 84.322268 Mkt&Fin 56.842827 25309.888805 True 2020-01-08 2020-10-15 12.0
1 1 008 Villanueva Radial\nWest Stevenmouth, OH 37507 M 68.906144 71.699329 Science 65.097049 Comm&Mgmt False 0 85.519603 Mkt&HR 67.350349 34367.434126 True 2020-05-01 2020-10-09 3.0
2 2 1958 Donna Stravenue\nSouth Kathyshire, NM 05485 M 63.670652 62.329728 Science 69.668128 Sci&Tech False 1 65.640111 Mkt&Fin 57.449744 21414.278457 True 2020-01-27 2020-10-10 3.0
3 3 USNV King\nFPO AA 69232 M 57.500631 49.887246 Science 61.399632 Comm&Mgmt False -1 65.430851 Mkt&Fin 53.379204 32104.657437 True 2020-01-20 2020-04-10 3.0
4 4 886 Grant Light\nPort Debbieport, WY 61384 M 55.893734 90.539365 Commerce 70.290758 Comm&Mgmt False -1 70.701578 Mkt&Fin 61.806672 29755.122881 True 2020-05-03 2020-10-22 3.0
In [31]: new_data_pii.address.isin(data_pii.address).sum()
Out[31]: 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 [32]: model = GaussianCopula(
....: primary_key='student_id',
....: anonymize_fields={
....: 'address': 'address'
....: },
....: field_transformers={
....: 'address': 'label_encoding'
....: }
....: )
....:
In [33]: model.fit(data_pii)
In [34]: new_data_pii = model.sample(200)
In [35]: new_data_pii.head()
Out[35]:
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 8320 Box 0974\nDPO AA 46029 M 61.638703 50.037470 Commerce 58.012356 Sci&Tech False 1 90.650590 Mkt&Fin 63.713748 NaN False NaT NaT NaN
1 1 01232 Matthew Creek\nNew Brian, WA 31672 M 68.454324 65.829807 Commerce 73.995860 Comm&Mgmt False 0 56.693998 Mkt&Fin 52.447181 31265.741492 True 2020-01-13 2020-05-05 3.0
2 2 5838 Johnson Lane Apt. 641\nWalkerchester, NM ... M 86.271561 79.116082 Science 65.535684 Sci&Tech False 1 94.951123 Mkt&Fin 69.351926 36748.016175 True 2020-01-18 2020-08-09 3.0
3 3 64485 Jones Island\nEast Samantha, RI 48952 M 79.923358 76.355261 Commerce 76.174380 Comm&Mgmt False 1 73.834702 Mkt&Fin 64.890534 24340.764918 True 2020-02-23 2020-04-14 3.0
4 4 712 Matthews Spring Suite 218\nLake Brandyview... F 77.209967 64.890306 Commerce 73.290472 Comm&Mgmt False 0 87.373672 Mkt&Fin 68.413053 NaN False NaT NaT NaN
```

### Exploring the Probability Distributions¶

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

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.

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:

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

Revert the sampled values by computing their standard normal CDF and then applyting 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 `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 [36]: model = GaussianCopula(
....: primary_key='student_id'
....: )
....:
In [37]: model.fit(data)
In [38]: distributions = model.get_distributions()
```

This will return us a `dict`

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

```
In [39]: distributions
Out[39]:
{'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 [40]: data.experience_years.value_counts()
Out[40]:
0 141
1 65
2 8
3 1
Name: experience_years, dtype: int64
In [41]: 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 `GaussianCopula`

able to capture this distribution on its own?

```
In [42]: distributions['experience_years']
Out[42]: '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 [43]: new_data.experience_years.value_counts()
Out[43]:
0 99
1 77
-1 19
2 5
Name: experience_years, dtype: int64
In [44]: new_data.experience_years.hist();
```

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 indvidual 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 `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.`gussian_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 [45]: from sdv.tabular import GaussianCopula
In [46]: model = GaussianCopula(
....: primary_key='student_id',
....: distribution={
....: 'experience_years': 'gamma'
....: }
....: )
....:
In [47]: model.fit(data)
```

After this, we can see how the `GaussianCopula`

used the indicated
distribution for the `experience_years`

column

```
In [48]: model.get_distributions()['experience_years']
Out[48]: '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 [49]: new_data = model.sample(len(data))
In [50]: new_data.experience_years.value_counts()
Out[50]:
0 198
1 16
6 1
Name: experience_years, dtype: int64
In [51]: 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
`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 Evaluating Synthetic Data guide.