# GaussianCopula Model¶

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

model, including how
to:

Create an instance of a

`GaussianCopula`

.Fit the instance to your data.

Generate synthetic versions of your data.

Use

`GaussianCopula`

to anonymize PII information.Customize the data transformations to improve the learning process.

Specify the column distributions to improve the output quality.

## What is GaussianCopula?¶

The `sdv.tabular.GaussianCopula`

model is based on
copula funtions.

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

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

model.

## Quick Usage¶

We will start by loading one of our demo datasets, the
`student_placements`

, which contains information about MBA students
that applied for placements during the year 2020.

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

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

Their id and gender

Their grades and specializations

Their work experience

The salary that they were offered

The duration and dates of their placement

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

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

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

Let us use the `GaussianCopula`

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

Import the

`sdv.tabular.GaussianCopula`

class and create an instance of it.Call its

`fit`

method passing our table.Call its

`sample`

method indicating the number of synthetic rows that you want to generate.

```
In [4]: from sdv.tabular import GaussianCopula
In [5]: model = GaussianCopula()
In [6]: model.fit(data)
```

Note

Notice that the model `fitting`

process took care of transforming the
different fields using the appropriate Reversible Data
Transforms to ensure that the data
has a format that the `GaussianMultivariate`

model can handle.

### Generate synthetic data from the model¶

Once the modeling has finished you are ready to generate new synthetic
data by calling the `sample`

method from your model passing the number
of rows that we want to generate.

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

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

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

Note

You can control the number of rows by specifying the number of
`samples`

in the `model.sample(<num_rows>)`

. To test, try
`model.sample(10000)`

. Note that the original table only had ~200
rows.

### Save and Load the model¶

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

from it.

Let’s see how this process works.

#### Load the model and generate new data¶

The file you just generated can be sent over to the system where the
synthetic data will be generated. Once it is there, you can load it
using the `GaussianCopula.load`

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

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

Warning

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

installed, otherwise it will not be able to load the model and
use it.

### Specifying the Primary Key of the table¶

One of the first things that you may have noticed when looking at the demo
data is that there is a `student_id`

column which acts as the primary
key of the table, and which is supposed to have unique values. Indeed,
if we look at the number of times that each value appears, we see that
all of them appear at most once:

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

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

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

This happens because the model was not notified at any point about the
fact that the `student_id`

had to be unique, so when it generates new
data it will provoke collisions sooner or later. In order to solve this,
we can pass the argument `primary_key`

to our model when we create it,
indicating the name of the column that is the index of the table.

```
In [14]: model = GaussianCopula(
....: primary_key='student_id'
....: )
....:
In [15]: model.fit(data)
In [16]: new_data = model.sample(200)
In [17]: new_data.head()
Out[17]:
student_id gender second_perc high_perc high_spec degree_perc degree_type work_experience experience_years employability_perc mba_spec mba_perc salary placed start_date end_date duration
0 0 M 61.916813 67.128159 Commerce 62.174657 Comm&Mgmt False 0 80.625020 Mkt&Fin 63.140435 32761.012958 True 2020-02-11 2020-08-24 12.0
1 1 M 72.314817 84.230085 Commerce 67.307607 Comm&Mgmt False 1 86.392786 Mkt&Fin 71.948674 27656.562043 True 2020-02-04 2020-08-24 3.0
2 2 M 84.745332 71.180452 Science 71.889331 Sci&Tech False 0 54.779427 Mkt&Fin 70.355750 NaN False NaT NaT NaN
3 3 M 55.229688 57.048697 Commerce 49.239246 Comm&Mgmt False 1 62.714429 Mkt&HR 55.396712 NaN False NaT NaT NaN
4 4 F 48.038052 49.056623 Commerce 52.901254 Comm&Mgmt False 0 79.342439 Mkt&HR 53.274493 NaN False NaT NaT NaN
```

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

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

### Anonymizing Personally Identifiable Information (PII)¶

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

Let’s load a new dataset that contains a PII field, the
`student_placements_pii`

demo, and try to generate synthetic versions
of it that do not contain any of the PII fields.

Note

The `student_placements_pii`

dataset is a modified version of the
`student_placements`

dataset with one new field, `address`

, which
contains PII information about the students. Notice that this additional
`address`

field has been simulated and does not correspond to data
from the real users.

```
In [19]: data_pii = load_tabular_demo('student_placements_pii')
In [20]: data_pii.head()
Out[20]:
student_id address gender second_perc high_perc high_spec degree_perc degree_type work_experience experience_years employability_perc mba_spec mba_perc salary placed start_date end_date duration
0 17264 70304 Baker Turnpike\nEricborough, MS 15086 M 67.00 91.00 Commerce 58.00 Sci&Tech False 0 55.0 Mkt&HR 58.80 27000.0 True 2020-07-23 2020-10-12 3.0
1 17265 805 Herrera Avenue Apt. 134\nMaryview, NJ 36510 M 79.33 78.33 Science 77.48 Sci&Tech True 1 86.5 Mkt&Fin 66.28 20000.0 True 2020-01-11 2020-04-09 3.0
2 17266 3702 Bradley Island\nNorth Victor, FL 12268 M 65.00 68.00 Arts 64.00 Comm&Mgmt False 0 75.0 Mkt&Fin 57.80 25000.0 True 2020-01-26 2020-07-13 6.0
3 17267 Unit 0879 Box 3878\nDPO AP 42663 M 56.00 52.00 Science 52.00 Sci&Tech False 0 66.0 Mkt&HR 59.43 NaN False NaT NaT NaN
4 17268 96493 Kelly Canyon Apt. 145\nEast Steven, NC 3... M 85.80 73.60 Commerce 73.30 Comm&Mgmt False 0 96.8 Mkt&Fin 55.50 42500.0 True 2020-07-04 2020-09-27 3.0
```

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

```
In [21]: model = GaussianCopula(
....: primary_key='student_id',
....: )
....:
In [22]: model.fit(data_pii)
In [23]: new_data_pii = model.sample(200)
In [24]: new_data_pii.head()
Out[24]:
student_id address gender second_perc high_perc high_spec degree_perc degree_type work_experience experience_years employability_perc mba_spec mba_perc salary placed start_date end_date duration
0 0 Unit 3091 Box 7338\nDPO AP 23696 M 49.989625 37.268740 Science 55.228111 Sci&Tech False 1 77.571994 Mkt&HR 63.043014 NaN False NaT NaT NaN
1 1 39392 Dodson Club\nYoungberg, SC 75263 F 75.985240 66.897008 Science 77.166625 Sci&Tech False 1 76.142784 Mkt&Fin 65.388418 22550.807273 True 2020-01-17 2020-07-30 NaN
2 2 526 Patricia Parks\nMccoyport, DC 77793 M 44.575775 61.812223 Commerce 48.892362 Comm&Mgmt False 0 75.621465 Mkt&HR 50.130206 NaN False NaT NaT NaN
3 3 90563 Charles Road\nSouth Melinda, MA 00878 F 64.458887 67.186594 Commerce 75.001889 Comm&Mgmt False 0 59.264294 Mkt&Fin 61.248955 NaN False NaT NaT NaN
4 4 46861 Hanson Ridges Suite 587\nNorth Timstad, ... M 79.381381 73.236458 Science 74.429158 Sci&Tech False 0 68.908282 Mkt&Fin 60.739729 28501.868703 True 2020-02-01 2020-07-23 3.0
```

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

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

In order to solve this, we can pass an additional argument
`anonymize_fields`

to our model when we create the instance. This
`anonymize_fields`

argument will need to be a dictionary that
contains:

The name of the field that we want to anonymize.

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

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

name

address

country

city

ssn

credit_card_number

credit_card_expire

credit_card_security_code

email

telephone

…

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

```
In [26]: model = GaussianCopula(
....: primary_key='student_id',
....: anonymize_fields={
....: 'address': 'address'
....: }
....: )
....:
In [27]: model.fit(data_pii)
```

As a result, we can see how the real `address`

values have been
replaced by other fake addresses:

```
In [28]: new_data_pii = model.sample(200)
In [29]: new_data_pii.head()
Out[29]:
student_id address gender second_perc high_perc high_spec degree_perc degree_type work_experience experience_years employability_perc mba_spec mba_perc salary placed start_date end_date duration
0 0 3600 Cole Camp Suite 398\nNew Tinashire, MD 02387 M 50.614977 56.803428 Commerce 52.656126 Comm&Mgmt False 0 54.155383 Mkt&HR 64.019490 NaN False NaT NaT NaN
1 1 USS Alexander\nFPO AE 95941 M 57.896030 63.404704 Commerce 58.939304 Comm&Mgmt False 0 84.119119 Mkt&HR 72.922585 NaN False NaT NaT NaN
2 2 1478 Darrell Forest Apt. 702\nRayfort, OR 68993 M 50.650849 74.550421 Commerce 67.508372 Comm&Mgmt False 1 81.554426 Mkt&Fin 60.903375 28837.902553 True 2020-01-26 2020-06-03 3.0
3 3 Unit 2353 Box 1545\nDPO AE 19682 M 47.338609 59.746061 Commerce 55.873947 Comm&Mgmt False 1 63.006357 Mkt&HR 56.387225 NaN False NaT NaT NaN
4 4 15001 Alexander Knolls Apt. 083\nWest Gregoryv... F 75.244101 80.523194 Science 67.900379 Comm&Mgmt False 0 96.751812 Mkt&Fin 67.930548 30092.464629 True 2020-04-29 2020-11-10 3.0
```

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

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

## Advanced Usage¶

Now that we have discovered the basics, let’s go over a few more
advanced usage examples and see the different arguments that we can pass
to our `GaussianCopula`

Model in order to customize it to our needs.

### How to set transforms to use?¶

One thing that you may have noticed when executing the previous steps is
that the fitting process took much longer on the
`student_placements_pii`

dataset than it took on the previous version
that did not contain the student `address`

. This happens because the
`address`

field is interpreted as a categorical variable, which the
`GaussianCopula`

one-hot
encoded generating 215 new
columns that it had to learn afterwards.

This transformation, which in this case was very inefficient, happens
because the Tabular Models apply Reversible Data
Transforms under the hood to
transform all the non-numerical variables, which the underlying models
cannot handle, into numerical representations which they can properly
work with. In the case of the `GaussianCopula`

, the default
transformation is a One-Hot encoding, which can work very well with
variables that have a small number of different values, but which is
very inefficient in cases where there is a large number of values.

For this reason, the Tabular Models have an additional argument called
`field_transformers`

that let you select which transformer to apply to
each column. This `field_transformers`

argument must be passed as a
`dict`

which contains the name of the fields for which we want to use
a transformer different than the default, and the name of the
transformer that we want to use.

Possible transformer names are:

`integer`

: Uses a`NumericalTransformer`

of dtype`int`

.`float`

: Uses a`NumericalTransformer`

of dtype`float`

.`categorical`

: Uses a`CategoricalTransformer`

without gaussian noise.`categorical_fuzzy`

: Uses a`CategoricalTransformer`

adding gaussian noise.`one_hot_encoding`

: Uses a`OneHotEncodingTransformer`

.`label_encoding`

: Uses a`LabelEncodingTransformer`

.`boolean`

: Uses a`BooleanTransformer`

.`datetime`

: Uses a`DatetimeTransformer`

.

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

Let’s now try to improve the previous fitting process by changing the
transformer that we use for the `address`

field to something other
than the default. As an example, we will use the `label_encoding`

transformer, which instead of generating one column for each possible
value, it just replaces each value with a unique integer value.

```
In [31]: model = GaussianCopula(
....: primary_key='student_id',
....: anonymize_fields={
....: 'address': 'address'
....: },
....: field_transformers={
....: 'address': 'label_encoding'
....: }
....: )
....:
In [32]: model.fit(data_pii)
In [33]: new_data_pii = model.sample(200)
In [34]: new_data_pii.head()
Out[34]:
student_id address gender second_perc high_perc high_spec degree_perc degree_type work_experience experience_years employability_perc mba_spec mba_perc salary placed start_date end_date duration
0 0 124 Cassandra Rest\nIanview, MA 80481 F 80.938672 70.652100 Commerce 70.486247 Comm&Mgmt False 0 52.297210 Mkt&HR 74.823515 NaN False NaT NaT NaN
1 1 617 Perry Shoal Suite 605\nLake Brendatown, NJ... M 58.787360 47.928114 Commerce 65.202339 Comm&Mgmt False -1 63.889376 Mkt&Fin 62.842863 NaN False NaT NaT NaN
2 2 52821 Kenneth Inlet\nNew David, AZ 17442 M 69.681745 65.516798 Commerce 67.164067 Comm&Mgmt False 0 73.452358 Mkt&HR 58.690001 NaN False NaT NaT NaN
3 3 PSC 7660, Box 0654\nAPO AE 60516 M 72.778515 70.696675 Science 54.180383 Sci&Tech False 0 76.134726 Mkt&Fin 59.180392 27491.293008 True 2020-04-15 2020-11-08 3.0
4 4 661 Hicks Cliffs Suite 523\nLake Laura, ID 17335 M 63.807890 72.174068 Commerce 66.568022 Comm&Mgmt False 0 67.332621 Mkt&HR 65.104357 NaN False NaT NaT 3.0
```

### Exploring the Probability Distributions¶

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

it performed the following operations:

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 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 `GaussianCopula`

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

used to model each column using its
`get_distributions`

method:

```
In [35]: model = GaussianCopula(
....: primary_key='student_id'
....: )
....:
In [36]: model.fit(data)
In [37]: distributions = model.get_distributions()
```

This will return us a `dict`

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

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

Note

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

Let’s explore the individual distribution of one of the columns in our
data to better understand how the `GaussianCopula`

processed them and
see if we can improve the results by manually specifying a different
distribution. For example, let’s explore the `experience_years`

column
by looking at the frequency of its values within the original data:

```
In [39]: data.experience_years.value_counts()
Out[39]:
0 141
1 65
2 8
3 1
Name: experience_years, dtype: int64
In [40]: data.experience_years.hist();
```

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

Was the `GaussianCopula`

able to capture this distribution on its own?

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

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

```
In [42]: new_data.experience_years.value_counts()
Out[42]:
0 103
1 76
-1 15
2 6
Name: experience_years, dtype: int64
In [43]: new_data.experience_years.hist();
```

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

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

### Setting distributions for individual variables¶

The `GaussianCopula`

class offers the possibility to indicate which
distribution to use for each one of the columns in the table, in order
to solve situations like the one that we just described. In order to do
this, we need to pass a `field_distributions`

argument with `dict`

that indicates the distribution that we want to use for each column.

Possible values for the distribution argument are:

`univariate`

: Let`copulas`

select the optimal univariate distribution. This may result in non-parametric models being used.`parametric`

: Let`copulas`

select the optimal univariate distribution, but restrict the selection to parametric distributions only.`bounded`

: Let`copulas`

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

: Let`copulas`

select the optimal univariate distribution, but restrict the selection to semi-bounded distributions only. This may result in non-parametric models being used.`parametric_bounded`

: Let`copulas`

select the optimal univariate distribution, but restrict the selection to parametric and bounded distributions only.`parametric_semi_bounded`

: Let`copulas`

select the optimal univariate distribution, but restrict the selection to parametric and semi-bounded distributions only.`gaussian`

: Use a Gaussian distribution.`gamma`

: Use a Gamma distribution.`beta`

: Use a Beta distribution.`student_t`

: Use a Student T distribution.`gaussian_kde`

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

unusable.`truncated_gaussian`

: Use a Truncated Gaussian distribution.

Let’s see what happens if we make the `GaussianCopula`

use the
`gamma`

distribution for our column.

```
In [44]: from sdv.tabular import GaussianCopula
In [45]: model = GaussianCopula(
....: primary_key='student_id',
....: field_distributions={
....: 'experience_years': 'gamma'
....: }
....: )
....:
In [46]: model.fit(data)
```

After this, we can see how the `GaussianCopula`

used the indicated
distribution for the `experience_years`

column

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

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

```
In [48]: new_data = model.sample(len(data))
In [49]: new_data.experience_years.value_counts()
Out[49]:
0 205
1 10
Name: experience_years, dtype: int64
In [50]: new_data.experience_years.hist();
```

Note

Even though there are situations like the one shown above where manually
choosing a distribution seems to give better results, in most cases the
`GaussianCopula`

will be able to find the optimal distribution on its
own, making this manual search of the marginal distributions necessary
on very little occasions.

### Conditional Sampling¶

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

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

parameter in the `sample`

method either as a dataframe or a dictionary.

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

.

```
In [51]: conditions = {
....: 'gender': 'M'
....: }
....:
In [52]: model.sample(5, conditions=conditions)
Out[52]:
student_id gender second_perc high_perc high_spec degree_perc degree_type work_experience experience_years employability_perc mba_spec mba_perc salary placed start_date end_date duration
0 0 M 63.295295 63.587375 Commerce 73.258294 Comm&Mgmt False 0 91.682132 Mkt&HR 64.850285 30336.255313 True 2020-02-20 2020-10-24 12.0
1 1 M 57.657967 61.087111 Arts 61.488033 Comm&Mgmt False 0 94.272689 Mkt&Fin 56.310621 30258.385719 True 2020-01-02 2020-05-08 12.0
2 2 M 46.403341 65.246935 Commerce 58.392598 Comm&Mgmt False 0 61.366822 Mkt&HR 64.126831 NaN True NaT NaT NaN
3 3 M 62.923403 51.052695 Science 63.794126 Comm&Mgmt False 0 61.633155 Mkt&Fin 55.973583 28622.954816 True 2020-02-21 2020-09-17 3.0
4 4 M 77.239896 68.927081 Science 67.538680 Sci&Tech False 0 69.123058 Mkt&HR 72.049664 NaN False NaT NaT NaN
```

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

.

```
In [53]: conditions = {
....: 'gender': 'M',
....: 'experience_years': 0
....: }
....:
In [54]: model.sample(5, conditions=conditions)
Out[54]:
student_id gender second_perc high_perc high_spec degree_perc degree_type work_experience experience_years employability_perc mba_spec mba_perc salary placed start_date end_date duration
0 0 M 71.161948 75.402258 Science 63.437086 Comm&Mgmt False 0 55.739497 Mkt&Fin 52.050836 20922.976136 True 2020-03-27 2020-05-16 3.0
1 1 M 47.145980 61.249953 Commerce 54.844547 Comm&Mgmt False 0 62.496271 Mkt&HR 50.735618 NaN False NaT NaT NaN
2 2 M 48.506886 67.449542 Science 59.979473 Sci&Tech False 0 91.643279 Mkt&HR 59.048889 NaN False NaT NaT NaN
3 3 M 55.449519 55.802401 Commerce 50.310803 Comm&Mgmt False 0 64.737907 Mkt&HR 54.455629 NaN False NaT NaT NaN
4 4 M 78.122196 68.900259 Commerce 57.200343 Comm&Mgmt False 0 58.558378 Mkt&HR 58.881269 28038.474493 True 2020-02-27 2020-06-30 3.0
```

The `conditions`

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

and three samples with `gender = F`

, we can do the
following:

```
In [55]: import pandas as pd
In [56]: conditions = pd.DataFrame({
....: 'gender': ['M', 'M', 'M', 'F', 'F', 'F'],
....: })
....:
In [57]: model.sample(conditions=conditions)
Out[57]:
student_id gender second_perc high_perc high_spec degree_perc degree_type work_experience experience_years employability_perc mba_spec mba_perc salary placed start_date end_date duration
0 0 M 80.134595 69.859909 Science 76.212891 Sci&Tech False 0 53.264885 Mkt&Fin 61.919393 38969.192086 True 2020-04-19 2020-08-29 3.0
1 1 M 64.981426 55.521510 Commerce 52.105234 Comm&Mgmt False 0 65.160272 Mkt&Fin 52.819546 30704.551333 True 2020-01-14 2020-06-26 NaN
2 2 M 81.212292 73.891487 Commerce 73.536962 Comm&Mgmt False 0 59.618138 Mkt&HR 59.840363 30734.670347 True 2020-03-05 2020-05-22 3.0
3 3 F 84.667818 78.284323 Science 77.592989 Sci&Tech False 0 71.713380 Mkt&Fin 75.400906 43669.416542 True 2020-06-03 2020-12-08 3.0
4 4 F 70.416175 63.036813 Commerce 60.056603 Comm&Mgmt False 0 63.945596 Mkt&HR 55.896563 30365.260073 True 2020-02-09 2020-09-19 3.0
5 5 F 69.901600 71.897945 Science 60.322364 Comm&Mgmt False 0 60.756485 Mkt&HR 76.073450 27276.141378 True 2020-01-10 2020-06-09 NaN
```

`GaussianCopula`

also supports conditioning on continuous values, as long as the values
are within the range of seen numbers. For example, if all the values of the
dataset are within 0 and 1, `GaussianCopula`

will not be able to set this value to 1000.

```
In [58]: conditions = {
....: 'degree_perc': 70.0
....: }
....:
In [59]: model.sample(5, conditions=conditions)
Out[59]:
student_id gender second_perc high_perc high_spec degree_perc degree_type work_experience experience_years employability_perc mba_spec mba_perc salary placed start_date end_date duration
0 0 M 70.854837 64.929051 Science 70.0 Comm&Mgmt False 0 59.094458 Mkt&Fin 54.968098 21128.085804 True 2020-01-20 2020-11-13 12.0
1 1 F 66.962165 62.908323 Commerce 70.0 Comm&Mgmt False 0 61.398723 Mkt&Fin 66.548545 28842.472844 True 2020-01-09 2020-04-15 NaN
2 2 M 64.743250 69.962120 Commerce 70.0 Comm&Mgmt False 0 80.570533 Mkt&HR 58.829075 NaN False NaT NaT NaN
3 3 F 64.726267 65.862592 Science 70.0 Comm&Mgmt False 0 77.714509 Mkt&HR 58.418535 20799.191219 True 2020-01-03 2020-01-26 3.0
4 4 F 68.228979 66.083443 Science 70.0 Comm&Mgmt False 0 73.511732 Mkt&HR 57.382507 23755.939815 False 2020-02-01 2020-10-20 NaN
```

Note

Currently, conditional sampling works through a rejection sampling process,
where rows are sampled repeatedly until one that satisfies the conditions is
found. In case you are running into a ```
Could not get enough valid rows within
x trials
```

or simply wish to optimize the results, there are three parameters
that can be fine-tuned: `max_rows_multiplier`

, `max_retries`

and `float_rtol`

.
More information about these parameters can be found in the API section.

### How do I specify constraints?¶

If you look closely at the data you may notice that some properties were
not completely captured by the model. For example, you may have seen
that sometimes the model produces an `experience_years`

number greater
than `0`

while also indicating that `work_experience`

is `False`

.
These types of properties are what we call `Constraints`

and can also
be handled using `SDV`

. For further details about them please visit
the Handling Constraints guide.

### Can I evaluate the Synthetic Data?¶

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

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

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