# ❖ XGaussianNormalizer

**Compatibility:** `numerical` data

{% hint style="info" %}
❖ **SDV Enterprise Bundle**. This feature is available as part of the **XSynthesizers Bundle**, an optional add-on to SDV Enterprise. For more information, please visit the [XSynthesizers Bundle](https://docs.sdv.dev/sdv/reference/explore-sdv/xsynthesizers-bundle) page.
{% endhint %}

{% hint style="warning" %}
To use this transformer, you must install the `copulas` module in addition to `rdt`. This is available in open source for all users.

```
pip install rdt[copulas]
```

{% endhint %}

The `XGaussianNormalizer` is an enhanced version of the [GaussianNormalizer](https://docs.sdv.dev/rdt/transformers-glossary/numerical/gaussiannormalizer). Similar to GaussianNormalizer, it approximates the shape of the overall column and converts it into a standard normal distribution (aka a bell curve with mean = 0 and standard deviation = 1).

**This transformer supports 100+ possible column shapes.**

![](https://2225246359-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FVGX92M819eIp0rMg5elc%2Fuploads%2F00IJManz7vohZtRuiauy%2Frdt_transformers-glossary-numerical-gaussian-normalizer_June%2002%202025.png?alt=media\&token=b72d98ec-7f94-4df1-a1c6-2ea8e3fcb4a6)

```python
from rdt.transformers.numerical import XGaussianNormalizer
transformer = XGaussianNormalizer()
```

## Parameters

**`missing_value_replacement`**: Add this argument to replace missing values during the transform phase

<table data-header-hidden><thead><tr><th width="212"></th><th></th></tr></thead><tbody><tr><td>(default) <code>'mean'</code></td><td>Replace all missing values with the average value.</td></tr><tr><td><code>'random'</code></td><td>Replace missing values with a random value. The value is chosen uniformly at random from the min/max range.</td></tr><tr><td><code>'mode'</code></td><td>Replace all missing values with the most frequently occurring value</td></tr><tr><td><code>&#x3C;number></code></td><td>Replace all missing values with the specified number (<code>0</code>, <code>-1</code>, <code>0.5</code>, etc.)</td></tr><tr><td><code>None</code></td><td>Do not replace missing values. The transformed data will continue to have missing values.</td></tr></tbody></table>

*(deprecated) `model_missing_values`: Use the `missing_value_generation` parameter instead.*

**`missing_value_generation`**: Add this argument to determine how to recreate missing values during the reverse transform phase

<table data-header-hidden><thead><tr><th width="203"></th><th></th></tr></thead><tbody><tr><td>(default) <code>'random'</code></td><td>Randomly assign missing values in roughly the same proportion as the original data.</td></tr><tr><td><code>'from_column'</code></td><td>Create a new column to store whether the value should be missing. Use it to recreate missing values. <em>Note: Adding extra columns uses more memory and increases the RDT processing time.</em></td></tr><tr><td><code>None</code></td><td>Do not recreate missing values.</td></tr></tbody></table>

**`distribution`**: In the first step of the normalization, the transformer approximates the shape (aka distribution) of the overall column after searching through multiple options. Use this parameter to limit the options it searches through.

<table data-header-hidden><thead><tr><th width="262.5"></th><th></th></tr></thead><tbody><tr><td>(default) <code>'parametric'</code></td><td>Search through 1-dimensional distributions that have a set number of parameters.  This includes: <code>gaussian</code>, <code>gamma</code>, <code>beta</code>, <code>student_t</code> and <code>truncated_gaussian</code></td></tr><tr><td><code>&#x3C;name></code></td><td><p>Only consider the distribution that is named. Possible names include:</p><ul><li><code>'norm'</code> <code>'beta'</code>, <code>'truncnorm'</code>, <code>'uniform'</code>, <code>'gamma'</code> or <code>'gaussian_kde'</code> from the <a href="https://sdv.dev/Copulas/">SDV Copulas</a> library</li><li>Any continuous distribution from the <a href="https://docs.scipy.org/doc/scipy/reference/stats.html#continuous-distributions">scipy library</a>. Make sure to provide the full path, including the prefix <code>scipy.stats.</code> — for example <code>'scipy.stats.dweibull'</code>  to refer to <a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.dweibull.html#scipy.stats.dweibull">scipy's dweibull distribution</a>. </li></ul><p><br><em>Deprecated: <code>'gaussian'</code>, <code>'truncated_gaussian'</code> and <code>'student_t'</code>. Instead, please use the names <code>'norm'</code>, <code>'truncnorm'</code> and <code>'t'</code> (respectively).</em></p></td></tr><tr><td><code>&#x3C;copulas.univariate.Univariate></code></td><td>Use the Univariate object created from the Copulas library. See the <a href="https://sdv.dev/Copulas/tutorials/02_Univariate_Distributions.html">User Guide</a> for more information.</td></tr></tbody></table>

**`enforce_min_max_values`**: Add this argument to allow the transformer to learn the min and max allowed values from the data.

<table data-header-hidden><thead><tr><th width="270.5"></th><th></th></tr></thead><tbody><tr><td>(default) <code>False</code></td><td>Do not learn any min or max values from the dataset. When reverse transforming the data, the values may be above or below what was originally present.</td></tr><tr><td><code>True</code></td><td>Learn the min and max values from the input data. When reverse transforming the data, any out-of-bounds values will be clipped to the min or max value.</td></tr></tbody></table>

**`learn_rounding_scheme`**: Add this argument to allow the transformer to learn about rounded values in your dataset.

<table data-header-hidden><thead><tr><th width="249.5"></th><th></th></tr></thead><tbody><tr><td>(default) <code>False</code></td><td>Do not learn or enforce any rounding scheme. When reverse transforming the data, there may be many decimal places present.</td></tr><tr><td><code>True</code></td><td>Learn the rounding rules from the input data. When reverse transforming the data, round the number of digits to match the original.</td></tr></tbody></table>

## FAQ

<details>

<summary>When should I use this transformer?</summary>

Your decision to use this transformer is based on how you plan to use the transformed data. For example, algorithms such as the [Gaussian Copula ](https://en.wikipedia.org/wiki/Copula_\(probability_theory\)#Gaussian_copula)require normalized data. If you're planning to use such an algorithm, this transformer might be a good pre-processing step.

</details>

<details>

<summary>Which algorithm does this transformer use to normalize the data?</summary>

This transformer uses a [Probability Integral Transform](https://en.wikipedia.org/wiki/Probability_integral_transform) to transform the original data into a uniform distribution. From there, it converts the data to a standard normal (Gaussian) distribution.

</details>

<details>

<summary>Can you define the mathematical terms?</summary>

Below are some definitions for the mathematical terms we've used in this doc.

* A **distribution** is mathematical formula that describes the overall shape of data. A distribution has parameters that precisely describe it. For example a bell curve is a distribution with parameters for mean and standard deviation.
* A **parametric distribution** is a distribution that has a preset number of parameters with specific meanings. For example, a bell curve is a parametric distribution because we know it has 2 parameters (mean and standard deviation)
* A **gaussian** or **standard normal** distribution is a bell curve with mean = 0 and standard deviation = 1. Other distribution names such as **gamma**, **beta** and **student t** have precise meanings. Refer to [this list of probability distributions](https://en.wikipedia.org/wiki/List_of_probability_distributions) for more info.

</details>

<details>

<summary>How does the <code>distribution</code> parameter affect the transformation?</summary>

The `XGaussianNormalizer` approximates the column's shape (aka distribution) by searching through multiple options. The more accurate the approximation, the better the accuracy. However, there is a tradeoff between accuracy and the transformation time.

* Searching through more distributions takes a longer time but leads to greater accuracy. To save time, you can input a specific distribution if you already know the specific shape of the column.
* Searching through parametric distributions is faster that non-parametric distributions but can have lower accuracy. For the highest accuracy (that takes the longest amount of time) use the non-parametric `gaussian_kde` distribution.

</details>

<details>

<summary>When are the min/max and rounding schemes enforced?</summary>

Using these options will enforce the min/max values or rounding scheme when reverse transforming your data. Use these parameters if you want to recover data in the same format as the original.

</details>

<details>

<summary>When is it necessary to model missing values?</summary>

When setting the `missing_values_generation` parameter, consider whether the "missingness" of the data is something important. For example, maybe the user opted out of supplying the info on purpose, or maybe a missing value is highly correlated with another column your dataset. If "missingness" is something you want to account for, you should model missing values.

</details>