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# Gaussian Naive Bayes
Gaussian Naive Bayes is a version of the [Naive Bayes](naive-bayes.md) classifier for continuous features. It places a probability density function (PDF) over the features conditioned on a class basis and uses Bayes' Theorem to derive the final probabilities. In addition to the naive feature independence assumption, Gaussian Naive Bayes also assumes that all features are normally (Gaussian) distributed.

**Interfaces:** [Estimator](../estimator.md), [Learner](../learner.md), [Online](../online.md), [Probabilistic](../probabilistic.md), [Persistable](../persistable.md)

**Data Type Compatibility:** Continuous

## Parameters
| # | Name | Default | Type | Description |
|---|---|---|---|---|
| 1 | priors | null | array | The class prior probabilities as an associative array with class labels as keys and their prior probabilities as values totalling 1. If null, then priors will automatically be computed from the training data. |
| 2 | smoothing | 1e-9 | float | The amount of epsilon smoothing added to the variance of each feature. |

## Example
```php
use Rubix\ML\Classifiers\GaussianNB;

$estimator = new GaussianNB([
	'benign' => 0.9,
	'malignant' => 0.1,
], 1e-9);
```

## Additional Methods
Return the class prior probabilities:
```php
public priors() : float[]|null
```

Return the mean of each feature column for each class:
```php
public means() : array[]|null
```

Return the variance of each feature column for each class:
```php
public variances() : array[]|null
```

## References
[^1]: T. F. Chan et al. (1979). Updating Formulae and a Pairwise Algorithm for Computing Sample Variances.

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