# `Scholar.NaiveBayes.Multinomial`
[🔗](https://github.com/elixir-nx/scholar/blob/main/lib/scholar/naive_bayes/multinomial.ex#L1)

Naive Bayes classifier for multinomial models.

The multinomial Naive Bayes classifier is suitable for classification with
discrete features (e.g., word counts for text classification)

Time complexity is $O(K * N * C)$ where $N$ is the number of samples and $K$ is the number of features,
and $C$ is the number of classes.

# `fit`
[🔗](https://github.com/elixir-nx/scholar/blob/main/lib/scholar/naive_bayes/multinomial.ex#L153)

Fits a naive Bayes model. The function assumes that the targets `y` are integers
between 0 and `num_classes` - 1 (inclusive). Otherwise, those samples will not
contribute to `class_count`.

## Options

* `:num_classes` (`t:pos_integer/0`) - Required. Number of different classes used in training.

* `:alpha` - Additive (Laplace/Lidstone) smoothing parameter
  (set alpha to 0.0 and force_alpha to true, for no smoothing). The default value is `1.0`.

* `:force_alpha` (`t:boolean/0`) - If `false` and alpha is less than 1e-10, it will set alpha to
  1e-10. If `true`, alpha will remain unchanged. This may cause
  numerical errors if alpha is too close to 0. The default value is `true`.

* `:fit_priors` (`t:boolean/0`) - Whether to learn class prior probabilities or not.
  If `false`, a uniform prior will be used. The default value is `true`.

* `:class_priors` - Prior probabilities of the classes. If specified, the priors are not
  adjusted according to the data.

* `:sample_weights` - List of `num_samples` elements.
  A list of 1.0 values is used if none is given.

## Return Values

The function returns a struct with the following parameters:

  * `:class_count` - Number of samples encountered for each class during fitting. This
      value is weighted by the sample weight when provided.

  * `:class_log_priors` - Smoothed empirical log probability for each class.

  * `:feature_count` - Number of samples encountered for each (class, feature)
      during fitting. This value is weighted by the sample weight when
      provided.

  * `:feature_log_probability` - Empirical log probability of features
      given a class, ``P(x_i|y)``.

## Examples

    iex> x = Nx.iota({4, 3})
    iex> y = Nx.tensor([1, 2, 0, 2])
    iex> Scholar.NaiveBayes.Multinomial.fit(x, y, num_classes: 3)
    %Scholar.NaiveBayes.Multinomial{
      feature_count: Nx.tensor(
        [
          [6.0, 7.0, 8.0],
          [0.0, 1.0, 2.0],
          [12.0, 14.0, 16.0]
        ]
      ),
      class_count: Nx.tensor(
        [1.0, 1.0, 2.0]
      ),
      class_log_priors: Nx.tensor(
        [-1.3862943649291992, -1.3862943649291992, -0.6931471824645996]
      ),
      feature_log_probability: Nx.tensor(
        [
          [-1.232143759727478, -1.0986123085021973, -0.9808292388916016],
          [-1.7917594909667969, -1.0986123085021973, -0.6931471824645996],
          [-1.241713285446167, -1.0986123085021973, -0.9734492301940918]
        ]
      )
    }

    iex> x = Nx.iota({4, 3})
    iex> y = Nx.tensor([1, 2, 0, 2])
    iex> Scholar.NaiveBayes.Multinomial.fit(x, y, num_classes: 3, sample_weights: [1, 6, 2, 3])
    %Scholar.NaiveBayes.Multinomial{
      feature_count: Nx.tensor(
        [
          [12.0, 14.0, 16.0],
          [0.0, 1.0, 2.0],
          [45.0, 54.0, 63.0]
        ]
      ),
      class_count: Nx.tensor(
        [2.0, 1.0, 9.0]
      ),
      class_log_priors: Nx.tensor(
        [-1.7917594909667969, -2.4849066734313965, -0.28768205642700195]
      ),
      feature_log_probability: Nx.tensor(
        [
          [-1.241713285446167, -1.0986123085021973, -0.9734492301940918],
          [-1.7917594909667969, -1.0986123085021973, -0.6931471824645996],
          [-1.2773041725158691, -1.0986123085021973, -0.9470624923706055]
        ]
      )
    }

# `predict`
[🔗](https://github.com/elixir-nx/scholar/blob/main/lib/scholar/naive_bayes/multinomial.ex#L299)

Perform classification on an array of test vectors `x` using `model`.

## Examples

    iex> x = Nx.iota({4, 3})
    iex> y = Nx.tensor([1, 2, 0, 2])
    iex> model = Scholar.NaiveBayes.Multinomial.fit(x, y, num_classes: 3)
    iex> Scholar.NaiveBayes.Multinomial.predict(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
    #Nx.Tensor<
      s32[2]
      [2, 2]
    >

# `predict_joint_log_probability`
[🔗](https://github.com/elixir-nx/scholar/blob/main/lib/scholar/naive_bayes/multinomial.ex#L373)

Return joint log probability estimates for the test vector `x` using `model`.

## Examples

    iex> x = Nx.iota({4, 3})
    iex> y = Nx.tensor([1, 2, 0, 2])
    iex> model = Scholar.NaiveBayes.Multinomial.fit(x, y, num_classes: 3)
    iex> Scholar.NaiveBayes.Multinomial.predict_joint_log_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
    #Nx.Tensor<
      f32[2][3]
      [
        [-14.899698257446289, -17.106664657592773, -14.23444938659668],
        [-25.563968658447266, -27.45175552368164, -24.880958557128906]
      ]
    >

# `predict_log_probability`
[🔗](https://github.com/elixir-nx/scholar/blob/main/lib/scholar/naive_bayes/multinomial.ex#L322)

Return log-probability estimates for the test vector `x` using `model`.

## Examples

    iex> x = Nx.iota({4, 3})
    iex> y = Nx.tensor([1, 2, 0, 2])
    iex> model = Scholar.NaiveBayes.Multinomial.fit(x, y, num_classes: 3)
    iex> Scholar.NaiveBayes.Multinomial.predict_log_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
    #Nx.Tensor<
      f32[2][3]
      [
        [-1.1167821884155273, -3.3237485885620117, -0.45153331756591797],
        [-1.141427993774414, -3.029214859008789, -0.4584178924560547]
      ]
    >

# `predict_probability`
[🔗](https://github.com/elixir-nx/scholar/blob/main/lib/scholar/naive_bayes/multinomial.ex#L352)

Return probability estimates for the test vector `x` using `model`.

## Examples

    iex> x = Nx.iota({4, 3})
    iex> y = Nx.tensor([1, 2, 0, 2])
    iex> model = Scholar.NaiveBayes.Multinomial.fit(x, y, num_classes: 3)
    iex> Scholar.NaiveBayes.Multinomial.predict_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
    #Nx.Tensor<
      f32[2][3]
      [
        [0.32733139395713806, 0.036017563194036484, 0.6366512179374695],
        [0.3193626403808594, 0.048353586345911026, 0.6322832107543945]
      ]
    >

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*Consult [api-reference.md](api-reference.md) for complete listing*