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 (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 (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 (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]
    ]
  )
}

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]
>

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]
  ]
>

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]
  ]
>

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]
  ]
>