Fits a complement naive Bayes classifier. 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

• :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.

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

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

• :sample_weights - List of n_samples elements. A list of 1.0 values is used if none is given.

• :norm (boolean/0) - Whether or not a second normalization of the weights is performed. The default value is false.

Return Values

The function returns a struct with the following parameters:

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

• :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.

• :classes - class labels known to the classifier.

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

• :feature_all - Number of samples encountered for each feature during fitting. This value is weighted by the sample_weights when provided.

Examples

iex> x = Nx.iota({4, 3})
iex> y = Nx.tensor([1, 2, 0, 2])
iex> Scholar.NaiveBayes.Complement.fit(x, y, num_classes: 3)
%Scholar.NaiveBayes.Complement{
  feature_log_probability: Nx.tensor(
    [
      [1.3062516450881958, 1.0986123085021973, 0.9267619848251343],
      [1.2452157735824585, 1.0986123085021973, 0.9707789421081543],
      [1.3499267101287842, 1.0986123085021973, 0.8979415893554688]
    ]
  ),
  class_count: Nx.tensor([1.0, 1.0, 2.0]),
  class_log_priors: Nx.tensor([-1.3862943649291992, -1.3862943649291992, -0.6931471824645996]),
  classes: Nx.tensor([0, 1, 2]),
  feature_count: Nx.tensor(
    [
      [6.0, 7.0, 8.0],
      [0.0, 1.0, 2.0],
      [12.0, 14.0, 16.0]
    ]
  ),
  feature_all: Nx.tensor([18.0, 22.0, 26.0])
}
iex> x = Nx.iota({4, 3})
iex> y = Nx.tensor([1, 2, 0, 2])
iex> Scholar.NaiveBayes.Complement.fit(x, y, num_classes: 3, sample_weights: [1, 6, 2, 3])
%Scholar.NaiveBayes.Complement{
  feature_log_probability: Nx.tensor(
    [
      [1.2953225374221802, 1.0986123085021973, 0.9343092441558838],
      [1.2722758054733276, 1.0986123085021973, 0.9506921768188477],
      [1.3062516450881958, 1.0986123085021973, 0.9267619848251343]
    ]
  ),
  class_count: Nx.tensor([2.0, 1.0, 9.0]),
  class_log_priors: Nx.tensor([-1.7917594909667969, -2.4849066734313965, -0.28768205642700195]),
  classes: Nx.tensor([0, 1, 2]),
  feature_count: Nx.tensor(
    [
      [12.0, 14.0, 16.0],
      [0.0, 1.0, 2.0],
      [45.0, 54.0, 63.0]
    ]
  ),
  feature_all: Nx.tensor([57.0, 69.0, 81.0])
}copy

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.Complement.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Complement.predict(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
#Nx.Tensor<
  s32[2]
  [2, 2]
>copy

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.Complement.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Complement.predict_joint_log_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
#Nx.Tensor<
  f32[2][3]
  [
    [13.741782188415527, 13.551634788513184, 13.888551712036133],
    [24.283931732177734, 24.19179916381836, 24.37394905090332]
  ]
>copy

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.Complement.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Complement.predict_log_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
#Nx.Tensor<
  f32[2][3]
  [
    [-1.0935745239257812, -1.283721923828125, -0.9468050003051758],
    [-1.1006698608398438, -1.1928024291992188, -1.0106525421142578]
  ]
>copy

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.Complement.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Complement.predict_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
#Nx.Tensor<
  f32[2][3]
  [
    [0.33501681685447693, 0.2770043909549713, 0.3879786431789398],
    [0.3326481878757477, 0.3033699095249176, 0.3639813959598541]
  ]
>copy