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.

• :binarize - Threshold for binarizing (mapping to booleans) of sample features. If nil, input is presumed to already consist of binary vectors. The default value is 0.0.

• :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.Bernoulli.fit(x, y, num_classes: 3, binarize: 1.0)
%Scholar.NaiveBayes.Bernoulli{
      feature_count: Nx.tensor(
        [
          [1.0, 1.0, 1.0],
          [0.0, 0.0, 1.0],
          [2.0, 2.0, 2.0]
        ]
      ),
      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(
        [
          [-0.40546512603759766, -0.40546512603759766, -0.40546512603759766],
          [-1.0986123085021973, -1.0986123085021973, -0.40546512603759766],
          [-0.28768205642700195, -0.28768205642700195, -0.28768205642700195]
        ]
      )
    }

iex> x = Nx.iota({4, 3})
iex> y = Nx.tensor([1, 2, 0, 2])
iex> Scholar.NaiveBayes.Bernoulli.fit(x, y, num_classes: 3, force_alpha: false, alpha: 0.0)
%Scholar.NaiveBayes.Bernoulli{
      feature_count: Nx.tensor(
        [
          [1.0, 1.0, 1.0],
          [0.0, 1.0, 1.0],
          [2.0, 2.0, 2.0]
        ]
      ),
      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(
        [
          [0.0, 0.0, 0.0],
          [-23.025850296020508, 0.0, 0.0],
          [0.0, 0.0, 0.0]
        ]
      )
    }copy

Perform classification on an array of test vectors x using model. You need to add sorted classes from the training data as the second argument.

Examples

iex> x = Nx.iota({4, 3})
iex> y = Nx.tensor([1, 2, 0, 2])
iex> model = Scholar.NaiveBayes.Bernoulli.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Bernoulli.predict(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]), Nx.tensor([0, 1, 2]))
#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.Bernoulli.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Bernoulli.predict_joint_log_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
#Nx.Tensor<
  f32[2][3]
  [
    [3.6356334686279297, -3.988985061645508, 8.331316947937012],
    [10.56710433959961, 0.16989731788635254, 19.317440032958984]
  ]
>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.Bernoulli.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Bernoulli.predict_log_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
#Nx.Tensor<
  f32[2][3]
  [
    [-4.704780578613281, -12.329399108886719, -0.009097099304199219],
    [-8.750494003295898, -19.147701263427734, -1.583099365234375e-4]
  ]
>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.Bernoulli.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Bernoulli.predict_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
#Nx.Tensor<
  f32[2][3]
  [
    [0.00905190035700798, 4.4198750401847064e-6, 0.9909441471099854],
    [1.5838305989746004e-4, 4.833469624543341e-9, 0.9998416900634766]
  ]
>copy