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.

• :min_categories - List of minimum number of categories per feature. Determines the number of categories automatically from the training data 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 - A (num_features, num_classes, num_categories) tensor tracking the weighted count of each (feature, class, category) combination. Calculated by summing the weighted occurrences of feature values for each class-label during fitting.

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

Examples

iex> x = Nx.tensor([[1, 2, 2], [1, 2, 1], [2, 2, 0]])
iex> y = Nx.tensor([0, 1, 1])
iex> Scholar.NaiveBayes.Categorical.fit(x, y, num_classes: 2)
%Scholar.NaiveBayes.Categorical{
  feature_count: Nx.tensor(
    [
      [
        [0.0, 1.0, 0.0],
        [0.0, 1.0, 1.0]
      ],
      [
        [0.0, 0.0, 1.0],
        [0.0, 0.0, 2.0]
      ],
      [
        [0.0, 0.0, 1.0],
        [1.0, 1.0, 0.0]
      ]
    ]
  ),
  class_count: Nx.tensor([1.0, 2.0]),
  class_log_priors: Nx.tensor([-1.0986123085021973, -0.40546512603759766]),
  feature_log_probability: Nx.tensor(
    [
      [
        [-1.3862943649291992, -0.6931471824645996, -1.3862943649291992],
        [-1.6094379425048828, -0.9162907600402832, -0.9162907600402832]
      ],
      [
        [-1.3862943649291992, -1.3862943649291992, -0.6931471824645996],
        [-1.6094379425048828, -1.6094379425048828, -0.5108256340026855]
      ],
      [
        [-1.3862943649291992, -1.3862943649291992, -0.6931471824645996],
        [-0.9162907600402832, -0.9162907600402832, -1.6094379425048828]
      ]
    ]
  )
}

iex> x = Nx.tensor([[1, 2, 2], [1, 2, 1], [2, 2, 0]])
iex> y = Nx.tensor([0, 1, 1])
iex> Scholar.NaiveBayes.Categorical.fit(x, y, num_classes: 2, force_alpha: false, alpha: 0.0)
%Scholar.NaiveBayes.Categorical{
  feature_count: Nx.tensor(
    [
      [
        [0.0, 1.0, 0.0],
        [0.0, 1.0, 1.0]
      ],
      [
        [0.0, 0.0, 1.0],
        [0.0, 0.0, 2.0]
      ],
      [
        [0.0, 0.0, 1.0],
        [1.0, 1.0, 0.0]
      ]
    ]
  ),
  class_count: Nx.tensor(
    [1.0, 2.0]
  ),
  class_log_priors: Nx.tensor(
    [-1.0986123085021973, -0.40546512603759766]
  ),
  feature_log_probability: Nx.tensor(
    [
      [
        [-23.025850296020508, 0.0, -23.025850296020508],
        [-23.718997955322266, -0.6931471824645996, -0.6931471824645996]
      ],
      [
        [-23.025850296020508, -23.025850296020508, 0.0],
        [-23.718997955322266, -23.718997955322266, 0.0]
      ],
      [
        [-23.025850296020508, -23.025850296020508, 0.0],
        [-0.6931471824645996, -0.6931471824645996, -23.718997955322266]
      ]
    ]
  )
}

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.Categorical.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Categorical.predict(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]), Nx.tensor([0, 1, 2]))
#Nx.Tensor<
  s32[2]
  [0, 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.Categorical.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Categorical.predict_joint_log_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
#Nx.Tensor<
  f32[2][3]
  [
    [-8.140898704528809, -8.83404541015625, -8.382061004638672],
    [-8.83404541015625, -8.83404541015625, -8.382061004638672]
  ]
>

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.Categorical.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Categorical.predict_log_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
#Nx.Tensor<
  f32[2][3]
  [
    [-0.8266787528991699, -1.5198254585266113, -1.0678410530090332],
    [-1.272965431213379, -1.272965431213379, -0.8209810256958008]
  ]
>

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.Categorical.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Categorical.predict_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
#Nx.Tensor<
  f32[2][3]
  [
    [0.43749991059303284, 0.21875005960464478, 0.34374985098838806],
    [0.28000006079673767, 0.28000006079673767, 0.4399997889995575]
  ]
>