View Source Scholar.NaiveBayes.Complement (Scholar v0.3.0)

The Complement Naive Bayes classifier.

It was designed to correct the assumption of Multinomial Naive Bayes that each class has roughly the same representation. It is particularly suited for imbalanced data sets.

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.

Reference:

Summary

Functions

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

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

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

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

Return probability estimates for the test vector x using model.

Functions

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

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])
}

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<
  s64[2]
  [2, 2]
>
Link to this function

predict_joint_log_probability(model, x)

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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]
  ]
>
Link to this function

predict_log_probability(model, x)

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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]
  ]
>
Link to this function

predict_probability(model, x)

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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]
  ]
>