View Source Scholar.NaiveBayes.Multinomial (Scholar v0.3.0)
Naive Bayes classifier for multinomial models.
The multinomial Naive Bayes classifier is suitable for classification with discrete features (e.g., word counts for text classification)
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.
Summary
Functions
Fits a naive Bayes model. The function assumes that targets y
are integers
between 0 and num_classes
- 1 (inclusive). Otherwise, those samples will not
contribute to class_count
.
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
Fits a naive Bayes model. The function assumes that 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 is1.0
.:force_alpha
(boolean/0
) - Iffalse
and alpha is less than 1e-10, it will set alpha to 1e-10. Iftrue
, alpha will remain unchanged. This may cause numerical errors if alpha is too close to 0. The default value istrue
.:fit_priors
(boolean/0
) - Whether to learn class prior probabilities or not. Iffalse
, a uniform prior will be used. The default value istrue
.:class_priors
- Prior probabilities of the classes. If specified, the priors are not adjusted according to the data.:sample_weights
- List ofnum_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<
s64[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]
]
>