View Source Scholar.NaiveBayes.Gaussian (Scholar v0.3.0)
Gaussian Naive Bayes algorithm for classification.
The likelihood of the features is assumed to be Gaussian: $$ P(x\_{i} | y) = \frac{1}{\sqrt{2\pi\sigma\_{y}^{2}}} \exp \left(-\frac{(x\_{i} - \mu\_{y})^2}{2\sigma\_{y}^{2}}\right) $$
The parameters $\sigma\_{y}$ and $\mu\_{y}$ are estimated using maximum likelihood.
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
Gaussian Naive Bayes.
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
Gaussian Naive Bayes.
Options
:var_smoothing(float/0) - Portion of the largest variance of all features that is added to variances for calculation stability. The default value is1.0e-9.:priors- Prior probabilities of the classes. If specified, the priors are not adjusted according to the data. We assume that priors are correct and sum(priors) == 1.:sample_weights- List ofn_sampleselements.A list of 1.0 values is used if none is given.
:num_classes(pos_integer/0) - Required. Number of different classes used in training.
Return Values
The function returns a struct with the following parameters:
:theta- mean of each feature per class.:var- Variance of each feature per class.:class_count- number of training samples observed in each class.:class_priors- probability of each class.:classes- class labels known to the classifier.:epsilon- absolute additive value to variances.
Examples
iex> x = Nx.iota({4, 3})
iex> y = Nx.tensor([1, 2, 0, 2])
iex> Scholar.NaiveBayes.Gaussian.fit(x, y, num_classes: 3)
%Scholar.NaiveBayes.Gaussian{
theta: Nx.tensor(
[
[6.0, 7.0, 8.0],
[0.0, 1.0, 2.0],
[6.0, 7.0, 8.0]
]
),
var: Nx.tensor(
[
[1.1250000042650754e-8, 1.1250000042650754e-8, 1.1250000042650754e-8],
[1.1250000042650754e-8, 1.1250000042650754e-8, 1.1250000042650754e-8],
[9.0, 9.0, 9.0]
]
),
class_count: Nx.tensor([1.0, 1.0, 2.0]),
class_priors: Nx.tensor([0.25, 0.25, 0.5]),
classes: Nx.tensor([0, 1, 2]),
epsilon: Nx.tensor(1.1250000042650754e-8)
}
iex> x = Nx.iota({4, 3})
iex> y = Nx.tensor([1, 2, 0, 2])
iex> Scholar.NaiveBayes.Gaussian.fit(x, y, num_classes: 3, sample_weights: [1, 6, 2, 3])
%Scholar.NaiveBayes.Gaussian{
theta: Nx.tensor(
[
[6.0, 7.0, 8.0],
[0.0, 1.0, 2.0],
[5.0, 6.0, 7.0]
]
),
var: Nx.tensor(
[
[1.1250000042650754e-8, 1.1250000042650754e-8, 1.1250000042650754e-8],
[1.1250000042650754e-8, 1.1250000042650754e-8, 1.1250000042650754e-8],
[8.0, 8.0, 8.0]
]
),
class_count: Nx.tensor([2.0, 1.0, 9.0]),
class_priors: Nx.tensor([0.1666666716337204, 0.0833333358168602, 0.75]),
classes: Nx.tensor([0, 1, 2]),
epsilon: Nx.tensor(1.1250000042650754e-8)
}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.Gaussian.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Gaussian.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.Gaussian.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Gaussian.predict_joint_log_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
#Nx.Tensor<
f32[2][3]
[
[-1822222336.0, -1822222208.0, -9.023576736450195],
[-399999968.0, -5733332992.0, -7.245799541473389]
]
>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.Gaussian.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Gaussian.predict_log_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
#Nx.Tensor<
f32[2][3]
[
[-1822222336.0, -1822222208.0, 0.0],
[-399999968.0, -5733332992.0, 0.0]
]
>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.Gaussian.fit(x, y, num_classes: 3)
iex> Scholar.NaiveBayes.Gaussian.predict_probability(model, Nx.tensor([[6, 2, 4], [8, 5, 9]]))
#Nx.Tensor<
f32[2][3]
[
[0.0, 0.0, 1.0],
[0.0, 0.0, 1.0]
]
>