`heat.naive_bayes.gaussianNB`

Distributed Gaussian Naive-Bayes classifier.

Module Contents

class GaussianNB(priors=None, var_smoothing=1e-09)

Bases: heat.ClassificationMixin, heat.BaseEstimator

Gaussian Naive Bayes (GaussianNB), based on scikit-learn.naive_bayes.GaussianNB. Can perform online updates to model parameters via method partial_fit(). For details on algorithm used to update feature means and variance online, see Chan, Golub, and LeVeque 1983 [1].

Parameters:

priors (DNDarray) – Prior probabilities of the classes, with shape (n_classes,). If specified, the priors are not adjusted according to the data.
var_smoothing (float, optional) – Portion of the largest variance of all features that is added to variances for calculation stability.

Variables:

class_count (DNDarray) – Number of training samples observed in each class. Shape = (n_classes,)
class_prior (DNDarray) – Probability of each class. Shape = (n_classes,)
classes (DNDarray) – Class labels known to the classifier. Shape = (n_classes,)
epsilon (float) – Absolute additive value to variances
sigma (DNDarray) – Variance of each feature per class. Shape = (n_classes, n_features)
theta (DNDarray) – Mean of each feature per class. Shape = (n_classes, n_features)

References

[1] Chan, Tony F., Golub, Gene H., and Leveque, Randall J., “Algorithms for Computing the Sample Variance: Analysis and Recommendations”, The American Statistician, 37:3, pp. 242-247, 1983

Examples

>>> import heat as ht
>>> X = ht.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]], dtype=ht.float32)
>>> Y = ht.array([1, 1, 1, 2, 2, 2])
>>> from heat.naive_bayes import GaussianNB
>>> clf = GaussianNB()
>>> clf.fit(X, Y)
<heat.naive_bayes.gaussianNB.GaussianNB object at 0x1a249f6dd8>
>>> print(clf.predict(ht.array([[-0.8, -1]])))
tensor([1])
>>> clf_pf = GaussianNB()
>>> clf_pf.partial_fit(X, Y, ht.unique(Y, sorted=True))
<heat.naive_bayes.gaussianNB.GaussianNB object at 0x1a249fbe10>
>>> print(clf_pf.predict(ht.array([[-0.8, -1]])))
tensor([1])

fit(x: heat.core.dndarray.DNDarray, y: heat.core.dndarray.DNDarray, sample_weight: heat.core.dndarray.DNDarray | None = None)

Fit Gaussian Naive Bayes according to x and y

Parameters:

x (DNDarray) – Training set, where n_samples is the number of samples and n_features is the number of features. Shape = (n_classes, n_features)
y (DNDarray) – Labels for training set. Shape = (n_samples, )
sample_weight (DNDarray, optional) – Weights applied to individual samples (1. for unweighted). Shape = (n_samples, )

__check_partial_fit_first_call(classes: heat.core.dndarray.DNDarray | None = None) → bool

Adapted to HeAT from scikit-learn.

This function returns True if it detects that this was the first call to partial_fit() on GaussianNB. In that case the classes_ attribute is also set on GaussianNB.

__update_mean_variance(n_past: int, mu: heat.core.dndarray.DNDarray, var: heat.core.dndarray.DNDarray, x: heat.core.dndarray.DNDarray, sample_weight: heat.core.dndarray.DNDarray | None = None) → Tuple[heat.core.dndarray.DNDarray, heat.core.dndarray.DNDarray]

Adapted to HeAT from scikit-learn. Compute online update of Gaussian mean and variance. Given starting sample count, mean, and variance, a new set of points x, and optionally sample weights, return the updated mean and variance. (NB - each dimension (column) in x is treated as independent – you get variance, not covariance). Can take scalar mean and variance, or vector mean and variance to simultaneously update a number of independent Gaussians. See Chan, Golub, and LeVeque 1983 [1]

Parameters:

n_past (int) – Number of samples represented in old mean and variance. If sample weights were given, this should contain the sum of sample weights represented in old mean and variance.
mu (DNDarray) – Means for Gaussians in original set. Shape = (number of Gaussians,)
var (DNDarray) – Variances for Gaussians in original set. Shape = (number of Gaussians,)
x (DNDarray) – Input data
sample_weight (DNDarray, optional) – Weights applied to individual samples (1. for unweighted). Shape = (n_samples,)

References

[1] Chan, Tony F., Golub, Gene H., and Leveque, Randall J., “Algorithms for Computing the Sample Variance: Analysis and Recommendations”, The American Statistician, 37:3, pp. 242-247, 1983

partial_fit(x: heat.core.dndarray.DNDarray, y: heat.core.dndarray.DNDarray, classes: heat.core.dndarray.DNDarray | None = None, sample_weight: heat.core.dndarray.DNDarray | None = None)

Adapted to HeAT from scikit-learn. Incremental fit on a batch of samples. This method is expected to be called several times consecutively on different chunks of a dataset so as to implement out-of-core or online learning. This is especially useful when the whole dataset is too big to fit in memory at once. This method has some performance and numerical stability overhead, hence it is better to call partial_fit() on chunks of data that are as large as possible (as long as fitting in the memory budget) to hide the overhead.

Parameters:

x (DNDarray) – Training set, where n_samples is the number of samples and n_features is the number of features. Shape = (n_samples, n_features)
y (DNDarray) – Labels for training set. Shape = (n_samples,)
classes (DNDarray, optional) – List of all the classes that can possibly appear in the y vector. Must be provided at the first call to partial_fit(), can be omitted in subsequent calls. Shape = (n_classes,)
sample_weight (DNDarray, optional) – Weights applied to individual samples (1. for unweighted). Shape = (n_samples,)

__partial_fit(x: heat.core.dndarray.DNDarray, y: heat.core.dndarray.DNDarray, classes: heat.core.dndarray.DNDarray | None = None, _refit: bool = False, sample_weight: heat.core.dndarray.DNDarray | None = None)

Actual implementation of Gaussian NB fitting. Adapted to HeAT from scikit-learn.

Parameters:

x (DNDarray) – Training set, where n_samples is the number of samples and n_features is the number of features. Shape = (n_samples, n_features)
y (DNDarray) – Labels for training set. Shape = (n_samples,)
classes (DNDarray, optional) – List of all the classes that can possibly appear in the y vector. Must be provided at the first call to partial_fit(), can be omitted in subsequent calls. Shape = (n_classes,)
_refit (bool, optional) – If True, act as though this were the first time __partial_fit() is called (ie, throw away any past fitting and start over).
sample_weight (DNDarray, optional) – Weights applied to individual samples (1. for unweighted). Shape = (n_samples,)

__joint_log_likelihood(x: heat.core.dndarray.DNDarray) → heat.core.dndarray.DNDarray: Adapted to HeAT from scikit-learn. Calculates joint log-likelihood for n_samples to be assigned to each class. Returns a DNDarray joint_log_likelihood(n_samples, n_classes).

logsumexp(a: heat.core.dndarray.DNDarray, axis: int | Tuple[int, Ellipsis] | None = None, b: heat.core.dndarray.DNDarray | None = None, keepdims: bool = False, return_sign: bool = False) → heat.core.dndarray.DNDarray

Adapted to HeAT from scikit-learn. Compute the log of the sum of exponentials of input elements. The result, np.log(np.sum(np.exp(a))) calculated in a numerically more stable way. If b is given then np.log(np.sum(b*np.exp(a))) is returned.

Parameters:

a (DNDarray) – Input array.
axis (None or int or Tuple [int,...], optional) – Axis or axes over which the sum is taken. By default axis is None, and all elements are summed.
keepdims (bool, optional) – If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array.
b (DNDarray, optional) – Scaling factor for exp(a) must be of the same shape as a or broadcastable to a. These values may be negative in order to implement subtraction.
return_sign (bool, optional) – If this is set to True, the result will be a pair containing sign information; if False, results that are negative will be returned as NaN. #TODO: returns NotImplementedYet error.
sgn (DNDarray, NOT IMPLEMENTED YET) – #TODO If return_sign is True, this will be an array of floating-point numbers matching res and +1, 0, or -1 depending on the sign of the result. If False, only one result is returned.

predict(x: heat.core.dndarray.DNDarray) → heat.core.dndarray.DNDarray

Adapted to HeAT from scikit-learn. Perform classification on a tensor of test data x.

Parameters:: x (DNDarray) – Input data with shape (n_samples, n_features)

predict_log_proba(x: heat.core.dndarray.DNDarray) → heat.core.dndarray.DNDarray

Adapted to HeAT from scikit-learn. Return log-probability estimates of the samples for each class in the model. The columns correspond to the classes in sorted order, as they appear in the attribute classes_.

Parameters:: x (DNDarray) – Input data. Shape = (n_samples, n_features).

predict_proba(x: heat.core.dndarray.DNDarray) → heat.core.dndarray.DNDarray

Adapted to HeAT from scikit-learn. Return probability estimates for the test tensor x of the samples for each class in the model. The columns correspond to the classes in sorted order, as they appear in the attribute classes_.

Parameters:: x (DNDarray) – Input data. Shape = (n_samples, n_features).

heat.naive_bayes.gaussianNB

Module Contents

`heat.naive_bayes.gaussianNB`