art.estimators.classification
¶
Classifier API for applying all attacks. Use the Classifier
wrapper to be able to apply an attack to a
preexisting model.
Mixin Base Class Classifier¶
Mixin Base Class Class Gradients¶

class
art.estimators.classification.
ClassGradientsMixin
¶ Mixin abstract base class defining classifiers providing access to class gradients. A classifier of this type can be combined with certain whitebox attacks. This mixin abstract base class has to be mixed in with class Classifier.

abstract
class_gradient
(x: numpy.ndarray, label: Optional[Union[int, List[int]]] = None, **kwargs) → numpy.ndarray¶ Compute perclass derivatives w.r.t. x.
 Return type
ndarray
 Parameters
x (np.ndarray or pandas.DataFrame) – Samples.
label – Index of a specific perclass derivative. If an integer is provided, the gradient of that class output is computed for all samples. If multiple values as provided, the first dimension should match the batch size of x, and each value will be used as target for its corresponding sample in x. If None, then gradients for all classes will be computed for each sample.
 Returns
Gradients of input features w.r.t. each class in the form (batch_size, nb_classes, input_shape) when computing for all classes, otherwise shape becomes (batch_size, 1, input_shape) when label parameter is specified.

abstract
BlackBox Classifier¶

class
art.estimators.classification.
BlackBoxClassifier
(predict: Callable, input_shape: Tuple[int, …], nb_classes: int, clip_values: Optional[CLIP_VALUES_TYPE] = None, preprocessing_defences: Optional[Union[Preprocessor, List[Preprocessor]]] = None, postprocessing_defences: Optional[Union[Postprocessor, List[Postprocessor]]] = None, preprocessing: PREPROCESSING_TYPE = 0, 1)¶ Wrapper class for blackbox classifiers.

__init__
(predict: Callable, input_shape: Tuple[int, …], nb_classes: int, clip_values: Optional[CLIP_VALUES_TYPE] = None, preprocessing_defences: Optional[Union[Preprocessor, List[Preprocessor]]] = None, postprocessing_defences: Optional[Union[Postprocessor, List[Postprocessor]]] = None, preprocessing: PREPROCESSING_TYPE = 0, 1)¶ Create a Classifier instance for a blackbox model.
 Parameters
predict (
Callable
) – Function that takes in one input of the data and returns the onehot encoded predicted class.input_shape (
Tuple
) – Size of input.nb_classes (
int
) – Number of prediction classes.clip_values – Tuple of the form (min, max) of floats or np.ndarray representing the minimum and maximum values allowed for features. If floats are provided, these will be used as the range of all features. If arrays are provided, each value will be considered the bound for a feature, thus the shape of clip values needs to match the total number of features.
preprocessing_defences – Preprocessing defence(s) to be applied by the classifier.
postprocessing_defences – Postprocessing defence(s) to be applied by the classifier.
preprocessing – Tuple of the form (subtrahend, divisor) of floats or np.ndarray of values to be used for data preprocessing. The first value will be subtracted from the input. The input will then be divided by the second one.

property
clip_values
¶ Return the clip values of the input samples.
 Returns
Clip values (min, max).

fit
(*args, **kwargs)¶ Fit the classifier on the training set (x, y).
 Parameters
x – Training data.
y – Labels, onevsrest encoding.
kwargs – Dictionary of frameworkspecific arguments. These should be parameters supported by the fit_generator function in Keras and will be passed to this function as such. Including the number of epochs or the number of steps per epoch as part of this argument will result in as error.
 Raises
NotImplementedException – This method is not supported for blackbox classifiers.

get_params
() → Dict[str, Any]¶ Get all parameters and their values of this estimator.
 Returns
A dictionary of string parameter names to their value.

property
input_shape
¶ Return the shape of one input sample.
 Returns
Shape of one input sample.

property
model
¶ Return the model.
 Returns
The model.

property
nb_classes
¶ Return the number of output classes.
 Returns
Number of classes in the data.

predict
(*args, **kwargs)¶ Perform prediction for a batch of inputs.
 Parameters
x – Test set.
batch_size – Size of batches.
 Returns
Array of predictions of shape (nb_inputs, nb_classes).

save
(filename: str, path: Optional[str] = None) → None¶ Save a model to file in the format specific to the backend framework. For Keras, .h5 format is used.
 Parameters
filename (
str
) – Name of the file where to store the model.path – Path of the folder where to store the model. If no path is specified, the model will be stored in the default data location of the library ART_DATA_PATH.
 Raises
NotImplementedException – This method is not supported for blackbox classifiers.

set_params
(**kwargs) → None¶ Take a dictionary of parameters and apply checks before setting them as attributes.
 Parameters
kwargs – A dictionary of attributes.

Keras Classifier¶

class
art.estimators.classification.
KerasClassifier
(**kwargs)¶ Wrapper class for importing Keras models.

__init__
(model: Union[keras.models.Model, tf.keras.models.Model], use_logits: bool = False, channel_index=<art.utils._Deprecated object>, channels_first: bool = False, clip_values: Optional[CLIP_VALUES_TYPE] = None, preprocessing_defences: Optional[Union[Preprocessor, List[Preprocessor]]] = None, postprocessing_defences: Optional[Union[Postprocessor, List[Postprocessor]]] = None, preprocessing: PREPROCESSING_TYPE = (0, 1), input_layer: int = 0, output_layer: int = 0) → None¶ Create a Classifier instance from a Keras model. Assumes the model passed as argument is compiled.
 Parameters
model – Keras model, neural network or other.
use_logits (
bool
) – True if the output of the model are logits; false for probabilities or any other type of outputs. Logits output should be favored when possible to ensure attack efficiency.channel_index (int) – Index of the axis in data containing the color channels or features.
channels_first (
bool
) – Set channels first or last.clip_values – Tuple of the form (min, max) of floats or np.ndarray representing the minimum and maximum values allowed for features. If floats are provided, these will be used as the range of all features. If arrays are provided, each value will be considered the bound for a feature, thus the shape of clip values needs to match the total number of features.
preprocessing_defences – Preprocessing defence(s) to be applied by the classifier.
postprocessing_defences – Postprocessing defence(s) to be applied by the classifier.
preprocessing – Tuple of the form (subtrahend, divisor) of floats or np.ndarray of values to be used for data preprocessing. The first value will be subtracted from the input. The input will then be divided by the second one.
input_layer (
int
) – The index of the layer to consider as input for models with multiple input layers. The layer with this index will be considered for computing gradients. For models with only one input layer this values is not required.output_layer (
int
) – Which layer to consider as the output when the models has multiple output layers. The layer with this index will be considered for computing gradients. For models with only one output layer this values is not required.

property
channel_index
¶  Returns
Index of the axis containing the color channels in the samples x.

property
channels_first
¶  Returns
Boolean to indicate index of the color channels in the sample x.

class_gradient
(*args, **kwargs)¶ Compute perclass derivatives w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
label – Index of a specific perclass derivative. If an integer is provided, the gradient of that class output is computed for all samples. If multiple values are provided, the first dimension should match the batch size of x, and each value will be used as target for its corresponding sample in x. If None, then gradients for all classes will be computed for each sample.
 Returns
Array of gradients of input features w.r.t. each class in the form (batch_size, nb_classes, input_shape) when computing for all classes, otherwise shape becomes (batch_size, 1, input_shape) when label parameter is specified.

property
clip_values
¶ Return the clip values of the input samples.
 Returns
Clip values (min, max).

custom_loss_gradient
(nn_function, tensors, input_values, name='default')¶ Returns the gradient of the nn_function with respect to model input
 Parameters
nn_function (a Keras tensor) – an intermediate tensor representation of the function to differentiate
tensors (list) – the tensors or variables to differentiate with respect to
input_values (list) – the inputs to evaluate the gradient
name (str) – The name of the function. Functions of the same name are cached
 Returns
the gradient of the function w.r.t vars
 Return type
np.ndarray

fit
(*args, **kwargs)¶ Fit the classifier on the training set (x, y).
 Parameters
x – Training data.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or index labels of shape (nb_samples,).
batch_size – Size of batches.
nb_epochs – Number of epochs to use for training.
kwargs – Dictionary of frameworkspecific arguments. These should be parameters supported by the fit_generator function in Keras and will be passed to this function as such. Including the number of epochs or the number of steps per epoch as part of this argument will result in as error.

fit_generator
(generator: DataGenerator, nb_epochs: int = 20, **kwargs) → None¶ Fit the classifier using the generator that yields batches as specified.
 Parameters
generator – Batch generator providing (x, y) for each epoch. If the generator can be used for native training in Keras, it will.
nb_epochs (
int
) – Number of epochs to use for training.kwargs – Dictionary of frameworkspecific arguments. These should be parameters supported by the fit_generator function in Keras and will be passed to this function as such. Including the number of epochs as part of this argument will result in as error.

get_activations
(*args, **kwargs)¶ Return the output of the specified layer for input x. layer is specified by layer index (between 0 and nb_layers  1) or by name. The number of layers can be determined by counting the results returned by calling layer_names.
 Parameters
x – Input for computing the activations.
layer – Layer for computing the activations.
batch_size – Size of batches.
framework – If true, return the intermediate tensor representation of the activation.
 Returns
The output of layer, where the first dimension is the batch size corresponding to x.

get_params
() → Dict[str, Any]¶ Get all parameters and their values of this estimator.
 Returns
A dictionary of string parameter names to their value.

property
input_shape
¶ Return the shape of one input sample.
 Returns
Shape of one input sample.

property
layer_names
¶ Return the names of the hidden layers in the model, if applicable.
 Returns
The names of the hidden layers in the model, input and output layers are ignored.
Warning
layer_names tries to infer the internal structure of the model. This feature comes with no guarantees on the correctness of the result. The intended order of the layers tries to match their order in the model, but this is not guaranteed either.

property
learning_phase
¶ The learning phase set by the user. Possible values are True for training or False for prediction and None if it has not been set by the library. In the latter case, the library does not do any explicit learning phase manipulation and the current value of the backend framework is used. If a value has been set by the user for this property, it will impact all following computations for model fitting, prediction and gradients.
 Returns
Learning phase.

loss
(x: numpy.ndarray, y: numpy.ndarray, **kwargs) → numpy.ndarray¶ Compute the loss of the neural network for samples x.
 Parameters
x (
ndarray
) – Samples of shape (nb_samples, nb_features) or (nb_samples, nb_pixels_1, nb_pixels_2, nb_channels) or (nb_samples, nb_channels, nb_pixels_1, nb_pixels_2).y (
ndarray
) – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
 Returns
Loss values.
 Return type
Format as expected by the model

loss_gradient
(*args, **kwargs)¶ Compute the gradient of the loss function w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
 Returns
Array of gradients of the same shape as x.

property
model
¶ Return the model.
 Returns
The model.

property
nb_classes
¶ Return the number of output classes.
 Returns
Number of classes in the data.

predict
(*args, **kwargs)¶ Perform prediction for a batch of inputs.
 Parameters
x – Test set.
batch_size – Size of batches.
 Returns
Array of predictions of shape (nb_inputs, nb_classes).

save
(filename: str, path: Optional[str] = None) → None¶ Save a model to file in the format specific to the backend framework. For Keras, .h5 format is used.
 Parameters
filename (
str
) – Name of the file where to store the model.path – Path of the folder where to store the model. If no path is specified, the model will be stored in the default data location of the library ART_DATA_PATH.

set_learning_phase
(train: bool) → None¶ Set the learning phase for the backend framework.
 Parameters
train (
bool
) – True to set the learning phase to training, False to set it to prediction.

set_params
(**kwargs) → None¶ Take a dictionary of parameters and apply checks before setting them as attributes.
 Parameters
kwargs – A dictionary of attributes.

MXNet Classifier¶

class
art.estimators.classification.
MXClassifier
(**kwargs)¶ Wrapper class for importing MXNet Gluon models.

__init__
(model: mx.gluon.Block, loss: Union[mx.nd.loss, mx.gluon.loss], input_shape: Tuple[int, ...], nb_classes: int, optimizer: Optional[mx.gluon.Trainer] = None, ctx: Optional[mx.context.Context] = None, channel_index=<art.utils._Deprecated object>, channels_first: bool = True, clip_values: Optional[CLIP_VALUES_TYPE] = None, preprocessing_defences: Optional[Union[Preprocessor, List[Preprocessor]]] = None, postprocessing_defences: Optional[Union[Postprocessor, List[Postprocessor]]] = None, preprocessing: PREPROCESSING_TYPE = (0, 1)) → None¶ Initialize an MXClassifier object. Assumes the model passed as parameter is a Gluon model.
 Parameters
model – The Gluon model. The output of the model can be logits, probabilities or anything else. Logits output should be preferred where possible to ensure attack efficiency.
loss – The loss function for which to compute gradients for training.
input_shape (
Tuple
) – The shape of one input instance.nb_classes (
int
) – The number of classes of the model.optimizer – The optimizer used to train the classifier. This parameter is only required if fitting will be done with method fit.
ctx – The device on which the model runs (CPU or GPU). If not provided, CPU is assumed.
channel_index (int) – Index of the axis in data containing the color channels or features.
channels_first (
bool
) – Set channels first or last.clip_values – Tuple of the form (min, max) of floats or np.ndarray representing the minimum and maximum values allowed for features. If floats are provided, these will be used as the range of all features. If arrays are provided, each value will be considered the bound for a feature, thus the shape of clip values needs to match the total number of features.
preprocessing_defences – Preprocessing defence(s) to be applied by the classifier.
postprocessing_defences – Postprocessing defence(s) to be applied by the classifier.
preprocessing – Tuple of the form (subtrahend, divisor) of floats or np.ndarray of values to be used for data preprocessing. The first value will be subtracted from the input. The input will then be divided by the second one.

property
channel_index
¶  Returns
Index of the axis containing the color channels in the samples x.

property
channels_first
¶  Returns
Boolean to indicate index of the color channels in the sample x.

class_gradient
(*args, **kwargs)¶ Compute perclass derivatives w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
label – Index of a specific perclass derivative. If an integer is provided, the gradient of that class output is computed for all samples. If multiple values as provided, the first dimension should match the batch size of x, and each value will be used as target for its corresponding sample in x. If None, then gradients for all classes will be computed for each sample.
 Returns
Array of gradients of input features w.r.t. each class in the form (batch_size, nb_classes, input_shape) when computing for all classes, otherwise shape becomes (batch_size, 1, input_shape) when label parameter is specified.

property
clip_values
¶ Return the clip values of the input samples.
 Returns
Clip values (min, max).

fit
(*args, **kwargs)¶ Fit the classifier on the training set (inputs, outputs).
 Parameters
x – Training data.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or index labels of shape (nb_samples,).
batch_size – Size of batches.
nb_epochs – Number of epochs to use for training.
kwargs – Dictionary of frameworkspecific arguments. This parameter is not currently supported for MXNet and providing it takes no effect.

fit_generator
(generator: DataGenerator, nb_epochs: int = 20, **kwargs) → None¶ Fit the classifier using the generator that yields batches as specified.
 Parameters
generator – Batch generator providing (x, y) for each epoch.
nb_epochs (
int
) – Number of epochs to use for training.kwargs – Dictionary of frameworkspecific arguments. This parameter is not currently supported for MXNet and providing it takes no effect.

get_activations
(*args, **kwargs)¶ Return the output of the specified layer for input x. layer is specified by layer index (between 0 and nb_layers  1) or by name. The number of layers can be determined by counting the results returned by calling layer_names.
 Parameters
x – Input for computing the activations.
layer – Layer for computing the activations
batch_size – Size of batches.
framework – If true, return the intermediate tensor representation of the activation.
 Returns
The output of layer, where the first dimension is the batch size corresponding to x.

get_params
() → Dict[str, Any]¶ Get all parameters and their values of this estimator.
 Returns
A dictionary of string parameter names to their value.

property
input_shape
¶ Return the shape of one input sample.
 Returns
Shape of one input sample.

property
layer_names
¶ Return the hidden layers in the model, if applicable.
 Returns
The hidden layers in the model, input and output layers excluded.
Warning
layer_names tries to infer the internal structure of the model. This feature comes with no guarantees on the correctness of the result. The intended order of the layers tries to match their order in the model, but this is not guaranteed either.

property
learning_phase
¶ The learning phase set by the user. Possible values are True for training or False for prediction and None if it has not been set by the library. In the latter case, the library does not do any explicit learning phase manipulation and the current value of the backend framework is used. If a value has been set by the user for this property, it will impact all following computations for model fitting, prediction and gradients.
 Returns
Learning phase.

loss
(x: numpy.ndarray, y: numpy.ndarray, **kwargs) → numpy.ndarray¶ Compute the loss of the neural network for samples x.
 Parameters
x (
ndarray
) – Samples of shape (nb_samples, nb_features) or (nb_samples, nb_pixels_1, nb_pixels_2, nb_channels) or (nb_samples, nb_channels, nb_pixels_1, nb_pixels_2).y (
ndarray
) – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
 Returns
Loss values.
 Return type
Format as expected by the model

loss_gradient
(*args, **kwargs)¶ Compute the gradient of the loss function w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
 Returns
Array of gradients of the same shape as x.

property
model
¶ Return the model.
 Returns
The model.

property
nb_classes
¶ Return the number of output classes.
 Returns
Number of classes in the data.

predict
(*args, **kwargs)¶ Perform prediction for a batch of inputs.
 Parameters
x – Test set.
batch_size – Size of batches.
 Returns
Array of predictions of shape (nb_inputs, nb_classes).

save
(filename: str, path: Optional[str] = None) → None¶ Save a model to file in the format specific to the backend framework. For Gluon, only parameters are saved in file with name <filename>.params at the specified path. To load the saved model, the original model code needs to be run before calling load_parameters on the generated Gluon model.
 Parameters
filename (
str
) – Name of the file where to store the model.path – Path of the folder where to store the model. If no path is specified, the model will be stored in the default data location of the library ART_DATA_PATH.

set_learning_phase
(train: bool) → None¶ Set the learning phase for the backend framework.
 Parameters
train (
bool
) – True to set the learning phase to training, False to set it to prediction.

set_params
(**kwargs) → None¶ Take a dictionary of parameters and apply checks before setting them as attributes.
 Parameters
kwargs – A dictionary of attributes.

PyTorch Classifier¶

class
art.estimators.classification.
PyTorchClassifier
(**kwargs)¶ This class implements a classifier with the PyTorch framework.

__init__
(model: torch.nn.Module, loss: torch.nn.modules.loss._Loss, input_shape: Tuple[int, ...], nb_classes: int, optimizer: Optional[torch.optim.Optimizer] = None, channel_index=<art.utils._Deprecated object>, channels_first: bool = True, clip_values: Optional[CLIP_VALUES_TYPE] = None, preprocessing_defences: Optional[Union[Preprocessor, List[Preprocessor]]] = None, postprocessing_defences: Optional[Union[Postprocessor, List[Postprocessor]]] = None, preprocessing: PREPROCESSING_TYPE = (0, 1), device_type: str = 'gpu') → None¶ Initialization specifically for the PyTorchbased implementation.
 Parameters
model – PyTorch model. The output of the model can be logits, probabilities or anything else. Logits output should be preferred where possible to ensure attack efficiency.
loss – The loss function for which to compute gradients for training. The target label must be raw categorical, i.e. not converted to onehot encoding.
input_shape (
Tuple
) – The shape of one input instance.optimizer – The optimizer used to train the classifier.
nb_classes (
int
) – The number of classes of the model.optimizer – The optimizer used to train the classifier.
channel_index (int) – Index of the axis in data containing the color channels or features.
channels_first (
bool
) – Set channels first or last.clip_values – Tuple of the form (min, max) of floats or np.ndarray representing the minimum and maximum values allowed for features. If floats are provided, these will be used as the range of all features. If arrays are provided, each value will be considered the bound for a feature, thus the shape of clip values needs to match the total number of features.
preprocessing_defences – Preprocessing defence(s) to be applied by the classifier.
postprocessing_defences – Postprocessing defence(s) to be applied by the classifier.
preprocessing – Tuple of the form (subtrahend, divisor) of floats or np.ndarray of values to be used for data preprocessing. The first value will be subtracted from the input. The input will then be divided by the second one.
device_type (
str
) – Type of device on which the classifier is run, either gpu or cpu.

property
channel_index
¶  Returns
Index of the axis containing the color channels in the samples x.

property
channels_first
¶  Returns
Boolean to indicate index of the color channels in the sample x.

class_gradient
(*args, **kwargs)¶ Compute perclass derivatives w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
label – Index of a specific perclass derivative. If an integer is provided, the gradient of that class output is computed for all samples. If multiple values as provided, the first dimension should match the batch size of x, and each value will be used as target for its corresponding sample in x. If None, then gradients for all classes will be computed for each sample.
 Returns
Array of gradients of input features w.r.t. each class in the form (batch_size, nb_classes, input_shape) when computing for all classes, otherwise shape becomes (batch_size, 1, input_shape) when label parameter is specified.

property
clip_values
¶ Return the clip values of the input samples.
 Returns
Clip values (min, max).

property
device
¶ Get current used device.
 Returns
Current used device.

fit
(*args, **kwargs)¶ Fit the classifier on the training set (x, y).
 Parameters
x – Training data.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or index labels of shape (nb_samples,).
batch_size – Size of batches.
nb_epochs – Number of epochs to use for training.
kwargs – Dictionary of frameworkspecific arguments. This parameter is not currently supported for PyTorch and providing it takes no effect.

fit_generator
(generator: DataGenerator, nb_epochs: int = 20, **kwargs) → None¶ Fit the classifier using the generator that yields batches as specified.
 Parameters
generator – Batch generator providing (x, y) for each epoch.
nb_epochs (
int
) – Number of epochs to use for training.kwargs – Dictionary of frameworkspecific arguments. This parameter is not currently supported for PyTorch and providing it takes no effect.

get_activations
(*args, **kwargs)¶ Return the output of the specified layer for input x. layer is specified by layer index (between 0 and nb_layers  1) or by name. The number of layers can be determined by counting the results returned by calling layer_names.
 Parameters
x – Input for computing the activations.
layer – Layer for computing the activations
batch_size – Size of batches.
framework – If true, return the intermediate tensor representation of the activation.
 Returns
The output of layer, where the first dimension is the batch size corresponding to x.

get_params
() → Dict[str, Any]¶ Get all parameters and their values of this estimator.
 Returns
A dictionary of string parameter names to their value.

property
input_shape
¶ Return the shape of one input sample.
 Returns
Shape of one input sample.

property
layer_names
¶ Return the names of the hidden layers in the model, if applicable.
 Returns
The names of the hidden layers in the model, input and output layers are ignored.
Warning
layer_names tries to infer the internal structure of the model. This feature comes with no guarantees on the correctness of the result. The intended order of the layers tries to match their order in the model, but this is not guaranteed either.

property
learning_phase
¶ The learning phase set by the user. Possible values are True for training or False for prediction and None if it has not been set by the library. In the latter case, the library does not do any explicit learning phase manipulation and the current value of the backend framework is used. If a value has been set by the user for this property, it will impact all following computations for model fitting, prediction and gradients.
 Returns
Learning phase.

loss
(x: numpy.ndarray, y: numpy.ndarray, **kwargs) → numpy.ndarray¶ Compute the loss function w.r.t. x.
 Return type
ndarray
 Parameters
x (
ndarray
) – Sample input with shape as expected by the model.y (
ndarray
) – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
 Returns
Array of losses of the same shape as x.

loss_gradient
(*args, **kwargs)¶ Compute the gradient of the loss function w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
 Returns
Array of gradients of the same shape as x.

loss_gradient_framework
(x: torch.Tensor, y: torch.Tensor, **kwargs) → torch.Tensor¶ Compute the gradient of the loss function w.r.t. x.
 Parameters
x – Input with shape as expected by the model.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
 Returns
Gradients of the same shape as x.

property
model
¶ Return the model.
 Returns
The model.

property
nb_classes
¶ Return the number of output classes.
 Returns
Number of classes in the data.

predict
(*args, **kwargs)¶ Perform prediction for a batch of inputs.
 Parameters
x – Test set.
batch_size – Size of batches.
 Returns
Array of predictions of shape (nb_inputs, nb_classes).

save
(filename: str, path: Optional[str] = None) → None¶ Save a model to file in the format specific to the backend framework.
 Parameters
filename (
str
) – Name of the file where to store the model.path – Path of the folder where to store the model. If no path is specified, the model will be stored in the default data location of the library ART_DATA_PATH.

set_learning_phase
(train: bool) → None¶ Set the learning phase for the backend framework.
 Parameters
train (
bool
) – True to set the learning phase to training, False to set it to prediction.

set_params
(**kwargs) → None¶ Take a dictionary of parameters and apply checks before setting them as attributes.
 Parameters
kwargs – A dictionary of attributes.

TensorFlow Classifier¶

class
art.estimators.classification.
TensorFlowClassifier
(**kwargs)¶ This class implements a classifier with the TensorFlow framework.

__init__
(input_ph: tf.Placeholder, output: tf.Tensor, labels_ph: Optional[tf.Placeholder] = None, train: Optional[tf.Tensor] = None, loss: Optional[tf.Tensor] = None, learning: Optional[tf.Placeholder] = None, sess: Optional[tf.Session] = None, channel_index=<art.utils._Deprecated object>, channels_first: bool = False, clip_values: Optional[CLIP_VALUES_TYPE] = None, preprocessing_defences: Optional[Union[Preprocessor, List[Preprocessor]]] = None, postprocessing_defences: Optional[Union[Postprocessor, List[Postprocessor]]] = None, preprocessing: PREPROCESSING_TYPE = (0, 1), feed_dict: Optional[Dict[Any, Any]] = None) → None¶ Initialization specific to TensorFlow models implementation.
 Parameters
input_ph – The input placeholder.
output – The output layer of the model. This can be logits, probabilities or anything else. Logits output should be preferred where possible to ensure attack efficiency.
labels_ph – The labels placeholder of the model. This parameter is necessary when training the model and when computing gradients w.r.t. the loss function.
train – The train tensor for fitting, including an optimizer. Use this parameter only when training the model.
loss – The loss function for which to compute gradients. This parameter is necessary when training the model and when computing gradients w.r.t. the loss function.
learning – The placeholder to indicate if the model is training.
sess – Computation session.
channel_index (int) – Index of the axis in data containing the color channels or features.
channels_first (
bool
) – Set channels first or last.clip_values – Tuple of the form (min, max) of floats or np.ndarray representing the minimum and maximum values allowed for features. If floats are provided, these will be used as the range of all features. If arrays are provided, each value will be considered the bound for a feature, thus the shape of clip values needs to match the total number of features.
preprocessing_defences – Preprocessing defence(s) to be applied by the classifier.
postprocessing_defences – Postprocessing defence(s) to be applied by the classifier.
preprocessing – Tuple of the form (subtrahend, divisor) of floats or np.ndarray of values to be used for data preprocessing. The first value will be subtracted from the input. The input will then be divided by the second one.
feed_dict – A feed dictionary for the session run evaluating the classifier. This dictionary includes all additionally required placeholders except the placeholders defined in this class.

property
channel_index
¶  Returns
Index of the axis containing the color channels in the samples x.

property
channels_first
¶  Returns
Boolean to indicate index of the color channels in the sample x.

class_gradient
(*args, **kwargs)¶ Compute perclass derivatives w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
label – Index of a specific perclass derivative. If an integer is provided, the gradient of that class output is computed for all samples. If multiple values as provided, the first dimension should match the batch size of x, and each value will be used as target for its corresponding sample in x. If None, then gradients for all classes will be computed for each sample.
 Returns
Array of gradients of input features w.r.t. each class in the form (batch_size, nb_classes, input_shape) when computing for all classes, otherwise shape becomes (batch_size, 1, input_shape) when label parameter is specified.

property
clip_values
¶ Return the clip values of the input samples.
 Returns
Clip values (min, max).

fit
(*args, **kwargs)¶ Fit the classifier on the training set (x, y).
 Parameters
x – Training data.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or index labels of shape (nb_samples,).
batch_size – Size of batches.
nb_epochs – Number of epochs to use for training.
kwargs – Dictionary of frameworkspecific arguments. This parameter is not currently supported for TensorFlow and providing it takes no effect.

fit_generator
(generator: DataGenerator, nb_epochs: int = 20, **kwargs) → None¶ Fit the classifier using the generator that yields batches as specified.
 Parameters
generator – Batch generator providing (x, y) for each epoch. If the generator can be used for native training in TensorFlow, it will.
nb_epochs (
int
) – Number of epochs to use for training.kwargs – Dictionary of frameworkspecific arguments. This parameter is not currently supported for TensorFlow and providing it takes no effect.

get_activations
(*args, **kwargs)¶ Return the output of the specified layer for input x. layer is specified by layer index (between 0 and nb_layers  1) or by name. The number of layers can be determined by counting the results returned by calling layer_names.
 Parameters
x – Input for computing the activations.
layer – Layer for computing the activations.
batch_size – Size of batches.
framework – If true, return the intermediate tensor representation of the activation.
 Returns
The output of layer, where the first dimension is the batch size corresponding to x.

get_params
() → Dict[str, Any]¶ Get all parameters and their values of this estimator.
 Returns
A dictionary of string parameter names to their value.

property
input_shape
¶ Return the shape of one input sample.
 Returns
Shape of one input sample.

property
layer_names
¶ Return the names of the hidden layers in the model, if applicable.
 Returns
The names of the hidden layers in the model, input and output layers are ignored.
Warning
layer_names tries to infer the internal structure of the model. This feature comes with no guarantees on the correctness of the result. The intended order of the layers tries to match their order in the model, but this is not guaranteed either.

property
learning_phase
¶ The learning phase set by the user. Possible values are True for training or False for prediction and None if it has not been set by the library. In the latter case, the library does not do any explicit learning phase manipulation and the current value of the backend framework is used. If a value has been set by the user for this property, it will impact all following computations for model fitting, prediction and gradients.
 Returns
Learning phase.

loss
(x: numpy.ndarray, y: numpy.ndarray, **kwargs) → numpy.ndarray¶ Compute the loss of the neural network for samples x.
 Parameters
x (
ndarray
) – Samples of shape (nb_samples, nb_features) or (nb_samples, nb_pixels_1, nb_pixels_2, nb_channels) or (nb_samples, nb_channels, nb_pixels_1, nb_pixels_2).y (
ndarray
) – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
 Returns
Loss values.
 Return type
Format as expected by the model

loss_gradient
(*args, **kwargs)¶ Compute the gradient of the loss function w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
 Returns
Array of gradients of the same shape as x.

property
model
¶ Return the model.
 Returns
The model.

property
nb_classes
¶ Return the number of output classes.
 Returns
Number of classes in the data.

predict
(*args, **kwargs)¶ Perform prediction for a batch of inputs.
 Parameters
x – Test set.
batch_size – Size of batches.
 Returns
Array of predictions of shape (num_inputs, nb_classes).

save
(filename: str, path: Optional[str] = None) → None¶ Save a model to file in the format specific to the backend framework. For TensorFlow, .ckpt is used.
 Parameters
filename (
str
) – Name of the file where to store the model.path – Path of the folder where to store the model. If no path is specified, the model will be stored in the default data location of the library ART_DATA_PATH.

property
sess
¶ Get current TensorFlow session.
 Returns
The current TensorFlow session.

set_learning_phase
(train: bool) → None¶ Set the learning phase for the backend framework.
 Parameters
train (
bool
) – True to set the learning phase to training, False to set it to prediction.

set_params
(**kwargs) → None¶ Take a dictionary of parameters and apply checks before setting them as attributes.
 Parameters
kwargs – A dictionary of attributes.

TensorFlow v2 Classifier¶

class
art.estimators.classification.
TensorFlowV2Classifier
(**kwargs)¶ This class implements a classifier with the TensorFlow v2 framework.

__init__
(model: Callable, nb_classes: int, input_shape: Tuple[int, ...], loss_object: Optional[tf.keras.losses.Loss] = None, train_step: Optional[Callable] = None, channel_index=<art.utils._Deprecated object>, channels_first: bool = False, clip_values: Optional[CLIP_VALUES_TYPE] = None, preprocessing_defences: Optional[Union[Preprocessor, List[Preprocessor]]] = None, postprocessing_defences: Optional[Union[Postprocessor, List[Postprocessor]]] = None, preprocessing: PREPROCESSING_TYPE = (0, 1)) → None¶ Initialization specific to TensorFlow v2 models.
 Parameters
model (
Callable
) – a python functions or callable class defining the model and providing it prediction as output.nb_classes (
int
) – the number of classes in the classification task.input_shape (
Tuple
) – shape of one input for the classifier, e.g. for MNIST input_shape=(28, 28, 1).loss_object (tf.keras.losses) – The loss function for which to compute gradients. This parameter is applied for training the model and computing gradients of the loss w.r.t. the input.
train_step – A function that applies a gradient update to the trainable variables with signature train_step(model, images, labels).
channel_index (int) – Index of the axis in data containing the color channels or features.
channels_first (
bool
) – Set channels first or last.clip_values – Tuple of the form (min, max) of floats or np.ndarray representing the minimum and maximum values allowed for features. If floats are provided, these will be used as the range of all features. If arrays are provided, each value will be considered the bound for a feature, thus the shape of clip values needs to match the total number of features.
preprocessing_defences – Preprocessing defence(s) to be applied by the classifier.
postprocessing_defences – Postprocessing defence(s) to be applied by the classifier.
preprocessing – Tuple of the form (subtrahend, divisor) of floats or np.ndarray of values to be used for data preprocessing. The first value will be subtracted from the input. The input will then be divided by the second one.

property
channel_index
¶  Returns
Index of the axis containing the color channels in the samples x.

property
channels_first
¶  Returns
Boolean to indicate index of the color channels in the sample x.

class_gradient
(*args, **kwargs)¶ Compute perclass derivatives w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
label – Index of a specific perclass derivative. If an integer is provided, the gradient of that class output is computed for all samples. If multiple values as provided, the first dimension should match the batch size of x, and each value will be used as target for its corresponding sample in x. If None, then gradients for all classes will be computed for each sample.
 Returns
Array of gradients of input features w.r.t. each class in the form (batch_size, nb_classes, input_shape) when computing for all classes, otherwise shape becomes (batch_size, 1, input_shape) when label parameter is specified.

property
clip_values
¶ Return the clip values of the input samples.
 Returns
Clip values (min, max).

fit
(*args, **kwargs)¶ Fit the classifier on the training set (x, y).
 Parameters
x – Training data.
y – Labels, onehotencoded of shape (nb_samples, nb_classes) or index labels of shape (nb_samples,).
batch_size – Size of batches.
nb_epochs – Number of epochs to use for training.
kwargs – Dictionary of frameworkspecific arguments. This parameter is not currently supported for TensorFlow and providing it takes no effect.

fit_generator
(generator: DataGenerator, nb_epochs: int = 20, **kwargs) → None¶ Fit the classifier using the generator that yields batches as specified.
 Parameters
generator – Batch generator providing (x, y) for each epoch. If the generator can be used for native training in TensorFlow, it will.
nb_epochs (
int
) – Number of epochs to use for training.kwargs – Dictionary of frameworkspecific arguments. This parameter is not currently supported for TensorFlow and providing it takes no effect.

get_activations
(*args, **kwargs)¶ Return the output of the specified layer for input x. layer is specified by layer index (between 0 and nb_layers  1) or by name. The number of layers can be determined by counting the results returned by calling layer_names.
 Parameters
x – Input for computing the activations.
layer – Layer for computing the activations.
batch_size – Batch size.
 Returns
The output of layer, where the first dimension is the batch size corresponding to x.

get_params
() → Dict[str, Any]¶ Get all parameters and their values of this estimator.
 Returns
A dictionary of string parameter names to their value.

property
input_shape
¶ Return the shape of one input sample.
 Returns
Shape of one input sample.

property
layer_names
¶ Return the hidden layers in the model, if applicable.
 Returns
The hidden layers in the model, input and output layers excluded.
Warning
layer_names tries to infer the internal structure of the model. This feature comes with no guarantees on the correctness of the result. The intended order of the layers tries to match their order in the model, but this is not guaranteed either.

property
learning_phase
¶ The learning phase set by the user. Possible values are True for training or False for prediction and None if it has not been set by the library. In the latter case, the library does not do any explicit learning phase manipulation and the current value of the backend framework is used. If a value has been set by the user for this property, it will impact all following computations for model fitting, prediction and gradients.
 Returns
Learning phase.

loss
(x: numpy.ndarray, y: numpy.ndarray, **kwargs) → numpy.ndarray¶ Compute the loss function w.r.t. x.
 Return type
ndarray
 Parameters
x (
ndarray
) – Sample input with shape as expected by the model.y (
ndarray
) – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
 Returns
Array of losses of the same shape as x.

loss_gradient
(*args, **kwargs)¶ Compute the gradient of the loss function w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
y – Correct labels, onevsrest encoding.
 Returns
Array of gradients of the same shape as x.

loss_gradient_framework
(x: tf.Tensor, y: tf.Tensor, **kwargs) → tf.Tensor¶ Compute the gradient of the loss function w.r.t. x.
 Parameters
x – Input with shape as expected by the model.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
 Returns
Gradients of the same shape as x.

property
model
¶ Return the model.
 Returns
The model.

property
nb_classes
¶ Return the number of output classes.
 Returns
Number of classes in the data.

predict
(*args, **kwargs)¶ Perform prediction for a batch of inputs.
 Parameters
x – Test set.
batch_size – Size of batches.
 Returns
Array of predictions of shape (nb_inputs, nb_classes).

save
(filename: str, path: Optional[str] = None) → None¶ Save a model to file in the format specific to the backend framework. For TensorFlow, .ckpt is used.
 Parameters
filename (
str
) – Name of the file where to store the model.path – Path of the folder where to store the model. If no path is specified, the model will be stored in the default data location of the library ART_DATA_PATH.

set_learning_phase
(train: bool) → None¶ Set the learning phase for the backend framework.
 Parameters
train (
bool
) – True to set the learning phase to training, False to set it to prediction.

set_params
(**kwargs) → None¶ Take a dictionary of parameters and apply checks before setting them as attributes.
 Parameters
kwargs – A dictionary of attributes.

Ensemble Classifier¶

class
art.estimators.classification.
EnsembleClassifier
(**kwargs)¶ Class allowing to aggregate multiple classifiers as an ensemble. The individual classifiers are expected to be trained when the ensemble is created and no training procedures are provided through this class.

__init__
(classifiers: List[art.estimators.classification.classifier.ClassifierNeuralNetwork], classifier_weights: Optional[Union[list, numpy.ndarray]] = None, channel_index=<art.utils._Deprecated object>, channels_first: bool = False, clip_values: Optional[CLIP_VALUES_TYPE] = None, preprocessing_defences: Optional[Union[Preprocessor, List[Preprocessor]]] = None, postprocessing_defences: Optional[Union[Postprocessor, List[Postprocessor]]] = None, preprocessing: PREPROCESSING_TYPE = (0, 1)) → None¶ Initialize a
EnsembleClassifier
object. The data range values and colour channel index have to be consistent for all the classifiers in the ensemble. Parameters
classifiers (
List
) – List ofClassifier
instances to be ensembled together.classifier_weights – List of weights, one scalar per classifier, to assign to their prediction when aggregating results. If None, all classifiers are assigned the same weight.
channel_index (int) – Index of the axis in data containing the color channels or features.
channels_first (
bool
) – Set channels first or last.clip_values – Tuple of the form (min, max) of floats or np.ndarray representing the minimum and maximum values allowed for features. If floats are provided, these will be used as the range of all features. If arrays are provided, each value will be considered the bound for a feature, thus the shape of clip values needs to match the total number of features.
preprocessing_defences – Preprocessing defence(s) to be applied by the classifier. Not applicable in this classifier.
postprocessing_defences – Postprocessing defence(s) to be applied by the classifier.
preprocessing – Tuple of the form (subtrahend, divisor) of floats or np.ndarray of values to be used for data preprocessing. The first value will be subtracted from the input. The input will then be divided by the second one. Not applicable in this classifier.

property
channel_index
¶  Returns
Index of the axis containing the color channels in the samples x.

property
channels_first
¶  Returns
Boolean to indicate index of the color channels in the sample x.

class_gradient
(*args, **kwargs)¶ Compute perclass derivatives w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
label – Index of a specific perclass derivative. If None, then gradients for all classes will be computed.
raw – Return the individual classifier raw outputs (not aggregated).
 Returns
Array of gradients of input features w.r.t. each class in the form (batch_size, nb_classes, input_shape) when computing for all classes, otherwise shape becomes (batch_size, 1, input_shape) when label parameter is specified. If raw=True, an additional dimension is added at the beginning of the array, indexing the different classifiers.

property
clip_values
¶ Return the clip values of the input samples.
 Returns
Clip values (min, max).

fit
(*args, **kwargs)¶ Fit the classifier on the training set (x, y). This function is not supported for ensembles.
 Parameters
x – Training data.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes).
batch_size – Size of batches.
nb_epochs – Number of epochs to use for training.
kwargs – Dictionary of frameworkspecific arguments.
 Raises
NotImplementedException – This method is not supported for ensembles.

fit_generator
(generator: DataGenerator, nb_epochs: int = 20, **kwargs) → None¶ Fit the classifier using the generator that yields batches as specified. This function is not supported for ensembles.
 Parameters
generator – Batch generator providing (x, y) for each epoch. If the generator can be used for native training in Keras, it will.
nb_epochs (
int
) – Number of epochs to use for trainings.kwargs – Dictionary of frameworkspecific argument.
 Raises
NotImplementedException – This method is not supported for ensembles.

get_activations
(*args, **kwargs)¶ Return the output of the specified layer for input x. layer is specified by layer index (between 0 and nb_layers  1) or by name. The number of layers can be determined by counting the results returned by calling layer_names. This function is not supported for ensembles.
 Parameters
x – Input for computing the activations.
layer – Layer for computing the activations.
batch_size – Size of batches.
framework – If true, return the intermediate tensor representation of the activation.
 Returns
The output of layer, where the first dimension is the batch size corresponding to x.
 Raises
NotImplementedException – This method is not supported for ensembles.

get_params
() → Dict[str, Any]¶ Get all parameters and their values of this estimator.
 Returns
A dictionary of string parameter names to their value.

property
input_shape
¶ Return the shape of one input sample.
 Returns
Shape of one input sample.

property
layer_names
¶ Return the hidden layers in the model, if applicable. This function is not supported for ensembles.
 Returns
The hidden layers in the model, input and output layers excluded.
 Raises
NotImplementedException – This method is not supported for ensembles.

property
learning_phase
¶ The learning phase set by the user. Possible values are True for training or False for prediction and None if it has not been set by the library. In the latter case, the library does not do any explicit learning phase manipulation and the current value of the backend framework is used. If a value has been set by the user for this property, it will impact all following computations for model fitting, prediction and gradients.
 Returns
Learning phase.

loss
(x: numpy.ndarray, y: numpy.ndarray, **kwargs) → numpy.ndarray¶ Compute the loss of the neural network for samples x.
 Parameters
x (
ndarray
) – Samples of shape (nb_samples, nb_features) or (nb_samples, nb_pixels_1, nb_pixels_2, nb_channels) or (nb_samples, nb_channels, nb_pixels_1, nb_pixels_2).y (
ndarray
) – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
 Returns
Loss values.
 Return type
Format as expected by the model

loss_gradient
(*args, **kwargs)¶ Compute the gradient of the loss function w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
raw – Return the individual classifier raw outputs (not aggregated).
 Returns
Array of gradients of the same shape as x. If raw=True, shape becomes [nb_classifiers, x.shape].

property
model
¶ Return the model.
 Returns
The model.

property
nb_classes
¶ Return the number of output classes.
 Returns
Number of classes in the data.

predict
(*args, **kwargs)¶ Perform prediction for a batch of inputs. Predictions from classifiers should only be aggregated if they all have the same type of output (e.g., probabilities). Otherwise, use raw=True to get predictions from all models without aggregation. The same option should be used for logits output, as logits are not comparable between models and should not be aggregated.
 Parameters
x – Test set.
batch_size – Size of batches.
raw – Return the individual classifier raw outputs (not aggregated).
 Returns
Array of predictions of shape (nb_inputs, nb_classes), or of shape (nb_classifiers, nb_inputs, nb_classes) if raw=True.

save
(filename: str, path: Optional[str] = None) → None¶ Save a model to file in the format specific to the backend framework. This function is not supported for ensembles.
 Parameters
filename (
str
) – Name of the file where to store the model.path – Path of the folder where to store the model. If no path is specified, the model will be stored in the default data location of the library ART_DATA_PATH.
 Raises
NotImplementedException – This method is not supported for ensembles.

set_learning_phase
(train: bool) → None¶ Set the learning phase for the backend framework.
 Parameters
train (
bool
) – True to set the learning phase to training, False to set it to prediction.

set_params
(**kwargs) → None¶ Take a dictionary of parameters and apply checks before setting them as attributes.
 Parameters
kwargs – A dictionary of attributes.

Scikitlearn Classifier Classifier¶

art.estimators.classification.
SklearnClassifier
(model: sklearn.base.BaseEstimator, clip_values: Optional[CLIP_VALUES_TYPE] = None, preprocessing_defences: Optional[Union[Preprocessor, List[Preprocessor]]] = None, postprocessing_defences: Optional[Union[Postprocessor, List[Postprocessor]]] = None, preprocessing: PREPROCESSING_TYPE = 0, 1) → ScikitlearnClassifier¶ Create a Classifier instance from a scikitlearn Classifier model. This is a convenience function that instantiates the correct wrapper class for the given scikitlearn model.
 Parameters
model – scikitlearn Classifier model.
clip_values – Tuple of the form (min, max) representing the minimum and maximum values allowed for features.
preprocessing_defences – Preprocessing defence(s) to be applied by the classifier.
postprocessing_defences – Postprocessing defence(s) to be applied by the classifier.
preprocessing – Tuple of the form (subtrahend, divisor) of floats or np.ndarray of values to be used for data preprocessing. The first value will be subtracted from the input. The input will then be divided by the second one.
GPy Gaussian Process Classifier¶

class
art.estimators.classification.
GPyGaussianProcessClassifier
(model: Optional[GPClassification] = None, clip_values: Optional[CLIP_VALUES_TYPE] = None, preprocessing_defences: Optional[Union[Preprocessor, List[Preprocessor]]] = None, postprocessing_defences: Optional[Union[Postprocessor, List[Postprocessor]]] = None, preprocessing: PREPROCESSING_TYPE = 0, 1)¶ Wrapper class for GPy Gaussian Process classification models.

__init__
(model: Optional[GPClassification] = None, clip_values: Optional[CLIP_VALUES_TYPE] = None, preprocessing_defences: Optional[Union[Preprocessor, List[Preprocessor]]] = None, postprocessing_defences: Optional[Union[Postprocessor, List[Postprocessor]]] = None, preprocessing: PREPROCESSING_TYPE = 0, 1) → None¶ Create a Classifier instance GPY Gaussian Process classification models.
 Parameters
model – GPY Gaussian Process Classification model.
clip_values – Tuple of the form (min, max) representing the minimum and maximum values allowed for features.
preprocessing_defences – Preprocessing defence(s) to be applied by the classifier.
postprocessing_defences – Postprocessing defence(s) to be applied by the classifier.
preprocessing – Tuple of the form (subtrahend, divisor) of floats or np.ndarray of values to be used for data preprocessing. The first value will be subtracted from the input. The input will then be divided by the second one.

class_gradient
(*args, **kwargs)¶ Compute perclass derivatives w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
label – Index of a specific perclass derivative. If an integer is provided, the gradient of that class output is computed for all samples. If multiple values as provided, the first dimension should match the batch size of x, and each value will be used as target for its corresponding sample in x. If None, then gradients for all classes will be computed for each sample.
eps – Fraction added to the diagonal elements of the input x.
 Returns
Array of gradients of input features w.r.t. each class in the form (batch_size, nb_classes, input_shape) when computing for all classes, otherwise shape becomes (batch_size, 1, input_shape) when label parameter is specified.

property
clip_values
¶ Return the clip values of the input samples.
 Returns
Clip values (min, max).

fit
(*args, **kwargs)¶ Fit the classifier on the training set (x, y).
 Parameters
x – Training data. Not used, as given to model in initialized earlier.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes).

get_params
() → Dict[str, Any]¶ Get all parameters and their values of this estimator.
 Returns
A dictionary of string parameter names to their value.

property
input_shape
¶ Return the shape of one input sample.
 Returns
Shape of one input sample.

loss_gradient
(*args, **kwargs)¶ Compute the gradient of the loss function w.r.t. x.
 Parameters
x – Sample input with shape as expected by the model.
y – Target values (class labels) onehotencoded of shape (nb_samples, nb_classes) or indices of shape (nb_samples,).
 Returns
Array of gradients of the same shape as x.

property
model
¶ Return the model.
 Returns
The model.

property
nb_classes
¶ Return the number of output classes.
 Returns
Number of classes in the data.

predict
(*args, **kwargs)¶ Perform prediction for a batch of inputs.
 Parameters
x – Test set.
logits – True if the prediction should be done without squashing function.
 Returns
Array of predictions of shape (nb_inputs, nb_classes).

predict_uncertainty
(x: numpy.ndarray) → numpy.ndarray¶ Perform uncertainty prediction for a batch of inputs.
 Return type
ndarray
 Parameters
x (
ndarray
) – Test set. Returns
Array of uncertainty predictions of shape (nb_inputs).

save
(filename: str, path: Optional[str] = None) → None¶ Save a model to file in the format specific to the backend framework.
 Parameters
filename (
str
) – Name of the file where to store the model.path – Path of the folder where to store the model. If no path is specified, the model will be stored in the default data location of the library ART_DATA_PATH.

set_params
(**kwargs) → None¶ Take a dictionary of parameters and apply checks before setting them as attributes.
 Parameters
kwargs – A dictionary of attributes.
