from itertools import chain
import numpy as np
from sklearn.base import OutlierMixin, _fit_context
from sklearn.utils import check_random_state
from sklearn.utils.validation import check_is_fitted
from sklearn.utils.extmath import safe_sparse_dot
from sklearn.utils.metaestimators import available_if
from sklearn.neural_network._multilayer_perceptron import (
BaseMultilayerPerceptron,
_STOCHASTIC_SOLVERS,
)
from sklearn.neural_network._base import DERIVATIVES
def hypersphere_loss(outputs, scores, center=1, nu=0.01, radius=0):
loss = radius**2 + (1 / nu) * np.mean(
np.hstack((np.zeros(scores.shape), scores)).max(1)
)
return loss
[docs]
class OneClassMLP(OutlierMixin, BaseMultilayerPerceptron):
"""
Unsupervised One-Class neural network. Can be used to project n-dimensional data into
a single dimension and for outlier detection. Also used to calculate the $\\alpha$
and $\\beta$ supports for the performance metrics used to assess synthetic data
quality.
Uses the loss function proposed in [1]_, which is optimized using LBFGS, stochastic
gradient descent, or adam. This implementation refers to the architecture described
in [2]_ using the soft-boundary objective.
Parameters
----------
hidden_layer_sizes : array-like of shape(n_layers - 2,), default=(500, 500)
The ith element represents the number of neurons in the ith
hidden layer.
activation : {'identity', 'logistic', 'tanh', 'relu'}, default='relu'
Activation function for the hidden layer.
- 'identity', no-op activation, useful to implement linear bottleneck,
returns f(x) = x
- 'logistic', the logistic sigmoid function,
returns f(x) = 1 / (1 + exp(-x)).
- 'tanh', the hyperbolic tan function,
returns f(x) = tanh(x).
- 'relu', the rectified linear unit function,
returns f(x) = max(0, x)
nu : float, default=0.01
Hyperparameter used in the loss function.
solver : {'lbfgs', 'sgd', 'adam'}, default='adam'
The solver for weight optimization.
- 'lbfgs' is an optimizer in the family of quasi-Newton methods.
- 'sgd' refers to stochastic gradient descent.
- 'adam' refers to a stochastic gradient-based optimizer proposed
by Kingma, Diederik, and Jimmy Ba
Note: The default solver 'adam' works pretty well on relatively
large datasets (with thousands of training samples or more) in terms of
both training time and validation score.
For small datasets, however, 'lbfgs' can converge faster and perform
better.
alpha : float, default=0.0001
Strength of the L2 regularization term. The L2 regularization term
is divided by the sample size when added to the loss.
batch_size : int, default=64
Size of minibatches for stochastic optimizers.
If the solver is 'lbfgs', the classifier will not use minibatch.
When set to "auto", `batch_size=min(200, n_samples)`.
learning_rate : {'constant', 'invscaling', 'adaptive'}, default='constant'
Learning rate schedule for weight updates.
- 'constant' is a constant learning rate given by
'learning_rate_init'.
- 'invscaling' gradually decreases the learning rate at each
time step 't' using an inverse scaling exponent of 'power_t'.
effective_learning_rate = learning_rate_init / pow(t, power_t)
- 'adaptive' keeps the learning rate constant to
'learning_rate_init' as long as training loss keeps decreasing.
Each time two consecutive epochs fail to decrease training loss by at
least tol, the current learning rate is divided by 5.
Only used when ``solver='sgd'``.
learning_rate_init : float, default=1e-5
The initial learning rate used. It controls the step-size
in updating the weights. Only used when solver='sgd' or 'adam'.
power_t : float, default=0.5
The exponent for inverse scaling learning rate.
It is used in updating effective learning rate when the learning_rate
is set to 'invscaling'. Only used when solver='sgd'.
max_iter : int, default=200
Maximum number of iterations. The solver iterates until convergence
(determined by 'tol') or this number of iterations. For stochastic
solvers ('sgd', 'adam'), note that this determines the number of epochs
(how many times each data point will be used), not the number of
gradient steps.
shuffle : bool, default=True
Whether to shuffle samples in each iteration. Only used when
solver='sgd' or 'adam'.
random_state : int, RandomState instance, default=None
Determines random number generation for weights and bias
initialization, train-test split if early stopping is used, and batch
sampling when solver='sgd' or 'adam'.
Pass an int for reproducible results across multiple function calls.
tol : float, default=0
Tolerance for the optimization. When the loss or score is not improving
by at least ``tol`` for ``n_iter_no_change`` consecutive iterations,
unless ``learning_rate`` is set to 'adaptive', convergence is
considered to be reached and training stops.
verbose : bool, default=False
Whether to print progress messages to stdout.
warm_start : bool, default=False
When set to True, reuse the solution of the previous
call to fit as initialization, otherwise, just erase the
previous solution.
momentum : float, default=0.9
Momentum for gradient descent update. Should be between 0 and 1. Only
used when solver='sgd'.
nesterovs_momentum : bool, default=True
Whether to use Nesterov's momentum. Only used when solver='sgd' and
momentum > 0.
beta_1 : float, default=0.9
Exponential decay rate for estimates of first moment vector in adam,
should be in [0, 1). Only used when solver='adam'.
beta_2 : float, default=0.999
Exponential decay rate for estimates of second moment vector in adam,
should be in [0, 1). Only used when solver='adam'.
epsilon : float, default=1e-8
Value for numerical stability in adam. Only used when solver='adam'.
n_iter_no_change : int, default=15
Maximum number of epochs to not meet ``tol`` improvement.
Only effective when solver='sgd' or 'adam'.
max_fun : int, default=15000
Only used when solver='lbfgs'. Maximum number of loss function calls.
The solver iterates until convergence (determined by 'tol'), number
of iterations reaches max_iter, or this number of loss function calls.
Note that number of loss function calls will be greater than or equal
to the number of iterations for the `OneClassMLP`.
Attributes
----------
center_ : float
The center of the euclidean ball used to calculate the loss.
radius_ : float
The radius of the euclidean ball used to calculate the loss.
loss_ : float
The current loss computed with the loss function.
best_loss_ : float or None
The minimum loss reached by the solver throughout fitting.
loss_curve_ : list of shape (`n_iter_`,)
The ith element in the list represents the loss at the ith iteration.
t_ : int
The number of training samples seen by the solver during fitting.
coefs_ : list of shape (n_layers - 1,)
The ith element in the list represents the weight matrix corresponding
to layer i.
intercepts_ : list of shape (n_layers - 1,)
The ith element in the list represents the bias vector corresponding to
layer i + 1.
n_features_in_ : int
Number of features seen during `fit`.
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during `fit`. Defined only when `X`
has feature names that are all strings.
n_iter_ : int
The number of iterations the solver has run.
n_layers_ : int
Number of layers.
n_outputs_ : int
Number of outputs.
out_activation_ : str
Name of the output activation function.
References
----------
.. [1] Scholkopf, B., Platt, J. C., Shawe-Taylor, J., Smola, A. J., and Williamson,
R. C. Estimating the support of a high- dimensional distribution. Neural
computation, 13(7): 1443–1471, 2001.
.. [2] Ruff, L., Vandermeulen, R., Goernitz, N., Deecke, L., Siddiqui, S. A., Binder,
A., Muller, E., and Kloft, M. Deep one-class classification. In International
conference on machine learning, pp. 4393–4402. PMLR, 2018.
"""
def __init__(
self,
hidden_layer_sizes=(500, 500),
activation="relu",
nu=0.01,
*,
solver="adam",
alpha=0.0001,
batch_size=64,
learning_rate="constant",
learning_rate_init=1e-5,
power_t=0.5,
max_iter=200,
shuffle=True,
random_state=None,
tol=0,
verbose=False,
warm_start=False,
momentum=0.9,
nesterovs_momentum=True,
beta_1=0.9,
beta_2=0.999,
epsilon=1e-8,
n_iter_no_change=15,
max_fun=15000,
):
super().__init__(
hidden_layer_sizes=hidden_layer_sizes,
activation=activation,
solver=solver,
alpha=alpha,
batch_size=batch_size,
learning_rate=learning_rate,
learning_rate_init=learning_rate_init,
power_t=power_t,
max_iter=max_iter,
loss=None,
shuffle=shuffle,
random_state=random_state,
tol=tol,
verbose=verbose,
warm_start=warm_start,
momentum=momentum,
nesterovs_momentum=nesterovs_momentum,
early_stopping=False,
validation_fraction=None,
beta_1=beta_1,
beta_2=beta_2,
epsilon=epsilon,
n_iter_no_change=n_iter_no_change,
max_fun=max_fun,
)
self.nu = nu
def _init_center(self, y_pred):
"""
Initialize hypersphere center c as the mean from an initial forward pass on the
data.
"""
self.center_ = y_pred.mean()
def _init_radius(self, y_pred):
dist = np.sum((y_pred - self.center_) ** 2, axis=1).reshape(-1, 1)
self.radius_ = np.quantile(np.sqrt(dist), 1 - self.nu)
def _initialize(self, layer_units, dtype):
# set all attributes, allocate weights etc. for first call
# Initialize parameters
self.n_iter_ = 0
self.t_ = 0
# Compute the number of layers
self.n_layers_ = len(layer_units)
# Output for regression
self.out_activation_ = "identity"
# Initialize coefficient and intercept layers
self.coefs_ = []
self.intercepts_ = []
for i in range(self.n_layers_ - 1):
coef_init, intercept_init = self._init_coef(
layer_units[i], layer_units[i + 1], dtype
)
self.coefs_.append(coef_init)
self.intercepts_.append(intercept_init)
if self.solver in _STOCHASTIC_SOLVERS:
self.loss_curve_ = []
self._no_improvement_count = 0
self.best_loss_ = np.inf
def _backprop(self, X, y, activations, deltas, coef_grads, intercept_grads):
"""Compute the MLP loss function and its corresponding derivatives
with respect to each parameter: weights and bias vectors.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The input data.
y : ndarray of shape (n_samples,)
The target values.
activations : list, length = n_layers - 1
The ith element of the list holds the values of the ith layer.
deltas : list, length = n_layers - 1
The ith element of the list holds the difference between the
activations of the i + 1 layer and the backpropagated error.
More specifically, deltas are gradients of loss with respect to z
in each layer, where z = wx + b is the value of a particular layer
before passing through the activation function
coef_grads : list, length = n_layers - 1
The ith element contains the amount of change used to update the
coefficient parameters of the ith layer in an iteration.
intercept_grads : list, length = n_layers - 1
The ith element contains the amount of change used to update the
intercept parameters of the ith layer in an iteration.
Returns
-------
loss : float
coef_grads : list, length = n_layers - 1
intercept_grads : list, length = n_layers - 1
"""
n_samples = X.shape[0]
# Forward propagate
activations = self._forward_pass(activations)
dist = np.sum((activations[-1] - self.center_) ** 2, axis=1).reshape(-1, 1)
scores = dist - self.radius_**2
# Get loss
loss = hypersphere_loss(
outputs=activations[-1],
scores=scores,
center=self.center_,
nu=self.nu,
radius=self.radius_,
)
# Backward propagate
last = self.n_layers_ - 2
# The calculation of delta[last] here works with following
# combinations of output activation and loss function:
# sigmoid and binary cross entropy, softmax and categorical cross
# entropy, and identity with squared loss
deltas[last] = scores
# Compute gradient for the last layer
self._compute_loss_grad(
last, n_samples, activations, deltas, coef_grads, intercept_grads
)
inplace_derivative = DERIVATIVES[self.activation]
# Iterate over the hidden layers
for i in range(self.n_layers_ - 2, 0, -1):
deltas[i - 1] = safe_sparse_dot(deltas[i], self.coefs_[i].T)
inplace_derivative(activations[i], deltas[i - 1])
self._compute_loss_grad(
i - 1, n_samples, activations, deltas, coef_grads, intercept_grads
)
return loss, coef_grads, intercept_grads
[docs]
@available_if(lambda est: est._check_solver())
@_fit_context(prefer_skip_nested_validation=True)
def partial_fit(self, X, y=None):
"""Update the model with a single iteration over the given data.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The input data.
y : ndarray of shape (n_samples,)
The target values.
Returns
-------
self : object
Trained MLP model.
"""
return self._fit(X, incremental=True)
[docs]
@_fit_context(prefer_skip_nested_validation=True)
def fit(self, X, y=None):
"""Fit the model to data matrix X.
Parameters
----------
X : ndarray or sparse matrix of shape (n_samples, n_features)
The input data.
Returns
-------
self : object
Returns a trained MLP model.
"""
return self._fit(X, incremental=False)
def _fit(self, X, incremental=False):
# Make sure self.hidden_layer_sizes is a list
hidden_layer_sizes = self.hidden_layer_sizes
if not hasattr(hidden_layer_sizes, "__iter__"):
hidden_layer_sizes = [hidden_layer_sizes]
hidden_layer_sizes = list(hidden_layer_sizes)
if np.any(np.array(hidden_layer_sizes) <= 0):
raise ValueError(
"hidden_layer_sizes must be > 0, got %s." % hidden_layer_sizes
)
first_pass = not hasattr(self, "coefs_") or (
not self.warm_start and not incremental
)
X = self._validate_input(X, incremental, reset=first_pass)
n_samples, n_features = X.shape
self.n_outputs_ = 1
layer_units = [n_features] + hidden_layer_sizes + [self.n_outputs_]
# check random state
self._random_state = check_random_state(self.random_state)
if first_pass:
# First time training the model
self._initialize(layer_units, X.dtype)
y_pred = self._forward_pass_fast(X, check_input=False)
self._init_center(y_pred)
self._init_radius(y_pred)
# Initialize lists
activations = [X] + [None] * (len(layer_units) - 1)
deltas = [None] * (len(activations) - 1)
coef_grads = [
np.empty((n_fan_in_, n_fan_out_), dtype=X.dtype)
for n_fan_in_, n_fan_out_ in zip(layer_units[:-1], layer_units[1:])
]
intercept_grads = [
np.empty(n_fan_out_, dtype=X.dtype) for n_fan_out_ in layer_units[1:]
]
# Run the Stochastic optimization solver
if self.solver in _STOCHASTIC_SOLVERS:
self._fit_stochastic(
X,
np.ones(X.shape[0]),
activations,
deltas,
coef_grads,
intercept_grads,
layer_units,
incremental,
)
# Run the LBFGS solver
elif self.solver == "lbfgs":
self._fit_lbfgs(
X,
np.ones(X.shape[0]),
activations,
deltas,
coef_grads,
intercept_grads,
layer_units,
)
# validate parameter weights
weights = chain(self.coefs_, self.intercepts_)
if not all(np.isfinite(w).all() for w in weights):
raise ValueError(
"Solver produced non-finite parameter weights. The input data may"
" contain large values and need to be preprocessed."
)
return self
def _validate_input(self, X, incremental, reset):
X = self._validate_data(
X,
accept_sparse=["csr", "csc"],
dtype=(np.float64, np.float32),
reset=reset,
)
return X
[docs]
def predict(self, X):
"""Predict using the multi-layer perceptron model.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The input data.
Returns
-------
y : ndarray of shape (n_samples, n_outputs)
The predicted values.
"""
check_is_fitted(self)
return self._predict(X)
def _predict(self, X, check_input=True):
"""Private predict method with optional input validation"""
scores = self._forward_pass_fast(X, check_input=check_input)
return scores.ravel()