from functools import partial
import numpy as np
import tensorflow as tf
from typing import Callable, Dict, Optional, Tuple, Union
from alibi_detect.cd.base import BaseLearnedKernelDrift
from alibi_detect.utils.tensorflow.data import TFDataset
from alibi_detect.utils.tensorflow.misc import clone_model
from alibi_detect.utils.tensorflow.distance import mmd2_from_kernel_matrix, batch_compute_kernel_matrix
from alibi_detect.utils.warnings import deprecated_alias
from alibi_detect.utils.frameworks import Framework
from alibi_detect.utils._types import OptimizerTF
[docs]
class LearnedKernelDriftTF(BaseLearnedKernelDrift):
[docs]
@deprecated_alias(preprocess_x_ref='preprocess_at_init')
def __init__(
self,
x_ref: Union[np.ndarray, list],
kernel: tf.keras.Model,
p_val: float = .05,
x_ref_preprocessed: bool = False,
preprocess_at_init: bool = True,
update_x_ref: Optional[Dict[str, int]] = None,
preprocess_fn: Optional[Callable] = None,
n_permutations: int = 100,
var_reg: float = 1e-5,
reg_loss_fn: Callable = (lambda kernel: 0),
train_size: Optional[float] = .75,
retrain_from_scratch: bool = True,
optimizer: OptimizerTF = tf.keras.optimizers.Adam,
learning_rate: float = 1e-3,
batch_size: int = 32,
batch_size_predict: int = 32,
preprocess_batch_fn: Optional[Callable] = None,
epochs: int = 3,
verbose: int = 0,
train_kwargs: Optional[dict] = None,
dataset: Callable = TFDataset,
input_shape: Optional[tuple] = None,
data_type: Optional[str] = None
) -> None:
"""
Maximum Mean Discrepancy (MMD) data drift detector where the kernel is trained to maximise an
estimate of the test power. The kernel is trained on a split of the reference and test instances
and then the MMD is evaluated on held out instances and a permutation test is performed.
For details see Liu et al (2020): Learning Deep Kernels for Non-Parametric Two-Sample Tests
(https://arxiv.org/abs/2002.09116)
Parameters
----------
x_ref
Data used as reference distribution.
kernel
Trainable TensorFlow model that returns a similarity between two instances.
p_val
p-value used for the significance of the test.
x_ref_preprocessed
Whether the given reference data `x_ref` has been preprocessed yet. If `x_ref_preprocessed=True`, only
the test data `x` will be preprocessed at prediction time. If `x_ref_preprocessed=False`, the reference
data will also be preprocessed.
preprocess_at_init
Whether to preprocess the reference data when the detector is instantiated. Otherwise, the reference
data will be preprocessed at prediction time. Only applies if `x_ref_preprocessed=False`.
update_x_ref
Reference data can optionally be updated to the last n instances seen by the detector
or via reservoir sampling with size n. For the former, the parameter equals {'last': n} while
for reservoir sampling {'reservoir_sampling': n} is passed.
preprocess_fn
Function to preprocess the data before applying the kernel.
n_permutations
The number of permutations to use in the permutation test once the MMD has been computed.
var_reg
Constant added to the estimated variance of the MMD for stability.
reg_loss_fn
The regularisation term reg_loss_fn(kernel) is added to the loss function being optimized.
train_size
Optional fraction (float between 0 and 1) of the dataset used to train the kernel.
The drift is detected on `1 - train_size`.
retrain_from_scratch
Whether the kernel should be retrained from scratch for each set of test data or whether
it should instead continue training from where it left off on the previous set.
optimizer
Optimizer used during training of the kernel.
learning_rate
Learning rate used by optimizer.
batch_size
Batch size used during training of the kernel.
batch_size_predict
Batch size used for the trained drift detector predictions.
preprocess_batch_fn
Optional batch preprocessing function. For example to convert a list of objects to a batch which can be
processed by the kernel.
epochs
Number of training epochs for the kernel. Corresponds to the smaller of the reference and test sets.
verbose
Verbosity level during the training of the kernel. 0 is silent, 1 a progress bar.
train_kwargs
Optional additional kwargs when training the kernel.
dataset
Dataset object used during training.
input_shape
Shape of input data.
data_type
Optionally specify the data type (tabular, image or time-series). Added to metadata.
"""
super().__init__(
x_ref=x_ref,
p_val=p_val,
x_ref_preprocessed=x_ref_preprocessed,
preprocess_at_init=preprocess_at_init,
update_x_ref=update_x_ref,
preprocess_fn=preprocess_fn,
n_permutations=n_permutations,
train_size=train_size,
retrain_from_scratch=retrain_from_scratch,
input_shape=input_shape,
data_type=data_type
)
self.meta.update({'backend': Framework.TENSORFLOW.value})
# define and compile kernel
self.original_kernel = kernel
self.kernel = clone_model(kernel)
self.dataset = partial(dataset, batch_size=batch_size, shuffle=True)
self.kernel_mat_fn = partial(
batch_compute_kernel_matrix, preprocess_fn=preprocess_batch_fn, batch_size=batch_size_predict
)
self.train_kwargs = {'optimizer': optimizer, 'epochs': epochs, 'learning_rate': learning_rate,
'reg_loss_fn': reg_loss_fn, 'preprocess_fn': preprocess_batch_fn, 'verbose': verbose}
if isinstance(train_kwargs, dict):
self.train_kwargs.update(train_kwargs)
self.j_hat = LearnedKernelDriftTF.JHat(self.kernel, var_reg)
[docs]
class JHat(tf.keras.Model):
"""
A module that wraps around the kernel. When passed a batch of reference and batch of test
instances it returns an estimate of a correlate of test power.
Equation 4 of https://arxiv.org/abs/2002.09116
"""
def __init__(self, kernel: tf.keras.Model, var_reg: float):
super().__init__()
self.config = {'kernel': kernel, 'var_reg': var_reg}
self.kernel = kernel
self.var_reg = var_reg
[docs]
def call(self, x: tf.Tensor, y: tf.Tensor) -> tf.Tensor:
k_xx, k_yy, k_xy = self.kernel(x, x), self.kernel(y, y), self.kernel(x, y)
h_mat = k_xx + k_yy - k_xy - tf.transpose(k_xy)
n = len(x)
mmd2_est = (tf.reduce_sum(h_mat)-tf.linalg.trace(h_mat))/(n*(n-1))
var_est = (4*tf.reduce_sum(tf.reduce_sum(h_mat, axis=-1)**2)/(n**3) -
4*tf.reduce_sum(h_mat)**2/(n**4))
reg_var_est = var_est + self.var_reg
return mmd2_est/tf.math.sqrt(reg_var_est)
[docs]
def score(self, x: Union[np.ndarray, list]) -> Tuple[float, float, float]:
"""
Compute the p-value resulting from a permutation test using the maximum mean discrepancy
as a distance measure between the reference data and the data to be tested. The kernel
used within the MMD is first trained to maximise an estimate of the resulting test power.
Parameters
----------
x
Batch of instances.
Returns
-------
p-value obtained from the permutation test, the MMD^2 between the reference and test set, \
and the MMD^2 threshold above which drift is flagged.
"""
x_ref, x_cur = self.preprocess(x)
(x_ref_tr, x_cur_tr), (x_ref_te, x_cur_te) = self.get_splits(x_ref, x_cur)
ds_ref_tr, ds_cur_tr = self.dataset(x_ref_tr), self.dataset(x_cur_tr)
self.kernel = clone_model(self.original_kernel) if self.retrain_from_scratch else self.kernel
train_args = [self.j_hat, (ds_ref_tr, ds_cur_tr)]
LearnedKernelDriftTF.trainer(*train_args, **self.train_kwargs)
if isinstance(x_ref_te, np.ndarray) and isinstance(x_cur_te, np.ndarray):
x_all = np.concatenate([x_ref_te, x_cur_te], axis=0)
else:
x_all = x_ref_te + x_cur_te
kernel_mat = self.kernel_mat_fn(x_all, x_all, self.kernel)
kernel_mat = kernel_mat - tf.linalg.diag(tf.linalg.diag_part(kernel_mat)) # zero diagonal
mmd2 = mmd2_from_kernel_matrix(kernel_mat, len(x_cur_te), permute=False, zero_diag=False).numpy()
mmd2_permuted = np.array(
[mmd2_from_kernel_matrix(kernel_mat, len(x_cur_te), permute=True, zero_diag=False).numpy()
for _ in range(self.n_permutations)]
)
p_val = (mmd2 <= mmd2_permuted).mean()
idx_threshold = int(self.p_val * len(mmd2_permuted))
distance_threshold = np.sort(mmd2_permuted)[::-1][idx_threshold]
return p_val, mmd2, distance_threshold
[docs]
@staticmethod
def trainer(
j_hat: JHat,
datasets: Tuple[tf.keras.utils.Sequence, tf.keras.utils.Sequence],
optimizer: OptimizerTF = tf.keras.optimizers.Adam,
learning_rate: float = 1e-3,
preprocess_fn: Callable = None,
epochs: int = 20,
reg_loss_fn: Callable = (lambda kernel: 0),
verbose: int = 1,
) -> None:
"""
Train the kernel to maximise an estimate of test power using minibatch gradient descent.
"""
ds_ref, ds_cur = datasets
optimizer = optimizer(learning_rate=learning_rate) if isinstance(optimizer, type) else optimizer
n_minibatch = min(len(ds_ref), len(ds_cur))
# iterate over epochs
loss_ma = 0.
for epoch in range(epochs):
if verbose:
pbar = tf.keras.utils.Progbar(n_minibatch, 1)
for step, (x_ref, x_cur) in enumerate(zip(ds_ref, ds_cur)):
if isinstance(preprocess_fn, Callable): # type: ignore
x_ref, x_cur = preprocess_fn(x_ref), preprocess_fn(x_cur)
with tf.GradientTape() as tape:
estimate = j_hat(x_ref, x_cur)
loss = -estimate + reg_loss_fn(j_hat.kernel) # ascent
grads = tape.gradient(loss, j_hat.trainable_weights)
optimizer.apply_gradients(zip(grads, j_hat.trainable_weights))
if verbose == 1:
loss_ma = loss_ma + (loss - loss_ma) / (step + 1)
pbar_values = [('loss', loss_ma)]
pbar.add(1, values=pbar_values)