import numpy as np
import tensorflow as tf
from typing import Callable, Dict, Optional, Tuple, Union
from alibi_detect.cd.base import BaseLSDDDrift
from alibi_detect.utils.tensorflow.kernels import GaussianRBF
from alibi_detect.utils.tensorflow.distance import permed_lsdds
from alibi_detect.utils.warnings import deprecated_alias
from alibi_detect.utils.frameworks import Framework
[docs]
class LSDDDriftTF(BaseLSDDDrift):
[docs]
@deprecated_alias(preprocess_x_ref='preprocess_at_init')
def __init__(
self,
x_ref: Union[np.ndarray, list],
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,
sigma: Optional[np.ndarray] = None,
n_permutations: int = 100,
n_kernel_centers: Optional[int] = None,
lambda_rd_max: float = 0.2,
input_shape: Optional[tuple] = None,
data_type: Optional[str] = None
) -> None:
"""
Least-squares density difference (LSDD) data drift detector using a permutation test.
Parameters
----------
x_ref
Data used as reference distribution.
p_val
p-value used for the significance of the permutation 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 computing the data drift metrics.
sigma
Optionally set the bandwidth of the Gaussian kernel used in estimating the LSDD. Can also pass multiple
bandwidth values as an array. The kernel evaluation is then averaged over those bandwidths. If `sigma`
is not specified, the 'median heuristic' is adopted whereby `sigma` is set as the median pairwise distance
between reference samples.
n_permutations
Number of permutations used in the permutation test.
n_kernel_centers
The number of reference samples to use as centers in the Gaussian kernel model used to estimate LSDD.
Defaults to 1/20th of the reference data.
lambda_rd_max
The maximum relative difference between two estimates of LSDD that the regularization parameter
lambda is allowed to cause. Defaults to 0.2 as in the paper.
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,
sigma=sigma,
n_permutations=n_permutations,
n_kernel_centers=n_kernel_centers,
lambda_rd_max=lambda_rd_max,
input_shape=input_shape,
data_type=data_type
)
self.meta.update({'backend': Framework.TENSORFLOW.value})
if self.preprocess_at_init or self.preprocess_fn is None or self.x_ref_preprocessed:
x_ref = tf.convert_to_tensor(self.x_ref)
self._configure_normalization(x_ref)
x_ref = self._normalize(x_ref)
self._initialize_kernel(x_ref)
self._configure_kernel_centers(x_ref)
self.x_ref = x_ref.numpy() # type: ignore[union-attr]
# For stability in high dimensions we don't divide H by (pi*sigma^2)^(d/2)
# Results in an alternative test-stat of LSDD*(pi*sigma^2)^(d/2). Same p-vals etc.
self.H = GaussianRBF(np.sqrt(2.) * self.kernel.sigma)(self.kernel_centers, self.kernel_centers)
def _initialize_kernel(self, x_ref: tf.Tensor):
if self.sigma is None:
self.kernel = GaussianRBF()
_ = self.kernel(x_ref, x_ref, infer_sigma=True)
else:
sigma = tf.convert_to_tensor(self.sigma)
self.kernel = GaussianRBF(sigma)
def _configure_normalization(self, x_ref: tf.Tensor, eps: float = 1e-12):
x_ref_means = tf.reduce_mean(x_ref, axis=0)
x_ref_stds = tf.math.reduce_std(x_ref, axis=0)
self._normalize = lambda x: (x - x_ref_means) / (x_ref_stds + eps)
self._unnormalize = lambda x: (x * (x_ref_stds + eps) + x_ref_means).numpy()
def _configure_kernel_centers(self, x_ref: tf.Tensor):
"Set aside reference samples to act as kernel centers"
perm = tf.random.shuffle(tf.range(self.x_ref.shape[0]))
c_inds, non_c_inds = perm[:self.n_kernel_centers], perm[self.n_kernel_centers:]
self.kernel_centers = tf.gather(x_ref, c_inds)
if np.unique(self.kernel_centers.numpy(), axis=0).shape[0] < self.n_kernel_centers:
perturbation = tf.random.normal(self.kernel_centers.shape, mean=0, stddev=1e-6)
self.kernel_centers = self.kernel_centers + perturbation
x_ref_eff = tf.gather(x_ref, non_c_inds) # the effective reference set
self.k_xc = self.kernel(x_ref_eff, self.kernel_centers)
[docs]
def score(self, x: Union[np.ndarray, list]) -> Tuple[float, float, float]:
"""
Compute the p-value resulting from a permutation test using the least-squares density
difference as a distance measure between the reference data and the data to be tested.
Parameters
----------
x
Batch of instances.
Returns
-------
p-value obtained from the permutation test, the LSDD between the reference and test set, \
and the LSDD threshold above which drift is flagged.
"""
x_ref, x = self.preprocess(x)
if self.preprocess_fn is not None and not self.preprocess_at_init and not self.x_ref_preprocessed:
self._configure_normalization(x_ref)
x_ref = self._normalize(x_ref)
self._initialize_kernel(x_ref)
self._configure_kernel_centers(x_ref)
self.H = GaussianRBF(np.sqrt(2.) * self.kernel.sigma)(self.kernel_centers, self.kernel_centers)
x = self._normalize(x)
k_yc = self.kernel(x, self.kernel_centers)
k_all_c = tf.concat([self.k_xc, k_yc], axis=0)
n_x = x_ref.shape[0] - self.n_kernel_centers
n_all = k_all_c.shape[0]
perms = [tf.random.shuffle(tf.range(n_all)) for _ in range(self.n_permutations)]
x_perms = [perm[:n_x] for perm in perms]
y_perms = [perm[n_x:] for perm in perms]
lsdd_permuted, _, lsdd = permed_lsdds( # type: ignore
k_all_c, x_perms, y_perms, self.H, lam_rd_max=self.lambda_rd_max, return_unpermed=True
)
p_val = tf.reduce_mean(tf.cast(lsdd <= lsdd_permuted, float))
idx_threshold = int(self.p_val * len(lsdd_permuted))
distance_threshold = np.sort(lsdd_permuted)[::-1][idx_threshold]
return float(p_val), float(lsdd), float(distance_threshold)