Source code for

from tqdm import tqdm
import numpy as np
import tensorflow as tf
from typing import Any, Callable, Optional, Union
from import BaseMultiDriftOnline
from alibi_detect.utils.tensorflow.kernels import GaussianRBF
from alibi_detect.utils.tensorflow import zero_diag, quantile, subset_matrix
from alibi_detect.utils.frameworks import Framework

[docs] class MMDDriftOnlineTF(BaseMultiDriftOnline): online_state_keys: tuple = ('t', 'test_stats', 'drift_preds', 'test_window', 'k_xy')
[docs] def __init__( self, x_ref: Union[np.ndarray, list], ert: float, window_size: int, preprocess_fn: Optional[Callable] = None, x_ref_preprocessed: bool = False, kernel: Callable = GaussianRBF, sigma: Optional[np.ndarray] = None, n_bootstraps: int = 1000, verbose: bool = True, input_shape: Optional[tuple] = None, data_type: Optional[str] = None ) -> None: """ Online maximum Mean Discrepancy (MMD) data drift detector using preconfigured thresholds. Parameters ---------- x_ref Data used as reference distribution. ert The expected run-time (ERT) in the absence of drift. For the multivariate detectors, the ERT is defined as the expected run-time from t=0. window_size The size of the sliding test-window used to compute the test-statistic. Smaller windows focus on responding quickly to severe drift, larger windows focus on ability to detect slight drift. preprocess_fn Function to preprocess the data before computing the data drift metrics. 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. kernel Kernel used for the MMD computation, defaults to Gaussian RBF kernel. sigma Optionally set the GaussianRBF kernel bandwidth. 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_bootstraps The number of bootstrap simulations used to configure the thresholds. The larger this is the more accurately the desired ERT will be targeted. Should ideally be at least an order of magnitude larger than the ERT. verbose Whether or not to print progress during configuration. 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, ert=ert, window_size=window_size, preprocess_fn=preprocess_fn, x_ref_preprocessed=x_ref_preprocessed, n_bootstraps=n_bootstraps, verbose=verbose, input_shape=input_shape, data_type=data_type ) self.backend = Framework.TENSORFLOW.value self.meta.update({'backend': self.backend}) # initialize kernel if isinstance(sigma, np.ndarray): sigma = tf.convert_to_tensor(sigma) self.kernel = kernel(sigma) if kernel == GaussianRBF else kernel # compute kernel matrix for the reference data self.k_xx = self.kernel(self.x_ref, self.x_ref, infer_sigma=(sigma is None)) self._configure_thresholds() self._configure_ref_subset() # self.initialise_state() called inside here
def _initialise_state(self) -> None: """ Initialise online state (the stateful attributes updated by `score` and `predict`). This method relies on attributes defined by `_configure_ref_subset`, hence must be called afterwards. """ super()._initialise_state() self.test_window = tf.gather(self.x_ref, self.init_test_inds) self.k_xy = self.kernel(tf.gather(self.x_ref, self.ref_inds), self.test_window) def _configure_ref_subset(self): """ Configure the reference data split. If the randomly selected split causes an initial detection, further splits are attempted. """ etw_size = 2 * self.window_size - 1 # etw = extended test window rw_size = self.n - etw_size # rw = ref window# # Make split and ensure it doesn't cause an initial detection mmd_init = None while mmd_init is None or mmd_init >= self.get_threshold(0): # Make split perm = tf.random.shuffle(tf.range(self.n)) self.ref_inds, self.init_test_inds = perm[:rw_size], perm[-self.window_size:] # Compute initial mmd to check for initial detection self._initialise_state() # to set self.test_window and self.k_xtc self.k_xx_sub = subset_matrix(self.k_xx, self.ref_inds, self.ref_inds) self.k_xx_sub_sum = tf.reduce_sum(zero_diag(self.k_xx_sub)) / (rw_size * (rw_size - 1)) k_yy = self.kernel(self.test_window, self.test_window) mmd_init = ( self.k_xx_sub_sum + tf.reduce_sum(zero_diag(k_yy)) / (self.window_size * (self.window_size - 1)) - 2 * tf.reduce_mean(self.k_xy) ) def _configure_thresholds(self): """ Configure the test statistic thresholds via bootstrapping. """ # Each bootstrap sample splits the reference samples into a sub-reference sample (x) # and an extended test window (y). The extended test window will be treated as W overlapping # test windows of size W (so 2W-1 test samples in total) w_size = self.window_size etw_size = 2 * w_size - 1 # etw = extended test window rw_size = self.n - etw_size # rw = ref window perms = [tf.random.shuffle(tf.range(self.n)) for _ in range(self.n_bootstraps)] x_inds_all = [perm[:-etw_size] for perm in perms] y_inds_all = [perm[-etw_size:] for perm in perms] if self.verbose: print("Generating permutations of kernel matrix..") # Need to compute mmd for each bs for each of W overlapping windows # Most of the computation can be done once however # We avoid summing the rw_size^2 submatrix for each bootstrap sample by instead computing the full # sum once and then subtracting the relavent parts (k_xx_sum = k_full_sum - 2*k_xy_sum - k_yy_sum). # We also reduce computation of k_xy_sum from O(nW) to O(W) by caching column sums k_full_sum = tf.reduce_sum(zero_diag(self.k_xx)) k_xy_col_sums_all = [ tf.reduce_sum(subset_matrix(self.k_xx, x_inds, y_inds), axis=0) for x_inds, y_inds in (tqdm(zip(x_inds_all, y_inds_all), total=self.n_bootstraps) if self.verbose else zip(x_inds_all, y_inds_all)) ] k_xx_sums_all = [( k_full_sum - tf.reduce_sum(zero_diag(subset_matrix(self.k_xx, y_inds, y_inds))) - 2 * tf.reduce_sum(k_xy_col_sums) ) / (rw_size * (rw_size - 1)) for y_inds, k_xy_col_sums in zip(y_inds_all, k_xy_col_sums_all)] k_xy_col_sums_all = [k_xy_col_sums / (rw_size * w_size) for k_xy_col_sums in k_xy_col_sums_all] # Now to iterate through the W overlapping windows thresholds = [] p_bar = tqdm(range(w_size), "Computing thresholds") if self.verbose else range(w_size) for w in p_bar: y_inds_all_w = [y_inds[w:w + w_size] for y_inds in y_inds_all] # test windows of size W mmds = [( k_xx_sum + tf.reduce_sum(zero_diag(subset_matrix(self.k_xx, y_inds_w, y_inds_w))) / (w_size * (w_size - 1)) - 2 * tf.reduce_sum(k_xy_col_sums[w:w + w_size])) for k_xx_sum, y_inds_w, k_xy_col_sums in zip(k_xx_sums_all, y_inds_all_w, k_xy_col_sums_all) ] mmds = tf.stack(mmds, axis=0) # an mmd for each bootstrap sample # Now we discard all bootstrap samples for which mmd is in top (1/ert)% and record the thresholds thresholds.append(quantile(mmds, 1 - self.fpr)) y_inds_all = [y_inds_all[i] for i in range(len(y_inds_all)) if mmds[i] < thresholds[-1]] k_xx_sums_all = [ k_xx_sums_all[i] for i in range(len(k_xx_sums_all)) if mmds[i] < thresholds[-1] ] k_xy_col_sums_all = [ k_xy_col_sums_all[i] for i in range(len(k_xy_col_sums_all)) if mmds[i] < thresholds[-1] ] self.thresholds = thresholds def _update_state(self, x_t: np.ndarray): # type: ignore[override] """ Update online state based on the provided test instance. Parameters ---------- x_t The test instance. """ self.t += 1 kernel_col = self.kernel(tf.gather(self.x_ref, self.ref_inds), x_t) self.test_window = tf.concat([self.test_window[(1 - self.window_size):], x_t], axis=0) self.k_xy = tf.concat([self.k_xy[:, (1 - self.window_size):], kernel_col], axis=1)
[docs] def score(self, x_t: Union[np.ndarray, Any]) -> float: """ Compute the test-statistic (squared MMD) between the reference window and test window. Parameters ---------- x_t A single instance to be added to the test-window. Returns ------- Squared MMD estimate between reference window and test window. """ x_t = super()._preprocess_xt(x_t) self._update_state(x_t) k_yy = self.kernel(self.test_window, self.test_window) mmd = ( self.k_xx_sub_sum + tf.reduce_sum(zero_diag(k_yy)) / (self.window_size * (self.window_size - 1)) - 2 * tf.reduce_mean(self.k_xy) ) return mmd.numpy()