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 import GaussianRBF, quantile, permed_lsdds
from alibi_detect.utils.frameworks import Framework

[docs] class LSDDDriftOnlineTF(BaseMultiDriftOnline): online_state_keys: tuple = ('t', 'test_stats', 'drift_preds', 'test_window', 'k_xtc')
[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, sigma: Optional[np.ndarray] = None, n_bootstraps: int = 1000, n_kernel_centers: Optional[int] = None, lambda_rd_max: float = 0.2, verbose: bool = True, input_shape: Optional[tuple] = None, data_type: Optional[str] = None ) -> None: """ Online least squares density difference (LSDD) data drift detector using preconfigured thresholds. Motivated by Bu et al. (2017): Modifications are made such that a desired ERT can be accurately targeted however. 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. 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_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. n_kernel_centers The number of reference samples to use as centers in the Gaussian kernel model used to estimate LSDD. Defaults to 2*window_size. 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. 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}) self.n_kernel_centers = n_kernel_centers self.lambda_rd_max = lambda_rd_max self._configure_normalization() # initialize kernel if sigma is None: self.kernel = GaussianRBF() _ = self.kernel(self.x_ref, self.x_ref, infer_sigma=True) else: sigma = tf.convert_to_tensor(sigma) self.kernel = GaussianRBF(sigma) if self.n_kernel_centers is None: self.n_kernel_centers = 2*window_size self._configure_kernel_centers() self._configure_thresholds() self._configure_ref_subset() # self.initialise_state() called inside here
def _configure_normalization(self, eps: float = 1e-12): """ Configure the normalization functions used to normalize reference and test data to zero mean and unit variance. The reference data `x_ref` is also normalized here. """ x_ref_means = tf.reduce_mean(self.x_ref, axis=0) x_ref_stds = tf.math.reduce_std(self.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() self.x_ref = self._normalize(self.x_ref) def _configure_kernel_centers(self): "Set aside reference samples to act as kernel centers" perm = tf.random.shuffle(tf.range(self.n)) self.c_inds, self.non_c_inds = perm[:self.n_kernel_centers], perm[self.n_kernel_centers:] self.kernel_centers = tf.gather(self.x_ref, self.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 self.x_ref_eff = tf.gather(self.x_ref, self.non_c_inds) # the effective reference set self.k_xc = self.kernel(self.x_ref_eff, self.kernel_centers) 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 nkc_size = self.n - self.n_kernel_centers # nkc = non-kernel-centers rw_size = nkc_size - etw_size # rw = ref-window perms = [tf.random.shuffle(tf.range(nkc_size)) for _ in range(self.n_bootstraps)] x_inds_all = [perm[:rw_size] for perm in perms] y_inds_all = [perm[rw_size:] for perm in perms] # 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. H = GaussianRBF(np.sqrt(2.)*self.kernel.sigma)(self.kernel_centers, self.kernel_centers) # Compute lsdds for first test-window. We infer regularisation constant lambda here. y_inds_all_0 = [y_inds[:w_size] for y_inds in y_inds_all] lsdds_0, H_lam_inv = permed_lsdds( self.k_xc, x_inds_all, y_inds_all_0, H, lam_rd_max=self.lambda_rd_max, ) # Can compute threshold for first window thresholds = [quantile(lsdds_0, 1-self.fpr)] # And now to iterate through the other W-1 overlapping windows p_bar = tqdm(range(1, w_size), "Computing thresholds") if self.verbose else range(1, w_size) for w in p_bar: y_inds_all_w = [y_inds[w:(w+w_size)] for y_inds in y_inds_all] lsdds_w, _ = permed_lsdds(self.k_xc, x_inds_all, y_inds_all_w, H, H_lam_inv=H_lam_inv) thresholds.append(quantile(lsdds_w, 1-self.fpr)) x_inds_all = [x_inds_all[i] for i in range(len(x_inds_all)) if lsdds_w[i] < thresholds[-1]] y_inds_all = [y_inds_all[i] for i in range(len(y_inds_all)) if lsdds_w[i] < thresholds[-1]] self.thresholds = thresholds self.H_lam_inv = H_lam_inv 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_eff, self.init_test_inds) self.k_xtc = self.kernel(self.test_window, self.kernel_centers) 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 nkc_size = self.n - self.n_kernel_centers # nkc = non-kernel-centers rw_size = nkc_size - etw_size # rw = ref-window # Make split and ensure it doesn't cause an initial detection lsdd_init = None while lsdd_init is None or lsdd_init >= self.get_threshold(0): # Make split perm = tf.random.shuffle(tf.range(nkc_size)) self.ref_inds, self.init_test_inds = perm[:rw_size], perm[-self.window_size:] self.c2s = tf.reduce_mean(tf.gather(self.k_xc, self.ref_inds), axis=0) # (below Eqn 21) # Compute initial lsdd to check for initial detection self._initialise_state() # to set self.test_window and self.k_xtc h_init = self.c2s - tf.reduce_mean(self.k_xtc, axis=0) # (Eqn 21) lsdd_init = h_init[None, :] @ self.H_lam_inv @ h_init[:, None] # (Eqn 11) def _update_state(self, x_t: tf.Tensor): """ Update online state based on the provided test instance. Parameters ---------- x_t The test instance. """ self.t += 1 k_xtc = self.kernel(x_t, self.kernel_centers) self.test_window = tf.concat([self.test_window[(1-self.window_size):], x_t], axis=0) self.k_xtc = tf.concat([self.k_xtc[(1-self.window_size):], k_xtc], axis=0)
[docs] def score(self, x_t: Union[np.ndarray, Any]) -> float: """ Compute the test-statistic (LSDD) between the reference window and test window. Parameters ---------- x_t A single instance to be added to the test-window. Returns ------- LSDD estimate between reference window and test window. """ x_t = super()._preprocess_xt(x_t) x_t = tf.convert_to_tensor(x_t) x_t = self._normalize(x_t) self._update_state(x_t) h = self.c2s - tf.reduce_mean(self.k_xtc, axis=0) # (Eqn 21) lsdd = h[None, :] @ self.H_lam_inv @ h[:, None] # (Eqn 11) return float(lsdd)