Detecting Drift in Datasets
What is it
When to use it
The dataeval.metrics.drift detector classes should be used when you would like to measure new data for operational drift.
Theory behind it
Cramér-von Mises
The CVM drift detector is a non-parametric drift detector, which applies feature-wise two-sample Cramér-von Mises (CVM) tests. For two empirical distributions \(F(z)\) and \(F_{ref}(z)\), the CVM test statistic is defined as
where \(k\) is the joint sample. The CVM test is an alternative to the [Kolmogorov-Smirnov] (K-S) two-sample test, which uses the maximum distance between two empirical distributions \(F(z)\) and \(F_{ref}(z)\). By using the full joint sample, the CVM can exhibit greater power against shifts in higher moments, such as variance changes.
For multivariate data, the detector applies a separate CVM test to each feature, and the p-values obtained for each feature are aggregated either via the [Bonferroni] or the [False Discovery Rate] (FDR) correction. The Bonferroni correction is more conservative and controls for the probability of at least one false positive. The FDR correction on the other hand allows for an expected fraction of false positives to occur. As with other univariate detectors such as the [Kolmogorov-Smirnov] detector, for high-dimensional data, we typically want to reduce the dimensionality before computing the feature-wise univariate FET tests and aggregating those via the chosen correction method.
Kolmogorov-Smirnov
The drift detector applies feature-wise two-sample [Kolmogorov-Smirnov] (K-S) tests. For multivariate data, the obtained p-values for each feature are aggregated either via the [Bonferroni] or the [False Discovery Rate] (FDR) correction. The Bonferroni correction is more conservative and controls for the probability of at least one false positive. The FDR correction on the other hand allows for an expected fraction of false positives to occur.
Maximum Mean Discrepancy
The [Maximum Mean Discrepancy] (MMD) detector is a kernel-based method for multivariate 2 sample testing. The MMD is a distance-based measure between 2 distributions p and q based on the mean embeddings \(\mu_{p}\) and \(\mu_{q}\) in a reproducing kernel Hilbert space \(F\):
We can compute unbiased estimates of \(MMD^2\) from the samples of the 2 distributions after applying the kernel trick. We use by default a radial basis function kernel, but users are free to pass their own kernel of preference to the detector. We obtain a \(p\)-value via a permutation test on the values of \(MMD^2\).
Classifier Uncertainty
The classifier uncertainty drift detector aims to directly detect drift that is likely to effect the performance of a model of interest. The approach is to test for change in the number of instances falling into regions of the input space on which the model is uncertain in its predictions. For each instance in the reference set the detector obtains the model’s prediction and some associated notion of uncertainty. The same is done for the test set and if significant differences in uncertainty are detected (via a [Kolmogorov-Smirnov] test) then drift is flagged. The detector’s reference set should be disjoint from the model’s training set (on which the model’s confidence may be higher).
GaussianRBF
The GaussianRBF class implements a Gaussian kernel, also known as a [radial basis function] (RBF) kernel. It is used to construct a covariance matrix for gaussian processes and is the default kernel used in the MMD drift detection test.