While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift---a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (\ie gradient with respect to the input)---which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models. We additionally develop methods for identifying when and where a shift occurs in multivariate time-series data and show results for multiple scenarios using realistic attack models on both simulated and real-world data.

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift---a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (\ie gradient with respect to the input)---which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models.

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift---a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (\ie gradient with respect to the input)---which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models.

In this paper, we address conditional testing problems through the conformal inference framework. We define the localized conformal p-values by inverting prediction intervals and prove their theoretical properties. These defined p-values are then applied to several conditional testing problems to illustrate their practicality. Firstly, we propose a conditional outlier detection procedure to test for outliers in the conditional distribution with finite-sample false discovery rate (FDR) control. We also introduce a novel conditional label screening problem with the goal of screening multivariate response variables and propose a screening procedure to control the family-wise error rate (FWER). Finally, we consider the two-sample conditional distribution test and define a weighted U-statistic through the aggregation of localized p-values. Numerical simulations and real-data examples validate the superior performance of our proposed strategies.