Measurement result analysis by anomaly detection and identification of anomalous variables

1. A computer implemented method of analyzing measurement results of a target system, the method comprising:

receiving a data sample comprising a plurality of variables representing the measurement results,

detecting that the data sample is an anomalous sample using an anomaly detection model,

processing the data sample by separately applying an imputation model to a plurality of selected subsets of variables of the data sample to obtain a plurality of imputed samples, and applying the anomaly detection model to the imputed samples to obtain respective anomaly scores,

determining anomalous variables of the data sample based on results from the processing of the data sample, and

outputting the anomalous variables of the data sample for management operations in the target system.

2. The method of claim 1 , wherein the target system is an industrial process.

3. The method of claim 2 , wherein the measurement results comprise sensor data from the industrial process.

4. The method of claim 1 , wherein the target system is a communication network.

5. The method of claim 4 , wherein the measurement results comprise performance metrics from the communication network.

6. The method of claim 1 , further comprising

separately applying the imputation model to a plurality of selected subsets of variables of the data sample to obtain a plurality of imputed samples comprising imputed variables,

applying the anomaly detection model to the imputed samples to obtain respective anomaly scores,

selecting the imputed sample with lowest anomaly score, and

choosing the imputed variables of the selected imputed sample as the anomalous variables of the data sample.

7. The method of claim 6 , wherein the subsets of the variables are preselected based on the target system.

8. The method of claim 1 , further comprising

separately imputing individual variables of the data sample using the imputation model to obtain a plurality of imputed samples comprising an imputed variable,

applying the anomaly detection model to the imputed samples to obtain respective anomaly scores,

selecting the imputed sample with lowest anomaly score and freezing value of an associated imputed variable,

repeating the imputing, applying and selecting phases for the variables with unfrozen values until anomaly score of the selected imputed sample ceases to indicate anomaly; and

choosing the variables with a frozen value as the anomalous variables of the data sample.

9. An apparatus comprising

a processor, and

a memory including computer program code; the memory and the computer program code configured to, with the processor, cause the apparatus to perform:

receiving a data sample comprising a plurality of variables representing the measurement results,

detecting that the data sample is an anomalous sample using an anomaly detection model,

processing the data sample by separately applying an imputation model to a plurality of selected subsets of variables of the data sample to obtain a plurality of imputed samples, and applying the anomaly detection model to the imputed samples to obtain respective anomaly scores,

determining anomalous variables of the data sample based on results from the processing of the data sample, and

outputting the anomalous variables of the data sample for management operations in the target system.

10. A non-transitory memory medium comprising computer executable program code which when executed by a processor causes an apparatus to perform:

receiving a data sample comprising a plurality of variables representing the measurement results,

detecting that the data sample is an anomalous sample using an anomaly detection model,

processing the data sample by separately applying an imputation model to a plurality of selected subsets of variables of the data sample to obtain a plurality of imputed samples, and applying the anomaly detection model to the imputed samples to obtain respective anomaly scores,

determining anomalous variables of the data sample based on results from the processing of the data sample, and

outputting the anomalous variables of the data sample for management operations in the target system.