Method and system for adaptively imputing sparse and missing data for predictive models
Described is an approach that provides an adaptive solution to missing data for machine learning systems. A gradient solution is provided that is attentive to imputation needs at each of several missingness levels. This multilevel approach treats data missingness at any of multiple severity levels while utilizing, as much as possible, the actual observed data.
1. A method for imputing data for a learning system, comprising:
collecting data from a monitored target system;
determining one or more levels of missingness for the data collected from the monitored target system, wherein
the one or more levels of missingness for the data at least comprise a first factor corresponding to a respective degree of missingness for each of a plurality of signal patterns in the data, wherein a signal pattern is comprised of at least one or more of a first value or one or more of a second value, the first value indicating that the data is missing and the second value indicating that the data is not missing, and a degree of missingness for a signal pattern is determined at least by identifying a percentage of the data that corresponds to the signal pattern;
adaptively selecting a technique to correct the data for missing data, wherein the data is selectively corrected by a first technique for a relatively lower level of the missing data or selectively corrected by a second technique for a relatively greater level of the missing data, wherein detection of a first missingness level is addressed by the first technique by imputing the missing data using an iterative imputation technique to generate training data without using new data from an external data source, and detection of a second missingness level that is greater than the first missingness level is addressed by the second technique to generate the training data by adding the new data from the external data source; and
performing model training with the training data.
2. The method of claim 1 , wherein
the one or more levels of missingness for the data comprise a second factor corresponding to an overall degree of missingness for the data.
3. The method of claim 1 , wherein
the technique is selected from a plurality of techniques that comprises some or all of a first imputation technique that performs expectation maximization to impute the missing data at the first missingness level, a second imputation technique that performs the expectation maximization with the new data from the external data source at the second missingness level, a third imputation technique that generates the training data using predicted values from a predictive model at a third missingness level, or a fourth imputation technique that performs simulation to generate the training data at a fourth missingness level.
4. The method of claim 1 , wherein
expectation maximization is selected as the selected technique based upon both an overall level of missing data and individual levels of missing data for signals.
5. The method of claim 4 , wherein
the external data source is accessed to generate an EM seed for the expectation maximization when insufficient seed data exists within the data collected from the monitored target system.
6. The method of claim 1 , wherein
a second imputation technique is selected to impute the missing data when a first imputation technique does not successfully generate the missing data.
7. The method of claim 1 , wherein
the model training generates a predictive model that is employed for health monitoring of a database system.
8. The method of claim 1 , wherein
the plurality of signal patterns in the data comprise at least a first pattern and a second pattern, wherein
the first pattern corresponds to a first permutation of missing and not missing signals and a second pattern corresponds to a second permutation of missing and not missing signals.
9. A system for imputing data for a machine learning system, comprising:
a processor; and
a memory for holding programmable code,
wherein the programmable code includes instructions for collecting data from a monitored target system;
determining one or more levels of missingness for the data collected from the monitored target system, wherein
the one or more levels of missingness for the data at least comprise a first factor corresponding to a respective degree of missingness for each of a plurality of signal patterns in the data, wherein a signal pattern is comprised of at least one or more of a first value or one or more of a second value, the first value indicating that the data is missing and the second value indicating that the data is not missing, and a degree of missingness for a signal pattern is determined at least by identifying a percentage of the data that corresponds to the signal pattern;
adaptively selecting a technique to correct the data for missing data, wherein the data is selectively corrected by a first technique for a relatively lower level of the missing data or selectively corrected by a second technique for a relatively greater level of the missing data, wherein detection of a first missingness level is addressed by the first technique by imputing the missing data using an iterative imputation technique to generate training data without using new data from an external data source, and detection of a second missingness level that is greater than the first missingness level is addressed by the second technique to generate the training data by adding the new data from the external data source; and
performing model training with the training data.
10. The system of claim 9 , wherein
the one or more levels of missingness for the data comprise a second factor corresponding to an overall degree of missingness for the data.
11. The system of claim 9 , wherein
the technique is selected from a plurality of techniques that comprises some or all of a first imputation technique that performs expectation maximization to impute the missing data at the first missingness level, a second imputation technique that performs the expectation maximization with the new data from the external data source at the second missingness level, a third imputation technique that generates the training data using predicted values from a predictive model at a third missingness level, or a fourth imputation technique that performs simulation to generate the training data at a fourth missingness level.
12. The system of claim 9 , wherein
expectation maximization is selected as the selected technique based upon both an overall level of missing data and individual levels of missing data for signals.
13. The system of claim 12 , wherein
the external data source is accessed to generate an EM seed for the expectation maximization when insufficient seed data exists within the data collected from the monitored target system.
14. The system of claim 9 , wherein
a second imputation technique is selected to impute the missing data when a first imputation technique does not successfully generate the missing data.
15. The system of claim 9 , wherein
the model training generates a predictive model that is employed for health monitoring of a database system.
16. A non-transitory computer readable medium having stored thereon a sequence of instructions which, when executed by a processor, executes a method comprising:
collecting data from a monitored target system;
determining one or more levels of missingness for the data collected from the monitored target system, wherein
the one or more levels of missingness for the data at least comprise a first factor corresponding to a respective degree of missingness for each of a plurality of signal patterns in the data, wherein a signal pattern is comprised of at least one or more of a first value or one or more of a second value, the first value indicating that the data is missing and the second value indicating that the data is not missing, and a degree of missingness for a signal pattern is determined at least by identifying a percentage of the data that corresponds to the signal pattern;
adaptively selecting a technique to correct the data for missing data, wherein the data is selectively corrected by a first technique for a relatively lower level of the missing data or selectively corrected by a second technique for a relatively greater level of the missing data, wherein detection of a first missingness level is addressed by the first technique by imputing the missing data using an iterative imputation technique to generate training data without using new data from an external data source, and detection of a second missingness level that is greater than the first missingness level is addressed by the second technique to generate the training data by adding the new data from the external data source; and
performing model training with the training data.
17. The non-transitory computer readable medium of claim 16 , wherein
the one or more levels of missingness for the data comprise a second factor corresponding to an overall degree of missingness for the data.
18. The non-transitory computer readable medium of claim 16 , wherein
the technique is selected from a plurality of techniques that comprises some or all of a first imputation technique that performs expectation maximization to impute the missing data at the first missingness level, a second imputation technique that performs the expectation maximization with the new data from the external data source at the second missingness level, a third imputation technique that generates the training data using predicted values from a predictive model at a third missingness level, or a fourth imputation technique that performs simulation to generate the training data at a fourth missingness level.
19. The non-transitory computer readable medium of claim 16 , wherein
expectation maximization is selected as the technique based upon both an overall level of missing data and individual levels of missing data for signals.
20. The non-transitory computer readable medium of claim 19 , wherein
the external data source is accessed to generate an EM seed for the expectation maximization when insufficient seed data exists within the data collected from the monitored target system.
21. The non-transitory computer readable medium of claim 16 , wherein
a second imputation technique is selected to impute the missing data when a first imputation technique does not successfully generate the missing data.
22. The non-transitory computer readable medium of claim 16 , wherein
the model training generates a predictive model that is employed for health monitoring of a database system.