Methods and apparatus for real-time anomaly detection over sets of time-series data

1. A method, comprising:

obtaining a state-space representation of a plurality of states of a given system and transitions between said states based on sets of historical time-series data, wherein the sets of historical time-series data comprise time-series data from a plurality of executions of one or more processes of the given system;

obtaining a plurality of event-anomaly models for respective ones of a plurality of different anomalies, wherein each event-anomaly model is separately learned using a supervised learning technique, wherein a given event-anomaly model of the plurality of event-anomaly models:

(i) comprises a support for one or more sequences of states that lead to a respective annotated anomaly, wherein the respective annotated anomaly is annotated in one or more of the sets of historical time-series data by a domain expert, wherein the support for a given sequence of states that leads to the respective annotated anomaly is based at least in part on a number of occurrences of instances of the given sequence of states that leads to the respective annotated anomaly in the sets of historical time-series data,

(ii) processes states derived from the sets of historical time-series data,

(iii) is separately learned, from the other event-anomaly models, to predict events comprising one or more sequences of states in the obtained state-space representation that lead to the respective annotated anomaly in the sets of historical time-series data, and

(iv) assigns a probability of occurrence to said events, wherein the probability of occurrence of a given event comprises an aggregation of the support for the one or more sequences of states of the given event,

wherein a learning of the given event-anomaly model evaluates a length of the sequences of states that lead to the respective annotated anomaly and updates the given event-anomaly model with the support of the sequences of states that lead to the respective annotated anomaly;

performing the following steps for real-time time-series data, for two or more of the plurality of event-anomaly models:

mapping a current time window of the real-time time-series data to at least one state in the real-time time-series data, wherein the real-time time-series data is obtained at least in part from one or more sensors;

determining a likelihood of one or more events in the real-time time-series data that comprise the at least one state; and

determining a probability of an instance of said respective anomaly associated with the respective event-anomaly model occurring in the real-time time-series data based at least in part on the determined likelihoods of the one or more events in the real-time time-series data that satisfy one or more predefined likelihood criteria; and

performing at least one automated action for a given instance of a particular anomaly detected based at least in part on the determined probabilities for respective ones of the plurality of different anomalies.

2. The method of claim 1 , wherein the step of determining said likelihood of said one or more events further comprises determining a likelihood of a next state based on probabilities of a prior state and a current time-series measurement.

3. The method of claim 1 , wherein the step of determining said probability of said instance of said respective anomaly associated with the event-anomaly model occurring in the real-time time-series data further comprises identifying a set of most likely state sequences based on a likelihood of said state sequences; determining a likelihood of incurring one or more of said annotated anomalies for each of said most likely state sequences from the event-anomaly model; and calculating said probability of said one or more states in the real-time time-series data incurring one or more of said annotated anomalies based on said likelihood of said most likely state sequences in said set with said likelihoods for each of said most likely state sequences from the event-anomaly model.

4. The method of claim 1 , wherein a particular observation from a set of time series in the state-space representation corresponds to a state originally observed in a different set of time-series data.

5. The method of claim 1 , wherein the supervised learning technique comprises a process mining technique.

6. The method of claim 1 , wherein said obtaining said state-space representation comprises extracting a Hidden Markov Model (HMM), wherein said transitions are weighted based on a probability of the respective transition.

7. The method of claim 6 , wherein the HMM is extracted using a sticky Hierarchical Dirichlet Processes Hidden Markov Model formulation, where a knowledge of the cardinality of a set of states of said Hidden Markov Model is not required.

8. The method of claim 1 , further comprising the step of distinguishing between anomalous behavior and previously unknown behavior based on a predefined likelihood threshold.

9. The method of claim 8 , wherein an observation in the real-time time-series data that does not satisfy the predefined likelihood threshold comprises a previously unknown state.

10. The method of claim 9 , wherein said previously unknown state is classified based on one or more of a substantially complete event-anomaly model and domain knowledge.

11. The method of claim 8 , further comprising the step of relearning said event-anomaly model in response to one or more states classified as previously unknown behavior.

12. A computer program product, comprising a non-transitory machine-readable storage medium having encoded therein executable code of one or more software programs, wherein the one or more software programs when executed by at least one processing device perform the following steps:

obtaining a state-space representation of a plurality of states of a given system and transitions between said states based on sets of historical time-series data, wherein the sets of historical time-series data comprise time-series data from a plurality of executions of one or more processes of the given system;

obtaining a plurality of event-anomaly models for respective ones of a plurality of different anomalies, wherein each event-anomaly model is separately learned using a supervised learning technique, wherein a given event-anomaly model of the plurality of event-anomaly models:

(i) comprises a support for one or more sequences of states that lead to a respective annotated anomaly, wherein the respective annotated anomaly is annotated in one or more of the sets of historical time-series data by a domain expert, wherein the support for a given sequence of states that leads to the respective annotated anomaly is based at least in part on a number of occurrences of instances of the given sequence of states that leads to the respective annotated anomaly in the sets of historical time-series data,

(ii) processes states derived from the sets of historical time-series data,

(iii) is separately learned, from the other event-anomaly models, to predict events comprising one or more sequences of states in the obtained state-space representation that lead to the respective annotated anomaly in the sets of historical time-series data, and

(iv) assigns a probability of occurrence to said events, wherein the probability of occurrence of a given event comprises an aggregation of the support for the one or more sequences of states of the given event,

wherein a learning of the given event-anomaly model evaluates a length of the sequences of states that lead to the respective annotated anomaly and updates the given event-anomaly model with the support of the sequences of states that lead to the respective annotated anomaly;

performing the following steps for real-time time-series data, for two or more of the plurality of event-anomaly models:

mapping a current time window of the real-time time-series data to at least one state in the real-time time-series data, wherein the real-time time-series data is obtained at least in part from one or more sensors;

determining a likelihood of one or more events in the real-time time-series data that comprise the at least one state; and

determining a probability of an instance of said respective anomaly associated with the respective event-anomaly model occurring in the real-time time-series data based at least in part on the determined likelihoods of the one or more events in the real-time time-series data that satisfy one or more predefined likelihood criteria; and

performing at least one automated action for a given instance of a particular anomaly detected based at least in part on the determined probabilities for respective ones of the plurality of different anomalies.

13. The computer program product of claim 12 , wherein the step of determining said likelihood of said one or more events further comprises determining a likelihood of a next state based on probabilities of a prior state and a current time-series measurement.

14. The computer program product of claim 12 , wherein the step of determining said probability of said instance of said respective anomaly associated with the event-anomaly model occurring in the real-time time-series data further comprises identifying a set of most likely state sequences based on a likelihood of said state sequences; determining a likelihood of incurring one or more of said annotated anomalies for each of said most likely state sequences from the event-anomaly model; and calculating said probability of said one or more states in the real-time time-series data incurring one or more of said annotated anomalies based on said likelihood of said most likely state sequences in said set with said likelihoods for each of said most likely state sequences from the event-anomaly model.

15. The computer program product of claim 12 , further comprising the step of distinguishing between anomalous behavior and previously unknown behavior based on a predefined likelihood threshold.

16. An apparatus, comprising:

a memory; and

at least one processing device, coupled to the memory, operative to implement the following steps:

obtaining a state-space representation of a plurality of states of a given system and transitions between said states based on sets of historical time-series data, wherein the sets of historical time-series data comprise time-series data from a plurality of executions of one or more processes of the given system;

obtaining a plurality of event-anomaly models for respective ones of a plurality of different anomalies, wherein each event-anomaly model is separately learned using a supervised learning technique, wherein a given event-anomaly model of the plurality of event-anomaly models:

(i) comprises a support for one or more sequences of states that lead to a respective annotated anomaly, wherein the respective annotated anomaly is annotated in one or more of the sets of historical time-series data by a domain expert, wherein the support for a given sequence of states that leads to the respective annotated anomaly is based at least in part on a number of occurrences of instances of the given sequence of states that leads to the respective annotated anomaly in the sets of historical time-series data,

(ii) processes states derived from the sets of historical time-series data,

(iii) is separately learned, from the other event-anomaly models, to predict events comprising one or more sequences of states in the obtained state-space representation that lead to the respective annotated anomaly in the sets of historical time-series data, and

(iv) assigns a probability of occurrence to said events, wherein the probability of occurrence of a given event comprises an aggregation of the support for the one or more sequences of states of the given event,

wherein a learning of the given event-anomaly model evaluates a length of the sequences of states that lead to the respective annotated anomaly and updates the given event-anomaly model with the support of the sequences of states that lead to the respective annotated anomaly;

performing the following steps for real-time time-series data, for two or more of the plurality of event-anomaly models:

mapping a current time window of the real-time time-series data to at least one state in the real-time time-series data, wherein the real-time time-series data is obtained at least in part from one or more sensors;

determining a likelihood of one or more events in the real-time time-series data that comprise the at least one state; and

determining a probability of an instance of said respective anomaly associated with the respective event-anomaly model occurring in the real-time time-series data based at least in part on the determined likelihoods of the one or more events in the real-time time-series data that satisfy one or more predefined likelihood criteria; and

performing at least one automated action for a given instance of a particular anomaly detected based at least in part on the determined probabilities for respective ones of the plurality of different anomalies.

17. The apparatus of claim 16 , wherein the step of determining said probability of said instance of said respective anomaly associated with the event-anomaly model occurring in the real-time time-series data further comprises identifying a set of most likely state sequences based on a likelihood of said state sequences; determining a likelihood of incurring one or more of said annotated anomalies for each of said most likely state sequences from the event-anomaly model; and calculating said probability of said one or more states in the real-time time-series data incurring one or more of said annotated anomalies based on said likelihood of said most likely state sequences in said set with said likelihoods for each of said most likely state sequences from the event-anomaly model.

18. The apparatus of claim 16 , wherein said obtaining said state-space representation comprises extracting a Hidden Markov Model (HMM), wherein said transitions are weighted based on a probability of the respective transition.

19. The apparatus of claim 16 , further comprising the steps of distinguishing between anomalous behavior and previously unknown behavior based on a predefined likelihood threshold and retraining said event-anomaly model in response to one or more states classified as previously unknown behavior.

20. The method of claim 1 , wherein the at least one automated action comprises one or more of implementing one or more policies to address a detected anomaly; and updating the state-space representation to account for previously unknown behavior.