Systems and methods for new time series model probabilistic ARMA

• US 7,580,813 B2
• Filed: 06/17/2003
• Issued: 08/25/2009
• Est. Priority Date: 06/17/2003
• Status: Active Grant

• Current Assignee: Microsoft Technology Licensing LLC (Microsoft Corporation)
• Original Assignee: Microsoft Corporation
• Inventors: Chickering, David M., Meek, Christopher A., Heckerman, David E., Thiesson, Bo
• Primary Examiner(s): PHAN, THAI Q
• Application Number:
  US10/463,145
• Publication Number:
  US 20040260664A1
• Time in Patent Office: 2,261 Days
• Field of Search: 703/2, 703/22, 700/31, 700/83, 700/51, 706/58, 706/20, 706/26
• US Class Current: 703/2
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04

Abstract

The present invention utilizes a cross-prediction scheme to predict values of discrete and continuous time observation data, wherein conditional variance of each continuous time tube variable is fixed to a small positive value. By allowing cross-predictions in an ARMA based model, values of continuous and discrete observations in a time series are accurately predicted. The present invention accomplishes this by extending an ARMA model such that a first time series “tube” is utilized to facilitate or “cross-predict” values in a second time series tube to form an “ARMAxp” model. In general, in the ARMAxp model, the distribution of each continuous variable is a decision graph having splits only on discrete variables and having linear regressions with continuous regressors at all leaves, and the distribution of each discrete variable is a decision graph having splits only on discrete variables and having additional distributions at all leaves.

Claims

1. A system that facilitates predicting values of time observation data in a time series, comprising:

at least one processor;

a memory communicatively coupled to the processor, the memory having stored therein processor-executable instructions configured to implement the time series prediction system including;

a component that receives a subset of time observation data that includes observations of at least one entity, the time observation data comprising at least one selected from the group consisting of discrete time observation data and continuous time observation data; and

an autoregressive, moving average cross-predictions (ARMAxp) model that predicts values of the time observation data, the ARMAxp model includes at least one variable that corresponds to the observations associated with the at least one entity and conditional variance of each continuous time tube variable is fixed to a small positive value.

2. The system of claim 1, the continuous time tube variable is approximately equal to a value of 0.01.

3. The system of claim 1, the at least one entity includes a continuous entity that varies over time.

4. The system of claim 1, the at least one entity includes a plurality of discrete and continuous entities that vary over time.

5. The system of claim 1, a distribution of each continuous variable is a decision graph having splits only on discrete variables and having linear regressions with continuous regressors at all leaves, and a distribution of each discrete variable is a decision graph having splits only on discrete variables and having additional distributions at all leaves.

6. The system of claim 5, the ARMAxp model employs exact directed acyclic graph (DAG) model inference to predict future observations of the at least one entity.

7. The system of claim 5, further comprising an expectation maximization (EM) component that learns the model based on EM.

8. The system of claim 1, further comprising a search component that identifies a model structure.

9. The system of claim 8, the search component improves a model score.

10. The system of claim 9, the search component utilizes a greedy search algorithm to improve the model score.

11. The system of claim 9, the model score is Bayesian Information Criteria (BIC).

12. A computer readable medium having stored thereon computer executable components of the system of claim 1.

13. A device employing the system of claim 1 comprising at least one selected from the group consisting of a computer, a server, and a handheld electronic device.

14. A method of predicting values of time observation data in a time series, comprising:

employing a processor executing processor-executable instructions stored on a processor-readable memory to implement one or more acts including;

providing a subset of time observation data that includes observations of at least one entity, the time observation data comprising at least one selected from the group consisting of discrete time observation data and continuous time observation data; and

predicting values of the time observation data utilizing an autoregressive, moving average cross-predictions (ARMAxp) model, the ARMAxp model includes at least one variable that corresponds to the observations associated with at least one entity; and

conditional variance of each continuous variable is fixed to a small positive value.

15. The method of claim 14, a distribution of each continuous time tube variable is a decision graph having splits only on discrete variables and having linear regressions with continuous regressors at all leaves, and a distribution of each discrete time tube variable is a decision graph having splits only on discrete variables and having additional distributions at all leaves.

16. The method of claim 15, further including:

employing exact directed acyclic graph (DAG) model inference to predict future observations of the at least one entity.

17. The method of claim 15, further including:

learning parameterization of a structure of the ARMAxp model based on an expectation maximization (EM) algorithm.

18. The method of claim 14, further including:

searching for an appropriate model structure utilizing a search component.

19. The method of claim 18, further including:

improving a model score via the search component.

20. The method of claim 19, further including:

utilizing Bayesian Information Criteria (BIC) for the model score.

21. The method of claim 14, the at least one entity includes a continuous entity varying over time.

22. The method of claim 14, the at least one entity includes a plurality of discrete and continuous entities varying over time.

23. The method of claim 14, the conditional variance of each continuous variable is approximately equal to a value of 0.01.

24. A device employing the method of claim 14 comprising at least one selected from the group consisting of a computer, a server, and a handheld electronic device.

25. A computer readable medium having stored thereon computer executable instructions for performing the method of claim 14.

26. A system for predicting values of time observation data in a time series, comprising:

means for executing computer-executable instructions stored on a computer-readable storage medium, the computer-executable instructions include;

means for predicting values of time observation data that includes observations of at least one entity utilizing an autoregressive, moving average cross-predictions (ARMAxp) model that includes at least one variable that corresponds to the observations associated with the at least one entity; and

conditional variance of each continuous time tube variable is fixed to a small positive value.

27. The system of claim 26, the time observation data comprising at least one selected from the group consisting of discrete time observation data and continuous observation data.

28. The system of claim 26, further comprising:

means for searching and scoring a model structure.

29. The system of claim 28, the means for searching and scoring including a means for improving a model score.

30. The system of claim 29, the means for improving a model score utilizing Bayesian Information Criteria (BIC) to score the model.