Change of variance detection in time series data

Patent metadata

Field	Value
Publication number	US-11222093-B2
Application number	US-202016839922-A
Country	US
Kind code	B2
Filing date	Apr 3, 2020
Priority date	Apr 3, 2020
Publication date	Jan 11, 2022
Grant date	Jan 11, 2022

Abstract

The present disclosure provides detecting change of variance points of a target time series based on baseline assumptions of statistical stationarity. A target time series signal is modeled as including a trend component signal and a residual component signal. A signal cost function including at least a difference penalty function and at least one regularization term is optimized for the target signal to output a trend component signal thereof. A signal cost function including at least a difference penalty function and at least one regularization term is optimized for the residual component signal to output estimated variance thereof. Both of these cost functions may be optimized by applying an augmented Lagrangian operator. A centered cumulative sum is computed based on a cumulative sum of the estimated variance. The centered cumulative sum is segmented to yield change of variance points thereof. Such methods may provide improved performance over existing methods.

First claim

What is claimed is:

1. A method comprising:
optimizing a variance filter signal cost function for a residual component signal of a target signal of a time series to output estimated variance thereof;
computing a centered cumulative sum of the estimated variance of the residual component signal over time;
segmenting the centered cumulative sum to yield one or more change of variance points of the target signal; and
optimizing a trend removal signal cost function for the target signal to output a trend component signal thereof,
wherein the residual component signal is obtained by a difference of the trend component signal subtracted from the target signal.

2. The method of claim 1 , wherein the residual component signal is obtained by further squaring the difference of the trend component signal subtracted from the target signal.

3. The method of claim 1 , wherein the trend removal signal cost function and the variance filter signal cost function each comprises, respectively, at least a difference penalty function and at least one regularization term.

4. The method of claim 3 , wherein each respective difference penalty function comprises a Huber loss function.

5. The method of claim 3 , wherein each respective at least one regularization term comprises a sparse regularization term.

6. The method of claim 1 , wherein optimizing the trend removal signal cost function and optimizing the variance filter signal cost function, respectively, each comprises optimizing an augmented Lagrangian operator.

7. A system comprising:
one or more processors; and
memory communicatively coupled to the one or more processors, the memory storing computer-executable modules executable by the one or more processors that, when executed by the one or more processors, perform associated operations, the computer-executable modules comprising:
a variance filtering module further comprising a variance filtering cost function optimizing module configured to optimize a variance filter signal cost function for a residual component signal of a target signal of a time series to output estimated variance thereof;
a change point locating module further comprising:
a centered cumulative sum computing submodule configured to compute a centered cumulative sum of the estimated variance of the residual component signal over time, and
a segmenting submodule configured to segment the centered cumulative sum to yield one or more change of variance points of the target signal;

a trend removal cost function optimizing submodule configured to optimize a trend removal signal cost function for the target signal to output a trend component signal thereof; and
a trend component subtracting submodule configured to obtain the residual component signal by a difference of the trend component signal subtracted from the target signal.

8. The system of claim 7 , wherein the variance filtering module further comprises a residual component squaring submodule configured to square the difference of the trend component signal subtracted from the target signal.

9. The system of claim 7 , wherein the trend removal signal cost function and the variance filter signal cost function each comprises, respectively, at least a difference penalty function and at least one regularization term.

10. The system of claim 9 , wherein each respective difference penalty function comprises a Huber loss function.

11. The system of claim 9 , wherein each respective at least one regularization term comprises a sparse regularization term.

12. The system of claim 7 , wherein the trend removal cost function optimizing submodule and the variance filtering cost function optimizing submodule are configured to optimize the trend removal signal cost function and optimize the variance filter signal cost function, respectively, by optimizing an augmented Lagrangian operator.

13. A computer-readable storage medium storing computer-readable instructions executable by one or more processors, that when executed by the one or more processors, cause the one or more processors to perform operations comprising:
optimizing a variance filter signal cost function for a residual component signal of a target signal of a time series to output estimated variance thereof;
computing a centered cumulative sum of the estimated variance of the residual component signal over time;
segmenting the centered cumulative sum to yield one or more change of variance points of the target signal;
optimizing a trend removal signal cost function for the target signal to output a trend component signal thereof,
wherein the residual component signal is obtained by a difference of the trend component signal subtracted from the target signal.

14. The computer-readable storage medium of claim 13 , wherein the residual component signal is obtained by further squaring the difference of the trend component signal subtracted from the target signal.

15. The computer-readable storage medium of claim 13 , wherein the trend removal signal cost function and the variance filter signal cost function each comprises, respectively, at least a difference penalty function and at least one regularization term.

16. The computer-readable storage medium of claim 15 , wherein each respective difference penalty function comprises a Huber loss function.

17. The computer-readable storage medium of claim 15 , wherein each respective at least one regularization term comprises a sparse regularization term.

18. The computer-readable storage medium of claim 13 , wherein optimizing the trend removal signal cost function and optimizing the variance filter signal cost function, respectively, each comprises optimizing an augmented Lagrangian operator.

Assignees

• Alibaba Group Holding Ltd

Inventors

• Wen Qingsong
• Sun Liang
• Xu Huan

Classifications

• G06F17/18 Primary

  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)} · CPC title

• G06F2111/04

  Constraint-based CAD · CPC title

• G06F30/20 Primary

  Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) · CPC title

• G06Q10/04

  Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem" (market predictions or forecasting for commercial activities G06Q30/0202) · CPC title

• G06F17/15

  Correlation function computation {including computation of convolution operations (arithmetic circuits for sum of products per se, e.g. multiply-accumulators G06F7/5443; digital filters, e.g. FIR, IIR, adaptive filters H03H17/00)} · CPC title