Information processing system, change point detection method, and recording medium

1. An information processing system comprising:

a memory storing instructions, and

one or more processors configured to execute the instructions to:

learn, with respect to each of a plurality of time series, models that approximate partial time series respectively and that are defined by parameters of the partial time series respectively, the partial time series being obtained by dividing a corresponding time series into a plurality of segments at change point candidates;

calculate, with respect to each of the change point candidates for the plurality of time series, a difference between a parameter of a first partial time series starting from a time point of a corresponding change point candidate and a parameter of a second partial time series before the corresponding change point candidate;

extract change point candidates for which the calculated difference exceeds a predetermined threshold as local change points;

detect a global change point that is a change point for the plurality of time series based on a distribution of the extracted local change points; and

output the global change point.

2. The information processing system according to claim 1 , wherein

the one or more processors is further configured to execute the instructions to:

set a loss function with respect to approximate values for values of a time series, the approximate values being calculated based on the parameters; and

set a first penalty term whose value increases as an amount of change in the parameters of a single time series out of the plurality of time series increases and a second penalty term whose value decreases as a number of the plurality of time series whose parameters change at a predetermined time increases out of the plurality of time series, and

parameters that minimize a sum of the loss function, the first penalty term, and the second penalty term for respective partial time series of all time series in the plurality of time series are calculated by using an optimization algorithm.

3. The information processing system according to claim 2 , wherein the one or more processors are further configured to execute the instructions to:

set, as the first penalty term, an absolute value sum of amounts of change in parameters at the respective change point candidates.

4. The information processing system according to claim 2 , wherein the one or more processors are further configured to execute the instructions to:

set, as the second penalty term, a square root of a square sum of amounts of change in parameters at the respective change point candidates, the square sum being taken over all time series is set.

5. The information processing system according to claim 2 , wherein the one or more processors are further configured to execute the instructions to:

use, as the optimization algorithm, an alternating direction method of multiplies.

6. The information processing system according to claim 1 , wherein the one or more processors are further configured to execute the instructions to:

output, with respect to the global change point, information indicating how and which time series causes a change point candidate to be detected as the global change point.

7. The information processing system according to claim 1 , wherein the one or more processors are further configured to execute the instructions to: detect, as the global change point, a time point that locally maximizes a density of the distribution of the extracted local change points.

8. The information processing system according to claim 1 , wherein the one or more processors are further configured to execute the instructions to: output the global change point to a display device that displays a graph indicating the global change point with the plurality of time series.

9. A change point detection method performed by a computer comprising:

learning, with respect to each of a plurality of time series, models that approximate partial time series respectively and that are defined by parameters of the partial time series respectively, the partial time series being obtained by dividing a corresponding time series into a plurality of segments at change point candidates;

calculating, with respect to each of the change point candidates for the plurality of time series, a difference between a parameter of a first partial time series starting from a time point of a corresponding change point candidate and a parameter of a second partial time series before the corresponding change point candidate;

extracting change point candidates for which the calculated difference exceeds a predetermined threshold as local change points;

detecting a global change point that is a change point for the plurality of time series based on a distribution of the extracted local change points; and

outputting the global change point.

10. A non-transitory computer readable storage medium recording thereon a program causing a computer to perform a method comprising:

learning, with respect to each of a plurality of time series, models that approximate partial time series respectively and that are defined by parameters of the partial time series respectively, the partial time series being obtained by dividing a corresponding time series into a plurality of segments at change point candidates;

calculating, with respect to each of the change point candidates for the plurality of time series, a difference between a parameter of a first partial time series starting from a time point of a corresponding change point candidate and a parameter of a second partial time series before the corresponding change point candidate;

extracting change point candidates for which the calculated difference exceeds a predetermined threshold as local change points;

detecting a global change point that is a change point for the plurality of time series based on a distribution of the extracted local change points; and

outputting the global change point.