KR20210027214A - Methods and apparatus for predicting data - Google Patents

Abstract

Disclosed are a method and device for predicting data. The method according to one embodiment of the present invention comprises the steps of: extracting change point information of given data by detecting a change in a covariance structure of a Gaussian process; updating the change point distribution in real time based on the change point information; and predicting data based on the updated change point distribution.

Description

Data prediction method and apparatus {METHODS AND APPARATUS FOR PREDICTING DATA}

The following embodiments relate to a method and apparatus for predicting data. Specifically, a Bayesian real-time change point in a covariance structure of a Gaussian process may be detected, and accuracy of data prediction may be improved by using the change point.

The problem of change point detection (CPD), such as data analysis to detect sudden changes in sequential data, is an important factor in improving the prediction of future events.

Change point detection is a specific sequential location where the underlying distribution changes. Change points play an important role in a number of areas, including climate modeling, speech recognition, image analysis, and human activity recognition.

Conventionally, the Bayesian change point detection method has been used to detect the change point. However, in the existing Bayesian real-time change point detection, the distribution of the change point is updated and calculated in real time, but it is difficult to guarantee the accuracy of the actual change point detection, and it is not possible to detect an appropriate change point according to the parameter, or it is meaningless. It has a limitation that it is greatly influenced by parameter settings such as detection.

In addition, when the mean changes during the Gaussian process, a statistical test was used to detect the point of change, but a statistical test for covariance changes that can model more diverse changes has not been conducted, and it is applied in real time. There is a limit to being difficult.

Embodiments attempt to detect a Bayesian real-time change point in a covariance structure of a Gaussian process.

Embodiments attempt to detect a change in covariance in a Gaussian process, update the distribution of change points in real time using this, and predict future data.

Embodiments attempt to output a predicted data value and a probability distribution of a change point.

Embodiments aim to improve the accuracy of prediction of future data through a corrected probability distribution of a change point.

A data prediction method according to an embodiment includes the steps of detecting a change in a covariance structure of a Gaussian process and extracting change point information of given data; Updating a change point distribution in real time based on the change point information; And predicting data based on the updated distribution of change points.

The extracting of the change point information may include setting a first hypothesis claiming the absence of the change point; Establishing a second hypothesis that asserts the existence of the change point; Calculating a likelihood ratio between the first hypothesis and the second hypothesis; And selecting one of the first hypothesis and the second hypothesis based on the likelihood ratio.

The selecting may include selecting the second hypothesis when the likelihood ratio is greater than or equal to a predetermined threshold value, and selecting the first hypothesis when the likelihood ratio is less than the threshold value.

In the updating step, when the change point is detected, the distribution of the change point may be updated through data after the change point.

In the step of extracting the change point information, the change point information may be extracted by performing a sliding window on the given data.

The updating may include correcting an error that may occur as a parameter using the change point information.

An apparatus for predicting data according to an embodiment includes: a memory storing at least one program; And a processor executing the at least one program, wherein the processor detects a change in a covariance structure of a Gaussian process, extracts change point information of given data, and distributes change point in real time based on the change point information Is updated, and data is predicted based on the updated distribution of change points.

The processor establishes a first hypothesis claiming the absence of the change point, establishes a second hypothesis claiming the existence of the change point, and a likelihood ratio between the first hypothesis and the second hypothesis. Is calculated, and one of the first hypothesis and the second hypothesis may be selected based on the likelihood ratio.

The processor may select the second hypothesis when the likelihood ratio is greater than or equal to a predetermined threshold value, and select the first hypothesis when the likelihood ratio is less than the threshold value.

When the change point is detected, the processor may update the distribution of the change point through data after the change point.

The processor may extract the change point information by performing a sliding window on the given data.

The processor may correct an error that may occur as a parameter by using the change point information.

Embodiments may detect a Bayesian real-time change point in a covariance structure of a Gaussian process.

Embodiments may detect a change in covariance in a Gaussian process, and use this to update a distribution of change points in real time and predict future data.

Embodiments may output a data predicted value and a probability distribution of a change point.

Embodiments may improve the accuracy of prediction of future data through the corrected probability distribution of change points.

1 is a flowchart illustrating a data prediction method according to an exemplary embodiment.
FIG. 2 is a diagram illustrating an effect of a method of detecting a change point of a covariance structure on a quality of a Gaussian process regression according to an exemplary embodiment.
3 is a diagram illustrating an output of a data prediction apparatus according to an exemplary embodiment.
4 is a block diagram of an apparatus for predicting data according to an exemplary embodiment.

Specific structural or functional descriptions disclosed in this specification are exemplified only for the purpose of describing embodiments according to a technical concept, and the embodiments may be implemented in various different forms and are limited to the embodiments described herein. It doesn't work.

Terms such as first or second may be used to describe various components, but these terms should be understood only for the purpose of distinguishing one component from other components. For example, a first component may be referred to as a second component, and similarly, a second component may be referred to as a first component.

When a component is referred to as being "connected" or "connected" to another component, it is understood that it may be directly connected or connected to the other component, but other components may exist in the middle. It should be. On the other hand, when a component is referred to as being "directly connected" or "directly connected" to another component, it should be understood that there is no other component in the middle. Expressions describing the relationship between the elements, for example, "between" and "just between" or "neighboring to" and "directly adjacent to" should be interpreted as well.

Singular expressions include plural expressions unless the context clearly indicates otherwise. In the present specification, terms such as "comprise" or "have" are intended to designate that the specified features, numbers, steps, actions, components, parts, or combinations thereof exist, but one or more other features or numbers, It is to be understood that the presence or addition of steps, actions, components, parts, or combinations thereof, does not preclude the possibility of preliminary exclusion.

Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the relevant technical field. Terms as defined in a commonly used dictionary should be construed as having a meaning consistent with the meaning of the related technology, and should not be interpreted as an ideal or excessively formal meaning unless explicitly defined in the present specification. Does not.

The embodiments may be implemented in various types of products such as a personal computer, a laptop computer, a tablet computer, a smart phone, a television, a smart home appliance, an intelligent vehicle, a kiosk, and a wearable device. Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. The same reference numerals shown in each drawing indicate the same members.

1 is a flowchart illustrating a data prediction method according to an exemplary embodiment.

Referring to FIG. 1, steps 110 to 130 according to an embodiment may be performed by a data prediction apparatus. The data prediction apparatus may be implemented by one or more hardware modules, one or more software modules, or various combinations thereof.

The data prediction method according to an embodiment may be divided into a statistical test part that detects a change in covariance of a Gaussian process and a Bayesian algorithm part that updates a distribution of change points in real time and predicts future data using the same.

In step 110, the apparatus for predicting data according to an exemplary embodiment detects a change in the covariance structure of a Gaussian process and extracts change point information of the given data. The data prediction apparatus sets a first hypothesis claiming the absence of the change point, sets a second hypothesis claiming the existence of the change point, and a likelihood ratio between the first hypothesis and the second hypothesis. ) Is calculated, and one of the first hypothesis and the second hypothesis can be selected based on the likelihood ratio.

For example, the data prediction apparatus may set a null hypothesis claiming the absence of a change point and an alternative hypothesis claiming the existence of a change point in order to perform a statistical test. The data prediction apparatus may calculate a likelihood ratio between two hypotheses and reject the null hypothesis if the likelihood ratio is greater than a threshold value. The threshold value may be determined so that the error value of the statistical test does not exceed a predetermined error value for the probability distribution of the likelihood ratio according to the probability process of the two hypotheses.

The data prediction apparatus may extract the change point information by performing a sliding window on the given data in order to apply it to a real-time algorithm.

In step 120, the data prediction apparatus updates the change point distribution in real time based on the change point information, and in step 130, the data prediction apparatus predicts data based on the updated change point distribution.

The data prediction apparatus according to an embodiment may appropriately adjust the Bayesian real-time change point detection algorithm according to the result of the statistical test. For example, if a change point is detected in the covariance structure of the Gaussian process as a result of a statistical test, the prediction model after the change point can be updated through data after the change point, and the data before the change point can be adjusted to consider less when predicting future data. . Conversely, if a change point is not detected as a result of a statistical test, the data prediction device may adjust to further consider data before the change point.

The data prediction apparatus according to an embodiment may perform a sliding window statistical test on given data and update a probability distribution of a change point according to a result. At this time, the existing Bayesian real-time change point detection algorithm may have fewer or more change points than the actual number of change points depending on the parameter, but using the presented statistical test method can compensate for the effects of inappropriate parameters. . The accuracy of prediction of future data can be improved through the corrected probability distribution of change points.

The apparatus for predicting data according to an embodiment may detect a change point in time series data having a change in a covariance structure, and perform more accurate real-time time series data prediction by using the change point information.

FIG. 2 is a diagram illustrating an effect of a method of detecting a change point of a covariance structure on a quality of a Gaussian process regression according to an exemplary embodiment.

Referring to FIG. 2, a diagram 210 shows a sample of a Gaussian process with an intended CP in the middle. Fig. 220 shows a sample of a Gaussian process model that has learned a hyper parameter using the entire data set. Fig. 230 shows a sample of a Gaussian process model in which the covariance structure is broken and hyperparameters are separately learned.

Referring to Figures 220 and 230, it can be seen that fitting anomalous data to a time-invariant Gaussian process generates an inaccurate model. Gaussian process regression with structural breaks in the covariance structure is more expressive and may be more suitable for analysis of anomalous data.

In the following, details on the statistical test method are first described, and then the Bayesian algorithm is described.

,

와 같이 정의할 수 있다.To construct a test to detect changes in the covariance structure, we define the null hypothesis as H0: Cov(Xi, Xj) = K(i, j) and the alternative hypothesis.

,

It can be defined as

는 아래 수학식 1과 같을 수 있다.Here, K, K', and K'' are kernel functions, and Σ and Σt' denote covariance matrices for _{H 0} and H _{1,t, respectively.} Likelihood rain

May be equal to Equation 1 below.

Under the null hypothesis, i.e. X to N (0, Σ),

는

의 아이젠밸류(eigenvalues)이고, ui, vi-는 차수가 1 인 카이 제곱 분포를 따른다.here

Is

Is the eigenvalues of, and ui and vi- follow a chi-square distribution of degree 1.

,

Under the alternative hypothesis, i.e.

,

는

의 아이젠밸류이고, ui, vi-는 차수가 1 인 카이 제곱 분포를 따른다.here

Is

Is the eigenvalue of, and ui and vi- follow the chi-square distribution of degree 1.

Equations 2 and 3 are the subtraction between a linear combination of a chi-square random variable with n degrees of freedom and an independent chi-square random variable with 1 degree of freedom in which the difference between two positive semi-denite quadratic terms is Shows that it can be expressed as

When the covariance structure is divided into two different kernels, H ₀ and H ₁ may be defined similarly as described above except that Kpj) = 0. Then, the corresponding covariance matrix may be written as in Equation 4 below.

When defined as X _a := X _1:t , X _b : = X _t+1:n , for r, c∈{a, b}, K _rc represents the covariance matrix between X _r and X _c. The likelihood ratio test can be defined as in Equation 5 below.

For additional basic form and theorem, the constant Ct can be defined as:

. 여기서

은 행렬 M의 가장 작은 고유 값을 나타낸다.For covariance matrices Σ and Σt '

. here

Represents the smallest eigenvalue of matrix M.

,

를 만족한다. 여기서 ∧는 최소 연산자를 의미한다.

,

Is satisfied. Here, ∧ means the minimum operator.

로 정의한다.Qt

It is defined as

이 귀무 가설 하에서 정확할 확률은

이상이다. 이를 수학식으로 나타내면, 수학식 6과 같다.

The probability of being correct under this null hypothesis is

That's it. If this is expressed by Equation 6, it is the same as Equation 6.

이 대립 가설 하에서 정확할 확률은

이상이다. 이를 수학식으로 나타내면, 수학식 7과 같다.

The probability of being correct under this alternative hypothesis is

That's it. If this is expressed by Equation 7, it is the same as Equation 7.

That is, the type I or type II error can be controlled to less than δ/2.

를 만족할 때, 조건부 탐지 오류 확률(conditional detection error probability)은 하기 수학식 8과 같이 제한될 수 있다.

When is satisfied, the conditional detection error probability may be limited as shown in Equation 8 below.

Using Equation 8, it is possible to ensure that the likelihood ratio test for the general covariance kernel change is statistically correct for the error boundary δ under a specified condition. By setting the threshold value equal to or greater than the epsilon upper limit of the null distribution, a limited type I error can be guaranteed. By setting the threshold value equal to or less than the epsilon lower limit of the replacement distribution, it may be possible to guarantee a limited type II error.

와

사이의 세 가지 가능한 불균형 케이스가 있을 수 있다.

>

인 경우, 유형 I 및 유형 II 오류를 모두 보장하는 임계 값은 없을 수 있다.

=

인 경우, 유형 I 및 유형 II 오류를 모두 보장 할 수있는 임계 값은 하나뿐이다.

<

인 경우, 유형 I 및 유형 II 오류를 모두 보장 할 수 있는 임계 값은 영역으로 존재할 수 있다.

Wow

There can be three possible unbalanced cases in between.

>

In the case of, there may not be a threshold that guarantees both type I and type II errors.

=

If so, there is only one threshold that can guarantee both Type I and Type II errors.

<

In the case of, a threshold value that can guarantee both type I and type II errors may exist as an area.

The Bayesian algorithm according to an embodiment may be shown in Table 1 below.

Algorithm 1 can propose a theoretically justified online change detection algorithm, CBOCPD (Conrmatory Bayesian Online CPD). The main idea of CBOCPD is to overcome the limitations of the assumption that the spacing between points of change is data independent.

Referring to Table 1, rows 1 and 2 indicate parameter initialization, and rows 3-13 may be expressed as Equation 9 below.

과

의 두 개의 우도 비 테스트가 있을 수 있다.Here

and

There may be two likelihood ratio tests.

Since the threshold values theoretically calculated in Equations 6 and 7 are not sufficient for practical use, an empirical threshold value can be used.

를 만족하는 경우,

로 정의할 수 있고,

를 만족하는 경우

으로 정의할 수 있다. 우도비 검정은 t 주변의 윈도우 W = xt-m : t + m 에 적용될 수 있다.

는 우도 비율을 최대화하는 윈도우의 시점이다(

). 여기서, CW⊆{t-m, ..., t + m}는 창에 대한 변화점 후보 집합이다.if

If you are satisfied with,

Can be defined as,

If you are satisfied

It can be defined as The likelihood ratio test can be applied to the window W = xt-m: t + m around t.

Is the point in time of the window to maximize the likelihood ratio (

). Here, CW⊆{tm, ..., t + m} is a set of candidate change points for the window.

에서 두 우도비 검정을 통과하고,

가 t와 일치하면 t가 변화점이라고 결정하고 BOCPD 프레임 워크의 변경 가능성

을 높일 수 있다.

Passes the two likelihood ratio tests at,

If is coincident with t, it is determined that t is the point of change and the possibility of change in the BOCPD framework

Can increase.

Conversely, if both tests fail, you can strongly believe that there is no change, reducing the likelihood of changes to the BOCPD framework.

3 is a diagram illustrating an output of a data prediction apparatus according to an exemplary embodiment.

Referring to FIG. 3, the apparatus for predicting data according to an embodiment may output a predicted value of future data and a probability distribution of a change point.

가 200일 때의 출력이고, 도면(320)은 시간 스케일(timescale)

가 25일 때의 출력이다. 도면(310) 및 도면(320)을 참조하면, CBOCPD가 통계 테스트를 통해 데이터의 매끄러운 정도의 변경을 식별하는 반면 BOCPD는 변경을 너무 적거나 너무 많이 캡처한다는 것을 보여준다.More specifically, the diagram 310 is a time scale (timescale)

Is the output when is 200, and the drawing 320 is a timescale

This is the output when is 25. Referring to Figures 310 and 320, it is shown that CBOCPD identifies a smooth degree of change in the data through statistical testing, whereas BOCPD captures too little or too many changes.

4 is a block diagram of an apparatus for predicting data according to an exemplary embodiment.

Referring to FIG. 4, the apparatus 400 for predicting data according to an embodiment includes a processor 410. The data prediction apparatus 400 may further include a memory 430 and a communication interface 450. The processor 410, the memory 430, and the communication interface 450 may communicate with each other through a communication bus 405.

At least one program may be stored in the memory 430, and the processor 410 may execute at least one program.

The processor 410 detects a change in the covariance structure of the Gaussian process, extracts change point information of the given data, updates the change point distribution in real time based on the change point information, and based on the updated change point distribution, the data Predict.

The memory 430 may be a volatile memory or a non-volatile memory.

According to an embodiment, the processor 410 establishes a first hypothesis claiming the absence of a change point, sets a second hypothesis claiming the existence of a change point, and the likelihood ratio between the first hypothesis and the second hypothesis ( likelihood ration) may be calculated, and one of the first hypothesis and the second hypothesis may be selected based on the likelihood ratio.

The processor 410 may select the second hypothesis when the likelihood ratio is greater than or equal to a predetermined threshold value, and select the first hypothesis when the likelihood ratio is less than the threshold value.

When the change point is detected, the processor 410 may update the distribution of the change point through data after the change point.

The processor 410 may extract change point information by performing a sliding window on the given data.

The processor 410 may correct an error that may occur as a parameter by using the change point information.

The embodiments described above may be implemented as a hardware component, a software component, and/or a combination of a hardware component and a software component. For example, the devices, methods, and components described in the embodiments are, for example, a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable gate (FPGA). array), programmable logic unit (PLU), microprocessor, or any other device capable of executing and responding to instructions. The processing device may execute an operating system (OS) and one or more software applications executed on the operating system. Further, the processing device may access, store, manipulate, process, and generate data in response to the execution of software. For the convenience of understanding, although it is sometimes described that one processing device is used, one of ordinary skill in the art, the processing device is a plurality of processing elements and/or a plurality of types of processing elements. It can be seen that it may include. For example, the processing device may include a plurality of processors or one processor and one controller. In addition, other processing configurations are possible, such as a parallel processor.

The software may include a computer program, code, instructions, or a combination of one or more of these, configuring the processing unit to operate as desired or processed independently or collectively. You can command the device. Software and/or data may be interpreted by a processing device or, to provide instructions or data to a processing device, of any type of machine, component, physical device, virtual equipment, computer storage medium or device. , Or may be permanently or temporarily embodyed in a transmitted signal wave. The software may be distributed over networked computer systems and stored or executed in a distributed manner. Software and data may be stored on one or more computer-readable recording media.

The method according to the embodiment may be implemented in the form of program instructions that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, and the like alone or in combination. The program instructions recorded on the medium may be specially designed and configured for the embodiment, or may be known and usable to those skilled in computer software. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tapes, optical media such as CD-ROMs and DVDs, and magnetic media such as floptical disks. -A hardware device specially configured to store and execute program instructions such as magneto-optical media, and ROM, RAM, flash memory, and the like. Examples of program instructions include not only machine language codes such as those produced by a compiler, but also high-level language codes that can be executed by a computer using an interpreter or the like.

As described above, although the embodiments have been described by the limited drawings, a person of ordinary skill in the art can apply various technical modifications and variations based on the above. For example, the described techniques are performed in a different order from the described method, and/or components such as systems, structures, devices, circuits, etc. described are combined or combined in a form different from the described method, or other components Alternatively, even if substituted or substituted by an equivalent, an appropriate result can be achieved.

Therefore, other implementations, other embodiments, and those equivalent to the claims also fall within the scope of the claims to be described later.

Claims (13)

Detecting a change in a covariance structure in a Gaussian process and extracting change point information of the given data;
Updating a change point distribution in real time based on the change point information; And
Predicting data based on the updated distribution of change points
Containing, data prediction method.
The method of claim 1,
The step of extracting the change point information
Establishing a first hypothesis asserting the absence of the point of change;
Establishing a second hypothesis that asserts the existence of the change point;
Calculating a likelihood ratio between the first hypothesis and the second hypothesis; And
Selecting one of a first hypothesis and a second hypothesis based on the likelihood ratio
Containing, data prediction method.
The method of claim 2,
The selecting step
Selecting the second hypothesis when the likelihood ratio is greater than or equal to a predetermined threshold value, and selecting the first hypothesis when the likelihood ratio is less than the threshold value
Containing, data prediction method.
The method of claim 1,
The updating step
When the change point is detected, updating the change point distribution through data after the change point
Containing, data prediction method.
The method of claim 1,
The step of extracting the change point information
Extracting the change point information by performing a sliding window on the given data
Containing, data prediction method.
The method of claim 1,
The updating step
Correcting an error that may occur as a parameter using the change point information
Containing, data prediction method.
A computer program stored in a medium for executing the method of any one of claims 1 to 6 in combination with hardware.
A memory in which at least one program is stored; And
And a processor that executes the at least one program,
The processor,
Detects the change in the covariance structure of the Gaussian process and extracts the change point information of the given data
Based on the change point information, update the change point distribution in real time,
A data prediction device that predicts data based on the updated distribution of change points.
The method of claim 8,
The processor is
Establish a first hypothesis asserting the absence of the above point of change,
Establish a second hypothesis that asserts the existence of the above point of change,
Calculate a likelihood ration between the first hypothesis and the second hypothesis,
A data prediction apparatus for selecting one of a first hypothesis and a second hypothesis based on the likelihood ratio.
The method of claim 9,
The processor is
When the likelihood ratio is greater than or equal to a predetermined threshold value, the second hypothesis is selected, and when the likelihood ratio is less than the threshold value, the first hypothesis is selected.
The method of claim 8,
The processor is
When the change point is detected, the change point distribution is updated through data after the change point.
The method of claim 8,
The processor is
A data prediction apparatus for extracting the change point information by performing a sliding window on the given data.
The method of claim 8,
The processor is
A data prediction apparatus for correcting an error that may occur as a parameter by using the change point information.

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