Sequence prediction method, sequence prediction device, and program

Abstract

To provide a technique of improving the prediction accuracy of series prediction.SOLUTION: A series prediction method of the present disclosure causes a computer to execute: upon receiving series data composed of one or more first observation data and information related to series representing the series data, prediction model learning procedures of learning a predetermined prediction model so as to satisfy the information related to the series and fit the series data; and upon receiving second observation data, based on the learned prediction model, prediction procedures of predicting third observation data at time before or after predetermined time for observation time at which the second observation data was observed.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present disclosure relates to a sequence prediction method, a sequence prediction device, and a program. [Background technology]

[0002] Improving the prediction accuracy of sequence prediction is important in various fields, such as physics, meteorology, and economics. Generally, prediction accuracy decreases when there is little training data. In response to this, a method has been proposed to improve prediction accuracy by utilizing other related sequence data (Non-Patent Document 1). [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Iwata, Tomoharu, and Yoshinobu Kawahara. "Meta-Learning for Koopman Spectral Analysis with Short Time-series." arXiv preprint arXiv:2102.04683 (2021). Summary of the Invention [Problem to be solved by the invention]

[0004] However, the method proposed in Non-Patent Document 1 has a problem in that it cannot be applied when other related sequence data is not available. Even if other related sequence data is available, it may be costly to do so.

[0005] The present disclosure has been made in consideration of the above points, and provides a technique for improving the prediction accuracy of sequence prediction. [Means for solving the problem]

[0006] A sequence prediction method according to one aspect of the present disclosure includes a prediction model training step in which, when sequence data consisting of one or more first observation data and information about a sequence represented by the sequence data are given, a predetermined prediction model is trained to satisfy the information about the sequence and to fit the sequence data; and a prediction step in which, when second observation data is given, the trained prediction model is used to predict third observation data at a time that is a predetermined time ahead or after the observation time at which the second observation data was observed. [Effects of the Invention]

[0007] Techniques are provided for improving the prediction accuracy of sequence prediction. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 1 is a diagram illustrating an example of a hardware configuration of a series prediction device according to an embodiment of the present invention. [Figure 2] FIG. 1 is a diagram illustrating an example of the functional configuration of a series prediction device according to an embodiment of the present invention. [Figure 3] 10 is a flowchart showing an example of the flow of processing executed by the series prediction device according to the present embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0009] An embodiment of the present invention will now be described, which is a sequence prediction device 10 that can improve prediction accuracy for sequence data even when there is a small amount of training data.

[0010] Here, the series prediction device 10 according to this embodiment has a learning phase for learning a prediction model and an inference phase for making a series prediction using the learned prediction model.

[0011] In the learning phase, sequence data for learning and information regarding the period and decay of the sequence represented by the sequence data are provided to sequence prediction device 10. Note that multiple pieces of sequence data may be provided as sequence data for learning.

[0012] Below, the learning sequence data is {(y n ,t n )|n=1, ,N}, where y n is the time t n ∈R (where R is the set of all real numbers). Also, t n+1 >t n where N is the length of the sequence data for learning. The time interval at which the observation vector is observed does not have to be a constant interval. n+1 -t n ≠t n'+1 -t n' There may exist n, n'∈{1, , N} such that (y, t) is also represented as y(t) below.

[0013] Also, information about attenuation

[0014]

number

[0015] Cycle information

[0016]

number

[0017] In this way, in the learning phase, not only the learning sequence data but also information about the period and decay of the sequence is provided. However, only information about the period or information about decay may be provided. Also, information about the decay rate or the range of the period may be provided.

[0018] On the other hand, in the inference phase, an observation vector y(t) at a certain time t is provided to the sequence prediction device 10. At this time, the objective is to predict with high accuracy the observation vector y(t+τ) at time t+τ, which is a time τ ahead of time t. Note that τ may be negative. A negative τ means that a past observation vector is predicted.

[0019] <Example of Hardware Configuration of Sequence Prediction Device 10> An example of the hardware configuration of a sequence prediction device 10 according to this embodiment is shown in Fig. 1. As shown in Fig. 1, sequence prediction device 10 according to this embodiment is realized by the hardware configuration of a general computer or computer system, and includes, for example, an input device 101, a display device 102, an external I / F 103, a communication I / F 104, a RAM (Random Access Memory) 105, a ROM (Read Only Memory) 106, an auxiliary storage device 107, and a processor 108. Each of these pieces of hardware is connected to each other via a bus 109 so as to be able to communicate with each other.

[0020] The input device 101 is, for example, a keyboard, a mouse, a touch panel, a physical button, etc. The display device 102 is, for example, a display, a display panel, etc. Note that the sequence prediction device 10 does not necessarily have to include at least one of the input device 101 and the display device 102, for example.

[0021] The external I / F 103 is an interface with an external device such as a recording medium 103a. The sequence prediction device 10 can read from and write to the recording medium 103a via the external I / F 103. Examples of the recording medium 103a include a flexible disk, a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card (Secure Digital memory card), and a USB (Universal Serial Bus) memory card.

[0022] The communication I / F 104 is an interface for connecting the sequence prediction device 10 to a communication network. The RAM 105 is a volatile semiconductor memory (storage device) that temporarily stores programs and data. The ROM 106 is a non-volatile semiconductor memory (storage device) that can store programs and data even when the power is turned off. The auxiliary storage device 107 is a storage device (storage device) such as an HDD (Hard Disk Drive), an SSD (Solid State Drive), or a flash memory. The processor 108 is an arithmetic device such as a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit).

[0023] A series prediction device 10 according to this embodiment has the hardware configuration shown in Fig. 1 and is capable of implementing various processes described below. Note that the hardware configuration shown in Fig. 1 is merely an example, and the hardware configuration of series prediction device 10 is not limited to this. For example, series prediction device 10 may have multiple auxiliary storage devices 107 or multiple processors 108, may not have some of the hardware shown in the figure, or may have various hardware components other than the hardware shown in the figure.

[0024] <Example of functional configuration of sequence prediction device 10> FIG. 2 shows an example of the functional configuration of sequence prediction apparatus 10 according to this embodiment. As shown in FIG. 2, sequence prediction apparatus 10 according to this embodiment includes a prediction model training unit 201 and a prediction unit 202. These units are implemented, for example, by one or more programs installed in sequence prediction apparatus 10, which are executed by processor 108. Sequence prediction apparatus 10 according to this embodiment also includes a storage unit 203. Storage unit 203 is implemented, for example, by auxiliary storage device 107. Note that storage unit 203 or a portion of its storage area may be implemented by a storage device (e.g., a database server) connected to sequence prediction apparatus 10 via a communications network.

[0025] The prediction model learning unit 201 uses the given attenuation information r * and information about the cycle ω * and the learning sequence data {(y n ,t n )|n=1, ,N}.

[0026] Attenuation information * and information about the cycle ω * Consider the prediction model shown in the following formula (1) as a prediction model that satisfies the above. Note that in the text of this specification, the hat "^" representing a predicted value will be written immediately before the character, not on the character. For example, in the text of this specification, the left side of the prediction model shown in the following formula (1) will be written as "^y(τ|y(t))".

[0027]

number

[0028] Λ is a matrix of eigenvalues ​​that represent the dynamics of the sequence, where the real part of the eigenvalue represents the decay rate and the imaginary part of the eigenvalue represents the frequency. For example, the eigenvalues ​​are real parameter

[0029]

number

[0030]

number

[0031]

number

[0032] In this case, the given damping information r * and information about the cycle ω * By using the above and fixing (some) of the parameters r and ω, it is possible to express a series that satisfies the given information on decay and period. The parameters that are not fixed are the parameters to be learned. If information on the range of the decay rate or period is given, the parameters are learned using that range as a constraint. For example, if information is given that the logarithm of the decay rate is negative, then r k =-exp(r k '), and for example, the decay rate can be start From end If the information is given that the range is k =r start +(r end -r start ) / (1+exp(-r k ')) and can be parameterized.

[0033] V is a matrix, real matrix

[0034]

number

[0035]

number

[0036] Model parameter r k ,ω k ,u k ,z k and functions φ,ψ (parameters), and the learning sequence data {(y n ,t n )|n=1, ,N} (where the decay information r * and information about the cycle ω * The parameter r fixed at k ,ω k is not a target of learning.) For example, learning can be done by minimizing the following prediction error:

[0037]

number

[0038] Although the time t is assumed to be continuous time in the above, this embodiment is also applicable when the time t is a discrete time. When the time t is a discrete time, the eigenvalue is expressed by the following formula instead of the above formula (2):

[0039]

number

[0040]

number

[0041] When an observation vector y(t) at a certain time t is given, the prediction unit 202 calculates the predicted value ^y(τ|y(t)) of the observation vector y(t+τ) after τ time using a prediction model having learned parameters (for example, the prediction model shown in the above formula (2) when time t is continuous time, or the prediction model shown in the above formula (6) when time t is discrete time). Note that, as mentioned above, τ may be negative.

[0042] The storage unit 203 stores various data. For example, in the learning phase, the storage unit 203 stores the learning sequence data {(y n ,t n )|n=1,···,N}, and the decay information r * , information about the period ω * , untrained parameter r k ,ω k ,u k ,z k , functions φ,ψ (parameters). On the other hand, for example, in the inference phase, the observation vector y(t) at a certain time t, the learned parameters r k ,ω k ,u k ,z k ,Memorize the learned functions φ,ψ (parameters).

[0043] <Processing flow> The flow of processing executed by the series prediction device 10 according to this embodiment will be described with reference to Fig. 3. Note that steps S101 to S102 in Fig. 3 are processing executed in the learning phase, and steps S201 to S202 are processing executed in the inference phase.

[0044] The prediction model learning unit 201 uses given learning sequence data {(y n ,t n )|n=1,···,N} and the decay information r * and period information ω * At least one of the above is input (step S101).

[0045] The prediction model learning unit 201 adjusts the parameter r of the prediction model shown in the above formula (1) so as to minimize the prediction error shown in the above formula (4), for example. k ,ω k ,u k ,z k and functions φ and ψ are learned (step S102). As a result, a learned prediction model is obtained.

[0046] The prediction unit 202 receives a given observation vector y(t) (step S201). At this time, τ may be given.

[0047] The prediction unit 202 uses, for example, the prediction model shown in the above formula (2) (where the parameter r k ,ω k ,u k ,z k The predicted value ^y(τ|y(t)) of the observation vector y(t+τ) after τ time is calculated using the function φ and ψ (the functions φ and ψ have already been learned) (step S202). This allows the observation vector after the desired time τ (τ may be negative) to be predicted for the observation vector y(t).

[0048] <Evaluation> The following describes an evaluation of the sequence prediction device 10 according to this embodiment. The sequence prediction device 10 according to this embodiment and existing methods were evaluated using a van der Pol oscillator. The evaluation results are shown in Table 1 below.

[0049] [Table 1] Here, "Proposed Method (Decay Rate)" is the result of evaluating sequence prediction device 10 by providing only information related to decay. "Proposed Method (Decay Rate, Period)" is the result of evaluating sequence prediction device 10 by providing both information related to decay and information related to period. "Neural Network" is the result of evaluating an existing method using a recursive neural network. The evaluation index was the prediction error.

[0050] As shown in Table 1 above, the proposed method (decay rate) and the proposed method (decay rate, period) achieve lower prediction errors than the existing methods. In addition, when comparing the proposed method (decay rate) and the proposed method (decay rate, period), it can be seen that by using information on the period in addition to information on decay, a lower prediction error can be achieved.

[0051] <Summary> As described above, the sequence prediction device 10 according to this embodiment constructs a prediction model for sequence prediction using not only the training sequence data but also information on the period and decay of the sequence. This makes it possible to construct a highly accurate prediction model even when the length of the training sequence data is relatively short (i.e., when there is little training data).

[0052] In the above embodiment, the same device is used to implement sequence prediction device 10 in both the learning phase and the inference phase, but this is not limiting and sequence prediction device 10 may be implemented by different devices in the learning phase and the inference phase. For example, the above embodiment may be implemented by a learning device having a prediction model learning unit 201 and an inference device having a prediction unit 202.

[0053] In the above embodiment, a case has been described in which a prediction model is constructed and then used to predict sequence data. However, this embodiment is not limited to such predictions; it can also be applied to cases in which it is desired to estimate the decay and period of time-series data for learning. That is, given decay information r * and information about the cycle ω * The parameter r is not fixed in k Yaω k The estimation result of can be used as the estimation result of the decay and period of the time series data for learning.

[0054] The sequence prediction device 10 according to this embodiment can be applied to various fields where sequence prediction is performed, such as physics, meteorology, and economics.

[0055] The present invention is not limited to the above-described specifically disclosed embodiments, and various modifications, changes, and combinations with known technologies are possible without departing from the scope of the claims. [Explanation of symbols]

[0056] 10 Sequence Prediction Device 101 Input Device 102 Display device 103 External I / F 103a Recording media 104 Communication I / F 105 RAM 106 ROM 107 Auxiliary storage 108 processors 109 Bus 201 Prediction Model Learning Unit 202 Prediction Department 203 Storage section

Claims

1. a prediction model training procedure for, when given sequence data consisting of one or more first observation data and information about a sequence represented by the sequence data, training a predetermined prediction model that satisfies the information about the sequence and is compatible with the sequence data; a prediction step of predicting, when second observation data is given, third observation data at a time that is a predetermined time ahead or after the observation time at which the second observation data is observed, using the trained prediction model; The computer executes A method for predicting a sequence, wherein the information about the sequence is at least one of information about the decay of the sequence and information about the period of the sequence.

2. the decay information is a logarithm of the decay rate of the sequence or a range of the decay rate of the sequence; the information about the period is the frequency of the sequence or the range of the period of the sequence; The predictive model is 2. The method of claim 1, wherein the model has a matrix of eigenvalues ​​that expresses the dynamics of the sequence and that is expressed by information about the attenuation and information about the period.

3. The predictive model is Let Λ be the matrix of eigenvalues ​​representing the dynamics of the sequence, φ and ψ be predetermined functions, y(t) be the observed data at time t, and V be a predetermined real matrix, then φ(Vexp(τΛ)V －１ ψ(y(t))) or φ(VΛ τ V －１ 3. The method of claim 2, wherein ψ(y(t))) is a model for predicting observed data τ hours ahead or after time t.

4. The predictive model is When the time t is continuous, φ(Vexp(τΛ)V －１ If the time t is a discrete time, it is expressed as φ(VΛ τ V －１ 4. The method of claim 3, wherein the time series is expressed as ψ(y(t)).

5. a prediction model training unit configured, when given sequence data consisting of one or more first observation data and information about a sequence represented by the sequence data, to train a predetermined prediction model that satisfies the information about the sequence and is compatible with the sequence data; a prediction unit configured, when given second observation data, to predict third observation data at a time that is a predetermined time ahead or after the observation time at which the second observation data is observed, using the trained prediction model; and A sequence prediction apparatus, wherein the information about the sequence is at least one of information about the decay of the sequence and information about the period of the sequence.

6. a prediction model training procedure for, when given sequence data consisting of one or more first observation data and information about a sequence represented by the sequence data, training a predetermined prediction model that satisfies the information about the sequence and is compatible with the sequence data; a prediction step of predicting, when second observation data is given, third observation data at a time that is a predetermined time ahead or after the observation time at which the second observation data is observed, using the trained prediction model; on the computer, The program, wherein the information about the sequence is at least one of information about the decay of the sequence and information about the period of the sequence.

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