WO2023223461A1 - 因果関係推定装置、因果関係推定方法、及び因果関係推定プログラム - Google Patents

因果関係推定装置、因果関係推定方法、及び因果関係推定プログラム Download PDF

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WO2023223461A1
WO2023223461A1 PCT/JP2022/020680 JP2022020680W WO2023223461A1 WO 2023223461 A1 WO2023223461 A1 WO 2023223461A1 JP 2022020680 W JP2022020680 W JP 2022020680W WO 2023223461 A1 WO2023223461 A1 WO 2023223461A1
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series data
causal relationship
time series
time
variables
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French (fr)
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良行 乗松
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Mitsubishi Electric Corp
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Mitsubishi Electric Corp
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Priority to CN202280095955.2A priority Critical patent/CN119317928A/zh
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Priority to JP2024513679A priority patent/JP7483180B2/ja
Priority to EP22942666.3A priority patent/EP4510048A4/en
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    • G06—COMPUTING OR CALCULATING; COUNTING
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N20/00—Machine learning
    • G06N20/10—Machine learning using kernel methods, e.g. support vector machines [SVM]
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N5/00—Computing arrangements using knowledge-based models
    • G06N5/01—Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound

Definitions

  • the present disclosure relates to a causal relationship estimation device, a causal relationship estimation method, and a causal relationship estimation program.
  • Patent Document 1 calculates the maximum mean discrepancy (MMD), which is the value that maximizes the difference between the kernel averages of bivariate time series data (also called “two-dimensional time series data”), and performs supervised learning. Discloses a device for clarifying causal relationships between variables.
  • MMD maximum mean discrepancy
  • Patent Document 1 has a problem in that it is not possible to estimate causal relationships between time-series data of an arbitrary number of variables (for example, three or more variables).
  • the present disclosure has been made to solve the above problems, and provides a causal relationship estimation device, an estimation method, and an estimation program that enable estimation of causal relationships between time-series data of an arbitrary number of variables. With the goal.
  • the causality estimation device of the present disclosure includes a data acquisition unit that acquires learning data including a set of time series data of a plurality of state variables and a set of time series data of a plurality of observed variables; Calculate a causal relationship parameter indicating a causal relationship between the time series data and the time series data of the plurality of observed variables, calculate a variance-covariance matrix of a Gaussian process from the learning data and the causal relationship parameter, a calculation unit that expresses the causality parameter using a multitask Gaussian process model; an optimization unit that calculates an optimization function based on the variance-covariance matrix and updates the causality parameter based on the optimization function; It is characterized by having the following.
  • Another causal relationship estimation device of the present disclosure reads a causal relationship parameter indicating a causal relationship for each layer between time series data of a plurality of state variables and time series data of a plurality of observation variables from a causal relationship parameter database.
  • a causal graph construction unit that rearranges the time-series data of the plurality of state variables and the time-series data of the plurality of observation variables for each layer based on the causal relationship parameter;
  • a data acquisition unit that acquires verification data including a set of data and a set of time series data of a plurality of observed variables; and a rearranged time series data of the plurality of state variables and a time series of the plurality of observed variables.
  • the present invention is characterized by comprising a causal graph verification unit that performs one or both of verification using the verification data of Granger causality and verification using the verification data of pseudo correlation on data.
  • FIG. 1 is a block diagram showing the configuration of a causal relationship estimation device according to Embodiment 1.
  • FIG. 2 is a diagram illustrating an example of the hardware configuration of the causal relationship estimation device in FIG. 1.
  • FIG. 2 is a block diagram showing the configuration of a preprocessing section of the data acquisition section in FIG. 1.
  • FIG. 2 is a diagram showing an example of time information before being dimensionally compressed by the preprocessing section of the data acquisition section of FIG. 1 and time information after being dimensionally compressed.
  • FIG. 2 is a diagram showing an example of angle information before being dimensionally expanded by a preprocessing unit of the data acquisition unit in FIG. 1 and angle information after being dimensionally expanded.
  • 2 is a diagram illustrating an example of processing performed by a calculation unit of the learning unit in FIG.
  • FIG. FIG. 2 is a diagram illustrating an example of processing performed by a time shift operator of the calculation unit of the learning unit in FIG. 1;
  • FIG. 2 is a diagram showing, in a table format, an example of initial values and numbers of causality parameters created by a calculation unit of a learning unit in FIG. 1;
  • 2 is a flowchart showing the operation of the causal relationship estimation device of FIG. 1.
  • FIG. FIG. 2 is a block diagram showing the configuration of a causal relationship estimation device according to a second embodiment.
  • 11 is a diagram illustrating an example of the hardware configuration of the causal relationship estimation device in FIG. 10.
  • FIG. 11 is a diagram showing a process of constructing a causal graph by a causal graph constructing unit of the constructing unit in FIG. 10.
  • FIG. 10 is a diagram showing a process of constructing a causal graph by a causal graph constructing unit of the constructing unit in FIG. 10.
  • 10A and 10B are diagrams illustrating an example of rearrangement processing of state information and observation information performed by the causal graph construction unit of the construction unit in FIG. 10.
  • FIG. (A) and (B) are diagrams illustrating an example of verification processing performed by the causal graph verification unit of the construction unit in FIG. 10.
  • (A) and (B) are diagrams showing other examples of the verification process performed by the causal graph verification unit of the construction unit in FIG. 10.
  • 11 is a flowchart showing the operation of the causality estimation device of FIG. 10.
  • 10A and 10B are diagrams showing a process of predicting unobserved time series data from relationships between time series data by the causality estimation device of FIG. 10.
  • FIG. 11 is a diagram illustrating an operation when the causal relationship estimation device of FIG. 10 uses a model that has learned change points or failures of sensor data by introducing a Change Point Kernel.
  • the causal relationship estimation device uses time-series data (X) regarding various economic indicators (for example, yen-dollar exchange rate, oil price, public investment, etc.) and time-series data (Y) on company stock prices. ) is given as a sample, the causal relationship between the time series data (X) and the time series data (Y) can be expressed as "X ⁇ Y", that is, "time series data ( This is a device for estimating that "X) is the cause and time series data (Y) is the result.”
  • Time series data (X) is called a state variable
  • time series data (Y) is called an observed variable.
  • a state variable is also called an explanatory variable or a latent variable.
  • Observed variables are also called objective variables, dependent variables, or explained variables.
  • both the time series data (X) and the time series data (Y) do not need to be one-dimensional time series data, but can be multidimensional time series data of two or more variables (i.e., multivariate time series data). It's okay.
  • the time series data (X) that is a state variable may be an observed variable of time series data (X') of another state variable.
  • the time series data (Y) that is an observation variable may be a state variable of time series data (Y') of another observation variable.
  • the causality estimation device is a machine learning device that generates a learned model (including causality parameters) from learning time series data.
  • the causality estimation device uses the causality parameters of the generated trained model (for example, the causality parameters generated by the causality estimation device according to the first embodiment) and the verification time series data. This is a device that constructs and outputs a causal graph.
  • the causality estimation device is a separate device from the causality estimation device according to the first embodiment, it may have the configuration of the causality estimation device according to the first embodiment.
  • the learning unit of the causal relationship estimation device models multidimensional time series data including correlations between data series and lag information between data series using, for example, a Gaussian process model.
  • a Gaussian process model known methods such as a Gauss Process Dynamical Model (GPDM) and a Multi Task Gauss Process (MTGP) model can be used.
  • GPDM is described in, for example, Non-Patent Document 1.
  • MTGP model is described in, for example, Non-Patent Document 2.
  • the causal relationship estimation device stores the causal relationship obtained through learning as a causal relationship parameter in a causal relationship parameter database (causal relationship parameter DB) of a storage device.
  • the causal relationship estimation device constructs a causal graph from the causal relationship parameters stored in the causal relationship parameter DB, and calculates the causal relationship using the time series data for verification stored in the time series data DB. Verify the graph and output the verified causal graph.
  • FIG. 1 is a block diagram showing the configuration of a causal relationship estimation device 100 according to the first embodiment.
  • the causal relationship estimation device 100 is a device that can implement the causal relationship estimation method (that is, the learning method) according to the first embodiment.
  • the causal relationship estimation device 100 includes a data acquisition section 10 and a learning section 20.
  • the causality estimation device 100 is, for example, a computer.
  • the causal relationship parameters obtained through learning are stored in the causal relationship parameter DB 26 in the storage section.
  • the causality parameter DB 26 may be stored in a storage unit (storage unit 103 in FIG.
  • causality estimation device 100 may be stored in an external device other than the causality estimation device 100 (for example, It may be stored in a storage unit of a server on a network that can communicate with the causal relationship estimation device 100.
  • the causality estimation device 100 acquires learning data including a set X (0:t) of time series data of a plurality of state variables and a set Y (0:t) of time series data of a plurality of observed variables, Calculate the causal relationship parameter ⁇ that indicates the causal relationship between the time series data of multiple state variables and the time series data of multiple observed variables, and calculate the variance-covariance matrix of the Gaussian process from the training data and the causal relationship parameter ⁇ .
  • the causality parameter ⁇ is a correlation coefficient that indicates the correlation between time series data of multiple state variables and time series data of multiple observed variables, and a correlation coefficient that indicates the correlation between time series data of multiple state variables and time series data of multiple observed variables.
  • the causal relationship estimation device 100 expresses the correlation as a linear correlation of an LMC (Linear Model of Corregion) kernel of the multi-task Gaussian process model.
  • the data acquisition unit 10 includes an input unit 14 that receives time series data from a time series data DB 12 and outputs the time series data to a preprocessing unit 16, and performs preprocessing on the time series data output from the input unit 14. It has a preprocessing unit 16 that outputs preprocessed time series data to the learning unit 20.
  • the time series data DB 12 may be stored in a storage unit (the storage unit 103 in FIG. 2 described later) as a part of the causality estimation device 100, but may be stored in an external device other than the causality estimation device 100 (for example, It may be stored in a storage unit of a server on a network that can communicate with the causal relationship estimation device 100.
  • the learning section 20 includes a calculation section 22 and an optimization section 24.
  • the calculation unit 22 initializes causality parameters and calculates a variance-covariance matrix.
  • the optimization unit 24 calculates an optimization function based on the variance-covariance matrix, and updates the causality parameter based on the optimization function. Details of each part will be described later.
  • FIG. 2 is a diagram showing an example of the hardware configuration of the causality estimation device 100.
  • the causality estimation device 100 includes a processor 101, a memory 102, and a storage unit 103 that is a nonvolatile storage device.
  • the causal relationship estimation device 100 may include a communication unit that communicates with other devices via a network.
  • the processor 101 is a CPU (Central Processing Unit) or the like.
  • the memory 102 is, for example, a volatile semiconductor memory such as RAM (Random Access Memory).
  • the storage unit 103 is a storage device such as a hard disk drive (HDD) or a solid state drive (SSD).
  • the storage unit 103 stores information (eg, various databases) and programs.
  • Each function of the causal relationship estimation device 100 is realized by a processing circuit.
  • the processing circuit may be dedicated hardware or may be the processor 101 that executes a program stored in the memory 102.
  • the processor 101 may be any one of a processing device, an arithmetic device, a microprocessor, a microcomputer, and a DSP (Digital Signal Processor).
  • the processing circuit may be, for example, a single circuit, a composite circuit, a programmed processor, an ASIC (Application Specific Integrated Circuit), an FPGA (Field-Programmable Gate Array), or Of these It is a combination of either.
  • ASIC Application Specific Integrated Circuit
  • FPGA Field-Programmable Gate Array
  • the causal relationship estimation program (that is, the learning program) according to the first embodiment is realized by software, firmware, or a combination of software and firmware.
  • Software and firmware are written as programs and stored in memory 102.
  • the processor 101 can realize the functions of each part shown in FIG. 1 by reading and executing a program stored in the memory 102.
  • the causal relationship estimation program is provided by downloading via a network or by a recording medium that records information such as an optical disk (i.e., a computer-readable storage medium), and is installed in the causal relationship estimation device 100. Ru.
  • the causal relationship estimation device 100 may be partially implemented using dedicated hardware and partially implemented using software or firmware. In this way, the processing circuit can implement the functions of each functional block shown in FIG. 1 using hardware, software, firmware, or any combination thereof.
  • Input section 14 The input unit 14 of the data acquisition unit 10 receives a set of time-series data of state variables X(0:t) (i.e., a plurality of time-series data) and a set of time-series data of observed variables Y( 0:t) (that is, a plurality of time series data) and outputs them to the preprocessing unit 16.
  • a set of time-series data of state variables X(0:t) i.e., a plurality of time-series data
  • Y( 0:t) that is, a plurality of time series data
  • the input unit 14 inputs time-series data x 1 (where Q is a positive integer) of state variables that are considered to have a cause-and-effect relationship from the time-series data DB 12. 0:t), x 2 (0:t),..., x Q (0:t) and time series data of D observed variables (D is a positive integer) y 1 (0:t) , y 2 (0:t), ..., y D (0:t), respectively.
  • time-series data of D observed variables are observed due to time-series data of Q state variables.
  • select the time series data of the angle ⁇ which is the state information as the time series data x q (0:t) of the state variable expand the dimension of the angle ⁇ which is the state information as described later, and create the time series data of sin ⁇ .
  • time series data of It may also be converted into two-dimensional time series data.
  • the input unit 14 inputs the time series data of the Q state variables selected from the time series data DB 12 and the time series data of the D observation variables to a length T (T is a positive integer). ) and a set of time-series data of state variables X(0:t) and a set of time-series data of observed variables Y(0:t) are obtained and passed to the preprocessing unit 16. Note that in X(0:t) and Y(0:t), 0:t in parentheses represents time series data from time 0 to time t. However, the time series data does not need to start with 0, and time series data having a length T at an arbitrary location may be selected from the time series data stored in the time series data DB 12.
  • x q (0:t) represents time-series data of state variables of state q.
  • y d (0:t) represents time-series data of the d-th dimension observed variable.
  • the preprocessing unit 16 of the data acquisition unit 10 acquires a set X (0:t) of time series data of state variables output from the input unit 14 and a set Y (0:t) of time series data of observed variables. Then, preprocessing is performed on these, and a set of preprocessed time series data of state variables X (0: t) and a set of preprocessed time series data of observed variables Y (0: t) are learned. It is output to the calculation section 22 of the section 20.
  • FIG. 3 is a block diagram showing the configuration of the preprocessing section 16 of the data acquisition section 10. As shown in FIG. 3, the preprocessing section 16 includes a dimension changing section 17 and a normalizing section 18.
  • the dimension change unit 17 performs dimension reduction processing (i.e. dimension compression processing) or dimension reduction processing appropriate for each state information on the time-series data x q (0:t) of state information whose dimensions need to be changed. Perform expansion processing.
  • dimension reduction processing i.e. dimension compression processing
  • dimension reduction processing i.e. dimension reduction processing
  • dimension reduction processing appropriate for each state information on the time-series data x q (0:t) of state information whose dimensions need to be changed.
  • Perform expansion processing When it is necessary to change the dimensions of the time series data x q (0:t) of the state information, for example, when the state information is periodic information such as time information or angle information, and when the dimensions of each side of a rectangle are For example, when the diagonal length is more effective than the length. Examples of dimension compression processing and dimension expansion processing are shown below. Note that it is also possible to perform the inverse processing of each of the following examples.
  • FIG. 4 is a diagram showing an example of time information before being dimensionally compressed by the dimension changing unit 17 of the preprocessing unit 16 (table on the left) and time information after being dimensionally compressed (table on the right).
  • the time information represents a periodicity of every 24 hours. Therefore, by integrating two pieces of information, ⁇ minutes'' and ⁇ hours,'' and compressing them into one piece of information, ⁇ hours and minutes,'' time information can be converted from 3D time series data to 2D time series data. Can be compressed.
  • FIG. 5 is a diagram showing an example of angle information before being dimensionally expanded by the dimension changing unit 17 of the preprocessing unit 16 and angle information after being dimensionally expanded.
  • the angle information is expanded from one piece of information, ⁇ angle ⁇ °,'' to a combination of two pieces of information, ⁇ sin ⁇ '' and ⁇ cos ⁇ .'' Data can be expanded to two-dimensional time series data.
  • the dimension changing unit 17 may use another dimension compression method (for example, principal component analysis, etc.) or another dimension expansion method.
  • the normalization unit 18 divides the set X (0:t) of time series data of state variables whose dimension has been changed and the set Y (0:t) of time series data of observed variables whose dimension has been changed into a set with an average of 0. Normalize so that the variance is 1.
  • the calculation unit 22 of the learning unit 20 receives from the preprocessing unit 16 a set of time series data of preprocessed state variables X(0:t) and a set of time series data of preprocessed observed variables Y(0:t). ), calculates the variance-covariance matrix K(X, X') of the Gaussian process, and outputs the variance-covariance matrix K(X, X') to the optimization unit 24.
  • FIG. 6 is a diagram showing an example of processing performed by the calculation unit 22 of the learning unit 20.
  • the correlation between time-series data of observed variables expressed in GPDM is expressed by the linear correlation of the LMC kernel of the MTGP model.
  • a specific example of the lag effect is that when the price of crude oil rises, the price of gasoline does not increase in tandem, but after a certain period of time (for example, until the next purchase is made), the price of gasoline increases. be.
  • another specific example of the lag effect is to raise gasoline prices first in anticipation of higher oil prices in the future.
  • the calculation unit 22 can take time series or periodicity into consideration. However, the calculation unit 22 may not consider the lag effect regarding time information.
  • X(t) represents a set of state variables ⁇ x 1 (t), x 2 (t), . . . , x Q (t) ⁇ .
  • u q (t) and v d (t) represent white Gaussian noise.
  • the state transition function f(x) and state function g(x) of the model are modeled by a Gaussian process, and using Gaussian process notation, the following equation (3) is generally used. It is expressed as (4).
  • Equation (3) represents the nonlinear time evolution of the state
  • Equation (4) represents the transformation from the state function to the observation function.
  • Kg and Kf represent Gram matrices.
  • the state function g q (x) in Equation (1) represents a Gaussian process model gp(0, k(x q , x q ′)) generated from the state information x q .
  • k q represents a positive definite kernel.
  • the positive definite kernel to be used one suitable for the data, such as an RBF kernel (Radial basis function kernel), is selected.
  • the RBF kernel is given by the following equation (5).
  • a d,q represents the linear correlation of the LMC of the conventional method, and represents the correlation coefficient from the state variable q to the observed variable d.
  • Equation (7) of Embodiment 1 is a time-shift operator newly introduced in the first embodiment, and L d,q represents a lag coefficient from state variable q to observation variable d.
  • F L represents a time-shift operator (lag operator) that shifts the state information of the state function to the future (or past) along the time axis, and is defined as in the following equation (8).
  • FIG. 7 is a diagram illustrating an example of processing performed by the time-shift operator of the calculation unit 22 of the learning unit 20.
  • FIG. 7 shows the operation of the time-shift operator FL .
  • the example in FIG. 7 shows a case where information is shifted into the future along the time axis t (L>0).
  • the direction of shift is the opposite direction to that in the case of FIG.
  • equation (7) When the observed data follows a Gaussian process, f is expressed by the multidimensional Gaussian distribution of equation (9) below.
  • K(X, X') is called a variance-covariance matrix (or Gram matrix), and is a matrix representing the similarity between state variables (that is, X ⁇ X').
  • the variance-covariance matrix K(X,X') is expressed as the following equations (11) and (12).
  • B q is called a coregionalization matrix, represents a linear transformation from a state function to an observation function, and is expressed as follows.
  • FIG. 8 is a diagram showing an example of the initial value and number of the causality parameter ⁇ in a table format. These causal relationship parameters are optimized by the optimization unit 24 of the learning unit 20.
  • the optimization unit 24 receives the variance-covariance matrix K(X, The process is performed and the optimized causal relationship parameter ⁇ is stored in the causal relationship parameter DB.
  • the marginal likelihood can be obtained by calculating as follows.
  • the probability that observation information is observed can be obtained from equation (13) as follows.
  • K ⁇ (X, X') represents the variance-covariance matrix K (X, X') calculated using the causality parameters.
  • N is the length of the feature vector X
  • D is the number of output dimensions of y.
  • the optimization unit 24 updates ⁇ so that the optimization function E in equation (15) is minimized. During optimization, if the causal relationship parameter ⁇ is updated, it is also necessary to update K ⁇ (X, X'), so the calculation unit 22 calculates K ⁇ (X, X').
  • the optimization unit 24 can use a known technique such as stochastic gradient descent during optimization. For example, L d,q can be optimized using a grid search, and the remaining causality parameters can be optimized using stochastic gradient descent.
  • each of the state variables and observation variables can have one or more dimensions, so it is possible to estimate the causal relationship between time series data of any number of variables, and it is possible to It is possible to estimate the causal relationship of time series data of variables (Q+D).
  • Embodiment 1 it becomes possible to understand the causal relationships between multiple state variables and multiple observed variables, and it is possible to estimate not only the causal relationships of bivariate time series data but also time series data of three or more variables. It is possible to infer causal relationships in data.
  • FIG. 9 is a flowchart showing the operation (ie, learning method) of the causal relationship estimation device 100 according to the first embodiment.
  • the input unit 14 obtains a set of time-series data of state variables X(0:t) and a set of time-series data of observed variables Y(0:t) from the time-series data DB 12.
  • step S102 the preprocessing unit 16 performs a dimension change (i.e., dimension compression) of the state variable x q (0:t) that requires dimension change in the state variable time series data set X (0:t). or dimension expansion).
  • a dimension change i.e., dimension compression
  • step S103 the preprocessing unit 16 normalizes the set of time-series data of state variables X(0:t) and the set of time-series data of observed variables Y(0:t).
  • step S104 the calculation unit 22 sets the following causal relationship parameter ⁇ to an initial value.
  • step S105 the calculation unit 22 calculates the variance-covariance matrix K ⁇ (X, ⁇ ) Calculate.
  • step S106 the optimization unit 24 calculates the optimization function E of equation (15).
  • step S107 the optimization unit 24 optimizes (that is, updates) the causality parameter ⁇ so that the optimization function E is minimized.
  • Steps S105 to S107 are repeated until the optimization function E converges.
  • the correlation coefficients a d, q and the lag coefficients L d, q, which are causal parameters are stored in the causal parameter DB 26 .
  • Embodiment 1 Effects According to Embodiment 1, it becomes possible to understand the causal relationships between multiple state variables and multiple observed variables, and it is possible to estimate the causal relationships of time-series data of any number of variables. Can be done.
  • Embodiment 2 ⁇ 2-1>> Configuration ⁇ 2-1-1>>
  • Causal relationship estimation device 200 The causal relationship estimation device 200 reads a causal relationship parameter ⁇ indicating a causal relationship for each layer between the time series data of a plurality of state variables and the time series data of a plurality of observed variables from the causal relationship parameter DB, and calculates the causal relationship.
  • the time series data of multiple state variables and the time series data of multiple observation variables are rearranged for each layer, and the set X(0:t) of time series data of multiple state variables and the time series data of multiple observed variables are Obtain verification data including a set Y(0:t) of time-series data of observed variables, and apply Granger causality to the rearranged time-series data of multiple state variables and time-series data of multiple observed variables.
  • One or both of the verification data using the verification data and the verification using the verification data of pseudo correlation are performed.
  • the causal relationship estimation device 200 is a causal graph construction device that has a causal graph construction function that constructs a causal graph.
  • a causal graph is a graph structure of a data item list with a "cause ⁇ effect" relationship based on the causal relationship information obtained in the first embodiment.
  • the state functions and observation functions that are elements of the constructed causal graph are rearranged based on the correlation coefficients a d, q and the lag coefficients L d, q stored in the causal relationship parameter DB.
  • the constructed causal graph is verified using Granger causality and pseudo-correlation.
  • the verified causal graph is output.
  • the causal relationship estimation device 200 constructs a causal graph using correlation coefficients a d, q and lag coefficients L d, q, which are causal relationship parameters.
  • the correlation coefficients a d, q and the lag coefficients L d, q, which are causal relationship parameters are, for example, causal relationship parameters of the learned model created by the causal relationship estimation device 100 according to the first embodiment.
  • the causality estimation device 200 is, for example, a computer.
  • Causal relationship estimation device 200 may be the same computer as the computer that constitutes causal relationship estimation device 100 according to Embodiment 1, or may be a different computer.
  • FIG. 10 is a block diagram showing the configuration of a causal relationship estimation device 200 according to the second embodiment.
  • the causal relationship estimation device 200 is a device that can perform the causal relationship estimation (that is, the causal graph construction method) according to the second embodiment.
  • the causality estimation device 200 includes a construction section 30, a data acquisition section 40, and an output section 90.
  • the construction unit 30 includes a causal graph construction unit 32 and a causal graph verification unit 34.
  • the construction unit 30 may include a causality parameter DB 80 that provides causality parameters to the causal graph construction unit 32.
  • the data acquisition section 40 includes an input section 44 and a preprocessing section 46.
  • the data acquisition unit 40 may include a time series data DB 42 that provides time series data to the input unit 44.
  • the output unit 90 outputs the causal graph constructed by the construction unit 30.
  • the time series data DB 42 and the causal relationship parameter DB 80 may be stored in a storage unit as part of the causal relationship estimation device 200 (storage unit 203 in FIG. It may be stored in a storage unit of an external device (for example, a server on a network that can communicate with the causal relationship estimation device 200).
  • FIG. 11 is a diagram showing an example of the hardware configuration of the causal relationship estimation device 200.
  • the causality estimation device 200 includes a processor 201, a memory 202, and a storage unit 203 that is a nonvolatile storage device.
  • the causal relationship estimation device 200 may include an interface with an external device, a communication unit that communicates with other devices via a network, and the like.
  • Processor 201 is a CPU or the like.
  • Memory 202 is, for example, a volatile semiconductor memory such as RAM.
  • the storage unit 203 is a storage device such as an HDD or an SSD.
  • the storage unit 203 stores information (eg, various databases) and programs.
  • Each function of the causality estimation device 200 is realized by a processing circuit.
  • the processing circuit may be dedicated hardware or may be the processor 201 that executes a program stored in the memory 202.
  • the estimation program (that is, the causal graph construction program) according to the second embodiment is realized by software, firmware, or a combination of software and firmware.
  • Software and firmware are written as programs and stored in memory 202.
  • the processor 201 can realize the functions of each section shown in FIG. 10 by reading and executing a program stored in the memory 202.
  • the program is installed in the causality estimation device 200 by downloading via a network or from a recording medium that records information, such as an optical disc.
  • the data acquisition unit 40 has the same functions as the data acquisition unit 10 of the first embodiment. However, the input unit 44 acquires data for verifying a causal graph using Granger causality and pseudo-correlation, which will be described later.
  • the causal graph construction unit 32 of the construction unit 30 uses the causal relationship parameters stored in the causal relationship parameter DB 80. is acquired, a causal graph is constructed using the causal relationship parameters, and the constructed causal graph is output to the causal graph verification unit 34.
  • FIG. 12 is a diagram showing the process of constructing a causal graph by the causal graph constructing unit 32 of the constructing unit 30.
  • y observation information
  • the correlation coefficient between x (state information) and y observation information
  • FIGS. 13A and 13B are diagrams illustrating an example of state information and observation information rearrangement processing performed by the causal graph construction unit 32 of the construction unit 30. As shown in FIGS. 13A and 13B, the state information and observation information are connected by an arrow pointing from the state information to the observation information.
  • FIG. 13(A) if the observation information has a lag (advancement) than the state function, the direction of the arrow is reversed.
  • FIG. 13(B) if the correlation coefficient is low, consider the possibility that it is a confounding factor or an intermediate factor, and rearrange the factor so as to move it to a higher position in the causal graph.
  • the causality parameter is calculated by the causality estimation device 100 according to the first embodiment using the state variables and observation variables after the rearrangement. Ask again.
  • FIGS. 14A and 14B are diagrams illustrating an example of verification processing performed by the causal graph verification unit 34 of the construction unit 30.
  • Granger causality is applied when observed variables y 1 and y 2 are predicted by state variables x 1 , x 2 , and x 3 including state variable x 2 (case 1).
  • the prediction accuracy is lower when the observed variables y 1 and y 2 are predicted by the state variables x 1 and x 3 (case 2) by deleting the state variable x 2. If the value decreases, the state variable x 2 is considered to have Granger causality with respect to the observed variables y 1 and y 2 .
  • the observed variables y 1 and y 2 were predicted by the state variables x 1 , x 2 , and x 3 (case 1)
  • the observed variables y 1 and y 2 were predicted by the state variables x 1 and x 3 .
  • the prediction accuracy increases in case 2
  • future predictions are made from the set of time-series data of state variables X(0:t) and the set of time-series data of observed variables Y(0:t) used for estimating the causal relationship in the causality estimation device 100.
  • a set of time-series data of state variables X (t+1:t+ ⁇ t) and a set of time-series data of future observed variables Y(t+1:t+ ⁇ t) may be used as prediction verification data (i.e., test data).
  • the prediction error can be evaluated using, for example, the following RMSE (Root Mean Squared Error).
  • FIGS. 15A and 15B are diagrams showing other examples of the verification process performed by the causal graph verification unit 34 of the construction unit 30. From Figures 15 (A) and (B), we can see how much a factor is affected in an unsteady state (a factor undergoes a sudden change due to an external factor (impulse response)) (or how much it remains constant without any change). It is also possible to verify this by estimating .
  • state variable x 2 affects both observed variables y 1 and y 2 , but state variables x 1 and x 3 are different from observed variables y 1 and y 2 , respectively.
  • x 2 does not change, such as taking a fixed value, x 2 does not change and does not affect observed variables y 1 and y 2 , so there is no correlation between observed variables y 1 and y 2 . It is thought that it will disappear.
  • the correlation between observed variables y 1 and y 2 remains even if the influence of x 2 disappears, or the correlation between x 1 and observed variables y 1 and between x 2 and y 2 is high. If a correlation is shown, the state variable x 2 is rearranged or deleted from the causal graph.
  • a causal graph By constructing a causal graph, it becomes possible to predict sensor values in places that cannot be directly measured or search for the cause of anomalies. Possible applications include predicting road damage based on traffic volume or weather information, predicting river water levels based on nearby rainfall and water level data, and predicting power demand using weather or economic status data in surrounding areas.
  • FIG. 16 is a flowchart showing the operation (ie, inference operation) of the causal relationship estimation device 200.
  • the construction unit 30 extracts the information for each layer from the causal relationship parameter DB. get.
  • step S202 the causal graph construction unit 32 arranges the state information and observation information in the order of "state information ⁇ observation information" for each layer.
  • step S203 the causal graph construction unit 32 corrects the causal direction (that is, the direction of the arrow).
  • step S204 the causal graph construction unit 32 rearranges the state information and observation information of the causal graph.
  • step S205 the input unit 44 acquires Granger causality verification data from the time series data DB 42.
  • step S206 the preprocessing unit 46 changes the dimension of the verification data.
  • step S207 the preprocessing unit 46 normalizes the verification data.
  • step S208 the causal graph verification unit 34 verifies the causal graph using Granger causality.
  • step S209 the input unit 44 acquires data for verification by pseudo correlation from the time series data DB 42.
  • step S210 the preprocessing unit 46 changes the dimension of the verification data.
  • step S211 the preprocessing unit 46 normalizes the verification data.
  • step S212 the causal graph verification unit 34 verifies the causal relationship using pseudo correlation.
  • the causal graph verified by the causal graph verification unit 34 is output to the output unit 90.
  • Embodiment 2 also includes, for example, predicting road surface damage from traffic volume or weather information, predicting river water level from nearby rainfall and water level data, predicting power demand using weather or economic status data of surrounding areas, It is applicable to
  • FIGS. 17A and 17B show a learning unit and an inference unit that perform a process of predicting unobserved time series data from the relationships between time series data by the causality estimation device 200.
  • the causal relationship estimation device 100 generates a learned model by performing multi-task learning on past congestion information of A1, A2, and A3 stations shown in FIG. 17(A).
  • the causal relationship estimation device 100 knows only the congestion information of A1 station and A2 station among A1 station, A2 station, and A3 station, and does not know the congestion information of A3 station (case of FIG. 17(B))
  • the inference unit uses the trained model generated by multi-task learning, it is possible for the inference unit to predict (infer) the degree of congestion at A3 station from the correlation or lag information of mutual congestion degrees.
  • FIG. 18 is a diagram illustrating an operation when changing points or failures in sensor data are learned by introducing a Change Point Kernel into the causal relationship estimation device 100. Failure prediction can be performed by using a trained model generated by learning sensor data change points or failures.
  • causal relationship estimation device 100 causal relationship estimation device, 200 causal relationship estimation device (causal graph construction device), 10 data acquisition unit, 12, 42 time series data DB, 14 input unit, 16 preprocessing unit, 17 dimension change unit, 18 normalization unit, 20 learning unit, 22 calculation unit, 24 optimization unit, 26, 80 causality parameter DB, 30 construction unit, 32 causal graph construction unit, 34 causal graph verification unit, 40 data acquisition unit, 44 input unit, 46 preprocessing unit , 90 output section.

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