WO2016194051A1 - Système de recherche d'ensemble de paramètres dans lequel une valeur statistique d'indice d'intérêt de système stochastique est réduite à un minimum - Google Patents

Système de recherche d'ensemble de paramètres dans lequel une valeur statistique d'indice d'intérêt de système stochastique est réduite à un minimum Download PDF

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WO2016194051A1
WO2016194051A1 PCT/JP2015/065588 JP2015065588W WO2016194051A1 WO 2016194051 A1 WO2016194051 A1 WO 2016194051A1 JP 2015065588 W JP2015065588 W JP 2015065588W WO 2016194051 A1 WO2016194051 A1 WO 2016194051A1
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parameter set
parameter
evaluated
attention index
value
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PCT/JP2015/065588
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Japanese (ja)
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幸二 福田
泰幸 工藤
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株式会社日立製作所
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Publication of WO2016194051A1 publication Critical patent/WO2016194051A1/fr

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N7/00—Computing arrangements based on specific mathematical models
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N99/00—Subject matter not provided for in other groups of this subclass
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"

Definitions

  • the present invention relates to a system for searching a parameter set that minimizes a statistic of a target index of a stochastic system.
  • the future behavior is predicted by simulating the behavior of the system modeled by the computer. For example, a certain physical phenomenon or a social phenomenon in which many elements are entangled cannot be described by a simple deterministic model, but is described as a complex and probabilistic model.
  • a deterministic system determines the future behavior of the system under a given initial condition.
  • the future behavior of the system is distributed according to a probability distribution.
  • a Monte Carlo simulation method is known as a method for a computer to predict and simulate the statistical behavior of such a stochastic system.
  • the Monte Carlo simulation method is a method for estimating a statistic relating to a target index by repeatedly performing a simulation simulating a stochastic behavior existing in a target system using random numbers. At this time, by increasing the number of simulations, it is considered that the statistic relating to the attention index approaches a true value according to the law of large numbers.
  • Patent Document 1 includes “a data acquisition step 0201 for acquiring a long-term forecast published by the Japan Meteorological Agency for meteorological physical quantities, a meteorological time series model creating step 0202 for creating a time series model according to meteorological physical quantities, and an estimation point in an estimation period.
  • a meteorological physical quantity simulation step 0203 for simulating the meteorological physical quantity for the number of simulations, a meteorological physical quantity estimation result output step 0204 for outputting the simulation result of the meteorological physical quantity as a meteorological physical quantity estimation result, and a meteorological time series model creation step 0202 are further included. It is composed of a time series model parameter estimation step 02021 and a weather time series model parameter correction step 02022 ”(see summary).
  • a stochastic model that is a target of Monte Carlo simulation has a plurality of parameters.
  • a set of a plurality of parameters existing in the system under consideration is referred to as a parameter set.
  • a plurality of parameters existing in the system are often optimized, that is, within a range of allowable parameter sets, for example, an estimation in a simulation technique described in Patent Document 1 is performed.
  • it is desired to search for a parameter set that minimizes or maximizes some statistic relating to the meteorological physical quantity at the estimated point in the period such as an expected value, a mode value, or a value at risk.
  • the computer first determines an initial value of an optimal parameter set candidate by some means, for example, by randomly selecting within an allowable parameter set range. After that, the computer evaluates the value of the optimization objective function in the current parameter set candidate by experiment or simulation, and updates the optimal parameter set candidate based on the evaluated objective function value. ,repeat. The computer performs the optimization by sequentially repeating the processing so that the optimum parameter set candidates are brought closer to the true parameter set.
  • the objective function of optimization is not the attention index itself but a statistic about the attention index.
  • the computer performs processing for evaluating the attention index in the current parameter set candidate, that is, calculation of the evaluation value of the attention index many times.
  • the calculator estimates a statistic from a large number of calculated evaluation values.
  • the computer needs to perform the process of evaluating the attention index in the parameter set many times each time the parameter set candidate is updated. Therefore, the processing amount becomes enormous.
  • the calculation of the evaluation value of the probabilistic system attention index described above is not necessarily performed by computer processing such as Monte Carlo simulation.
  • computer processing such as Monte Carlo simulation.
  • an evaluation process based on, for example, an experiment or an observation is performed instead of a simulation on a computer.
  • experiments and observations take a lot of time and cost, it is necessary to reduce the total number of experiments and observations performed until searching for an optimal parameter set as much as possible.
  • a system for searching a parameter set for minimizing a statistic of the attention index of a stochastic system that outputs an evaluation value of the attention index from a parameter set comprising: a processor; and a memory, Evaluation information including an evaluated parameter set and an evaluation value of the attention index of each of the evaluated parameter sets is held, and the processor repeats a search process, and the search process includes one or more parameter sets.
  • a first parameter set set is acquired and it is determined that the first parameter set set has not converged with a predetermined accuracy
  • a first evaluated parameter is determined from the evaluation information for each parameter set of the first parameter set set.
  • a set set and a corresponding evaluation value of the attention index are selected, and the first evaluation A first weight corresponding to an evaluation value of the attention index of each parameter set of the first evaluated parameter set set is calculated based on a distance from each parameter set of the first parameter set set, and the first evaluated parameter Based on the evaluation value of the attention index of each parameter set of the set set and the first weight, an estimated value of the statistics of the attention index of the parameter set of the first parameter set set is calculated, A new parameter set candidate composed of one or more parameter sets and different from the first parameter set set is generated using a predetermined algorithm, and each parameter set of the new parameter set set candidates is generated.
  • the estimated value of the statistic of the attention index is calculated, and the estimated value of the statistic of the attention index of each parameter set of the first parameter set set and the new parameter set set candidate is calculated based on From one parameter set set and the new parameter set set candidate, one or more parameter sets A parameter set to be included in the new parameter set set, and adopting the new parameter set set as a first parameter set set in the next search process.
  • Example 1 it is a block diagram showing an example of the whole structure of a parameter set optimization system.
  • 6 is a flowchart illustrating an example of overall processing of the parameter set optimization system in the first embodiment.
  • 6 is a flowchart illustrating an example of a statistic estimation process in the first embodiment.
  • Example 1 it is a figure explaining the concept of the distance between parameter sets in an example of the estimation process of a statistic.
  • it is a figure showing an example of the weight function in the estimation process of a statistic.
  • Example 1 it is a flowchart showing another example of the estimation process of a statistic.
  • it is a figure explaining the concept of the average radius in another example of the estimation process of a statistic.
  • Example 1 it is a figure showing an example of the weight function in another example of the estimation process of a statistic.
  • Example 1 is a flowchart showing another example of the estimation process of a statistic.
  • Example 1 it is a figure showing an example of estimation of the empirical distribution function in the estimation process of a statistic.
  • Example 1 it is a figure showing an example of the log output at the time of applying a well-known optimization method to the parameter set optimization process of a stochastic system.
  • Example 1 it is a figure showing an example of the log output of the parameter set optimization system in this invention.
  • Example 1 it is a figure showing an example of the setting screen of the parameter set optimization system in this invention.
  • Example 2 it is a circuit diagram showing an example of the circuit of the SRAM cell comprised by six transistors.
  • Example 3 it is a figure showing an example of the balance plan table of a bank.
  • Example 3 it is a figure which shows an example of the probability distribution of the profit of a bank.
  • This example describes a parameter set optimization system in a stochastic system.
  • a theoretical aspect for the parameter set optimization system of the present embodiment to perform parameter set optimization will be described.
  • a target index that is the target of optimization is represented by a random variable X.
  • the stochastic system is also simply referred to as a system. That is, the attention index of the stochastic system to be considered is modeled by the random variable X. X represents an actual value of X. The distribution of the attention index X depends on the parameter set z of the system, and the probability density function of X is expressed in the form of f (x, z).
  • parameter set z the parameter set z of the system is simply referred to as parameter set z. Further, when it is desired to emphasize that the random variable X depends on the parameter set z, the notation Xz or xz is used.
  • a (z) regarding the attention index X.
  • a (z) for example, when the probability density function f (x, z) of X z were considered as a function of x, a pan function that returns a single real number. Note that A (z) is a function of the parameter set z.
  • the parameter set optimizing device generates a large number of actual values x of the behavior of the system by Monte Carlo simulation, and simulates the distribution of X, that is, the cumulative distribution function F (x, z) by the empirical distribution.
  • the parameter set optimization apparatus can approximately calculate the value of the statistic A (z) related to the attention index from F (x, z).
  • the parameter set optimizing device F (x, z) Is simulated by an empirical distribution, the value of the statistic A (z) related to the attention index can be approximately calculated.
  • calculating the actual value x of the attention index is also referred to as evaluation of the attention index, and x is also referred to as the evaluation value of the attention index.
  • the distribution function F (x, z) is often continuous or at least piecewise continuous with respect to z. That is, if the difference (for example, Euclidean distance) between a certain parameter set z and a different parameter set z ′ is small, the difference between the respective distribution functions F (x, z) and F (x, z ′) (for example, F (x 1, z) in the x 1 at any point and F (x 1, z ') Euclidean distance between the like) may be considered to be small. Therefore, the difference (for example, Euclidean distance) between the statistics A (z) and A (z ′), which is a functional of F (x, z), is also considered to be small.
  • the parameter set optimization system is a different parameter set in which a statistic A (z) relating to an objective variable for optimization, that is, an attention index, in a given parameter set z is calculated in the past in the optimization process. Estimation is performed using the actual value x z ′ at z ′ .
  • the parameter set optimization system can greatly reduce the number of evaluations in each parameter set z, that is, experiments or simulations, by the above-described processing.
  • the “current parameter set” does not necessarily have to be one parameter set.
  • the parameter set is optimized by evaluating and updating a parameter set set including a plurality of parameter sets for each generation.
  • the “current parameter set” includes a parameter set set including a plurality of parameter sets unless otherwise specified.
  • FIG. 1 shows a configuration example of a parameter set optimization system 100 of the present embodiment.
  • the parameter set optimization system 100 is configured on a computer including a CPU 101, a memory 102, a communication interface 103, a secondary storage device 104, an input device 105, and an output device 106, for example.
  • the parameter set optimization system 100 is composed of one computer, but may be composed of a plurality of computers.
  • the CPU 101 includes a processor and / or a logic circuit that operates in accordance with a program, inputs / outputs data, reads / writes data, and executes each program described below.
  • the memory 102 temporarily loads and stores a program and data executed by the CPU 101, and holds each program and each data.
  • the communication interface 103 is an interface that inputs data from an external device or the like and outputs data to the external device or the like.
  • the secondary storage device 104 is a nonvolatile storage device such as an HDD, and holds programs and data. Part or all of the programs and data held in the memory 102 may be stored in the secondary storage device 104.
  • the input device 105 includes devices such as a mouse and a keyboard, for example, and receives input from a user or the like.
  • the output device 106 includes devices such as a printer and a display, and outputs processing results and the like.
  • the program is executed by the CPU 101, and a predetermined process is performed using the memory 102, the communication interface 103, and the like. Therefore, in the present embodiment and the other embodiments, the description with the program as the subject may be the description with the CPU 101 as the subject. Alternatively, the process executed by the program is a process performed by a computer and a computer system on which the program operates.
  • the CPU 101 operates as a functional unit that realizes a predetermined function by operating according to a program. For example, the CPU 101 performs an initial parameter set selection function by operating according to an initial parameter set selection unit 201 described later, and performs an index evaluation function by operating according to an index evaluation unit 202 described later. Furthermore, the CPU 101 also operates as a functional unit that realizes each of a plurality of processes executed by each program.
  • a computer and a computer system are an apparatus and a system including these functional units.
  • the memory 102 is an initial parameter set selection unit 201, an index evaluation unit 202, a current statistic estimation unit 204, a new parameter set candidate selection unit 205, a new statistic estimation unit 206, a parameter set selection unit 207, and an end program, respectively.
  • a condition determination unit 208 and an optimization processing overall control unit 209 are included.
  • the memory 102 also includes an evaluation value storage unit 203 that is an area for storing data and the like.
  • the optimization process overall control unit 209 controls the entire parameter set optimization system 100.
  • the overall optimization process control unit 209 controls the entire parameter set optimization process, which will be described later.
  • the optimization processing overall control unit 209 performs parameter set optimization processing for the attention index and some statistics specified by the user or the like.
  • the optimization process overall control unit 209 determines that the optimal parameter set has been searched with the required accuracy by the end condition determination unit 208, for example, the optimization process is ended and the processing result is output to the output device 106. Notice. Further, when the process cannot be continued for some reason during the process of parameter set optimization, the optimization process overall control unit 209 interrupts the process and performs a process of outputting an error message to the output device 106, for example. .
  • the initial parameter set selection unit 201 selects and outputs the initial value of the current parameter set from a predetermined range by a predetermined means.
  • the predetermined means will be described later.
  • the index evaluation unit 202 receives an input of the current parameter set z from the initial parameter set selection unit 201 or the parameter set selection unit 207, evaluates the attention index by means such as simulation, and outputs an evaluation result.
  • the index evaluation unit 202 may output an instruction for evaluation processing to the external system or the output device 106 instead of performing the evaluation by simulation or the like. At this time, for example, an external system or an experimenter performs an evaluation process according to the instruction, and inputs an evaluation result to the index evaluation unit 202.
  • the evaluation value storage unit 203 stores, for example, a set of the current parameter z input by the initial parameter set selection unit 201 or the parameter set selection unit 207 and the evaluation result input by the index evaluation unit 202.
  • the current statistic estimation unit 204 for example, evaluates the evaluation result under the current parameter set z evaluated by the index evaluation unit 202 and the evaluation under a past parameter set different from z held by the evaluation value storage unit 203. From the result, the estimated value A * (z) of the statistic A (z) in the current parameter set z is calculated and output. A specific calculation method will be described later.
  • the end condition determination unit 208 optimizes the parameter set based on A * (z) calculated by the current statistic estimation unit 204 and, if necessary, an estimated value of a statistic in a past parameter set different from z. However, for example, it is determined whether or not it has converged with the accuracy specified by the user.
  • the termination condition determination unit 208 notifies the optimization processing overall control unit 209 of the determination result.
  • the new parameter set candidate selection unit 205 selects a new parameter set candidate zN from a predetermined range based on the current parameter set z and A * (z) calculated by the statistic estimation unit 204. And output.
  • the new statistic estimation unit 206 calculates the statistic of the new parameter set candidate zN output by the new parameter set candidate selection unit 205 from the current and past parameter sets and the evaluation results of the current and past parameter sets. Estimated value A * (zN) is calculated and output. A specific calculation method of A * (zN) is the same as the estimation method in the current statistic estimation unit 204, for example, and details will be described later.
  • the parameter set selection unit 207 includes, for example, a set of the current parameter set z and A * (z) output by the current statistic estimation unit 204, and a new parameter set output by the new parameter set candidate selection unit 205.
  • the candidate zN and the set of A * (zN) output by the new statistic estimation unit 206 are compared.
  • the parameter set selection unit 207 determines whether to adopt or reject a new parameter set candidate zN based on the comparison.
  • the parameter set selection unit 207 outputs a new current parameter set z based on the determination result.
  • the new current parameter set z output from the parameter set selection unit 207 is evaluated by the index evaluation unit 202 again.
  • FIG. 2 shows an example of the entire process of the optimization method in this embodiment.
  • the initial parameter set selection unit 201 selects an initial value of the current parameter set from a predetermined range by some means (S211). For example, if the parameter set optimization system 100 holds prior knowledge about the optimal parameter set in advance, the initial parameter set selection unit 201 selects the initial value according to the prior knowledge. If the parameter set optimization system 100 does not hold the prior knowledge, the initial parameter set selection unit 201 may select the initial value from the range, for example, equally or randomly.
  • the index evaluation unit 202 evaluates the attention index under the current parameter set z (S212).
  • the index evaluation unit 202 evaluates the attention index for each parameter set. Since it is assumed that stochastic systems, indicator evaluating unit 202, evaluation value each time the evaluation under the same parameter set z, ie realization x z of interest indicator X z is to become every different value warn.
  • the index evaluation unit 202 may evaluate the attention index by a technique such as Monte Carlo simulation that simulates a stochastic behavior using random numbers. Note that the index evaluation unit 202 may evaluate the index in the current parameter set only once or a plurality of times. The index evaluation unit 202 can improve the accuracy of the estimated value A * (z) of the statistic in the current parameter set z, which is calculated in step S213 described later, by performing the evaluation a plurality of times.
  • the index evaluation unit 202 performs multiple evaluations using the current parameter set z, the number of evaluations for the entire optimization process increases accordingly.
  • the accuracy means, for example, the width of the confidence interval at the probability 95% of the estimated value A * (z), and the accuracy is higher as the confidence interval is narrower.
  • the index evaluation unit 202 may adaptively change the number of evaluations in step S212 based on the accuracy of an estimated value A * (z) of a statistic calculated in step S213 described later. Specifically, for example, if the accuracy of A * (z) calculated in step S213 does not reach a predetermined accuracy, the process returns to step S212 and the index evaluation unit 202 evaluates the attention index, and A * You may repeat until the precision of (z) reaches required precision.
  • the evaluation value storage unit 203 stores a combination of the current parameter set and the evaluation result of the attention index. Further, the evaluation process in step S212 may be performed by an external system by simulation or by an experimenter.
  • the current statistics estimating unit 204 the evaluation results under the current parameter set z calculated in step S212, the ie realized and the current value x z of X z, under the previous set of parameters different from the z
  • the estimated value A * (z) of the statistic in the current parameter set z is calculated based on a part or all of the evaluation result (S213).
  • the current statistic estimation unit 204 may not use the evaluation result under the current parameter set z in the calculation of A * (z). Further, in calculating A * (z), the current statistic estimation unit 204 may select and use a predetermined number of parameter sets in the order in which the adopted order is the newest among the past parameter sets.
  • the current statistic estimation unit 204 may estimate another quantity or function that can derive A * (z) instead of A * (z) itself in step S213. Specifically, the current statistic estimation unit 204 may estimate the distribution function F (x, z) of the attention index X instead of the statistic A (z), for example. In this case, the current statistic estimation unit 204 can calculate A * (z) from the estimated distribution function F * (x, z).
  • the evaluation value storage unit 203 stores a combination of the current parameter set and A * (z).
  • the end condition determination unit 208 uses the current parameter set, A * (z) calculated in step S213, and, if necessary, the estimated value of the statistic in a different parameter set in the past, as a parameter. It is determined whether the optimization of the set has converged with, for example, the accuracy specified by the user (S214).
  • the termination condition determination unit 208 performs convergence determination using, for example, the method described below.
  • the end condition determination unit 208 defines the distance between the parameter sets in the set by the root mean square or Mahalanobis distance, and calculates the magnitude of the variation of the parameter sets in the current parameter set set.
  • the end condition determination unit 208 determines that the parameter set has converged when the calculated variation is, for example, equal to or less than the threshold value specified by the user. judge.
  • the end condition determination unit 208 specifically, for example, the difference between the previous parameter set variation and the current parameter set variation is a predetermined threshold value. If it is below, it may be determined that it has converged, and if the decrease is not saturated, it may be determined that it has not converged.
  • the termination condition determination unit 208 may perform convergence determination using the distance between parameter sets taking into account the estimated value A * (z) of the statistic in each parameter set.
  • the end condition determination unit 208 uses the distance, even if the statistic A (z), which is the optimization objective function, changes abruptly with respect to z around the optimum value. Convergence can be judged with accuracy.
  • a * (z) is not used for determination in step S214, the order of step S213 and step S214 may be switched.
  • the end condition determination unit 208 When the current parameter set is only one parameter set, the end condition determination unit 208, for example, includes the current parameter set z and the parameter set most recently adopted among the past parameter sets different from z. , Calculate the distance. For example, the end condition determination unit 208 determines that the parameter set has converged if the calculated distance is equal to or less than a predetermined threshold, and determines that the parameter set has not converged if the calculated distance exceeds the predetermined threshold.
  • the optimization processing overall control unit 209 ends the optimization processing, and outputs, for example, information indicating the current parameter set z to the output device 106.
  • the optimization processing overall control unit 209 may output, for example, information indicating the set to the output device 106, or a predetermined size including the centroid of the parameter set of the set May be output to the output device 106.
  • the process proceeds to step S215.
  • the new parameter set candidate selection unit 205 selects a new parameter set candidate zN from a predetermined range based on the current parameter set z and A * (z) calculated in step S213 ( S215).
  • the new parameter set candidate selection unit 205 selects zN using, for example, a hill-climbing method, a quasi-Newton method, a differential evolution method, or a particle swarm optimization method.
  • the new parameter set candidate selection unit 205 may be, for example, a hill-climbing method or a quasi-Newton method It is desirable to use this method.
  • the new parameter set candidate selection unit 205 uses a broad evolutionary optimization method such as a differential evolution method or a particle swarm optimization method. Alternatively, it is desirable to use a technique such as annealing or tabu search.
  • the new statistic estimation unit 206 calculates, for example, the statistics of the new parameter set candidate zN selected in step S215 based on part or all of the set of the current and past parameter sets and the evaluation results.
  • An estimated value A * (zN) of the quantity is calculated (S216).
  • the new statistic estimation unit 206 may calculate A * (zN) using, for example, the same method as in step S213, and a specific calculation method will be described later with reference to FIG.
  • the parameter set selection unit 207 compares A * (z) calculated in step S213 with A * (zN) calculated in step S216, and adopts a new parameter set candidate zN. Whether to reject or not (S217).
  • the parameter set selection unit 207 updates the current parameter set based on the determination result.
  • the parameter set selection unit 207 adopts a new parameter set zN, and A * (zN) is greater than A * (z). Is too large, zN is rejected and the current parameter set z is adopted again.
  • the parameter set selection unit 207 adopts zN when A * (zN) is smaller than a times A * (z) for a real number a of 0 or more, and A * (zN) is A *. If it is larger than a times (z), zN may be rejected and z may be adopted again. In this case, if a is less than 1, a new parameter set zN is difficult to be adopted, and if a is greater than 1, a new parameter set zN is likely to be adopted, so that the optimization efficiency changes.
  • the parameter set selection unit 207 adopts zN when the ratio of A * (zN) to A * (z) is smaller than the random number generated in the computer, and zN when it is larger.
  • the determination may be made using a random selection algorithm that rejects and employs z again.
  • the parameter set selection unit 207 selects a predetermined number of estimated values of statistics corresponding to the parameter sets of the current parameter set set and the new parameter set set in ascending order. For example, the parameter set selection unit 207 sets a set of parameter sets corresponding to the selected estimated value as a new parameter set set.
  • the parameter set selection unit 207 assigns a random number to each of the estimated values, selects a predetermined number of estimated values in ascending order from the estimated values for which the assigned random number is equal to or larger than the predetermined value, and sets the selected estimated value to the selected estimated value.
  • a set of corresponding parameter sets may be set as a new parameter set set.
  • step S217 If the result of determination in step S217 is that a new parameter set zN is adopted, the parameter set selection unit 207 changes the current parameter set z to a new parameter set zN (S218), and returns to step S212. . On the other hand, if the result of determination in step S217 is that a new parameter set zN has not been adopted, the parameter set selection unit 207 returns to step S212 without changing the current parameter set z. Thereafter, the parameter set optimization system 100 repeatedly executes steps S212 to S213 until the optimization process in step S213 ends.
  • step S213 the method of calculating A * (z) in step S213 and the method of calculating A * (zN) in step S216 may be different from each other. Also, these calculation methods may be different for each loop in this flow.
  • FIG. 3 shows an example of the process of step S213 performed by the current statistic estimation unit 204.
  • the evaluation value storage unit 203 holds L parameter sets z 1 to z L and evaluation results x 1 to x L in the L parameter sets.
  • the L parameter sets may include a current parameter set z.
  • FIG. 3 shows an example of processing in which the current statistic estimation unit 204 calculates an estimated value A * (z) of a statistic in the current parameter set z using z 1 to z L and x 1 to x L. Indicates.
  • FIG. 3 shows an example in which the statistics are average values.
  • the current statistic estimation unit 204 performs a weight calculation process (S301).
  • the current statistic estimation unit 204 determines a predetermined distance function r between the current parameter set z and each of the L parameter sets z 1 to z L held by the evaluation value storage unit 203.
  • the current statistic estimation unit 204 may use, for example, the Euclidean distance, the Manhattan distance, or the Chebyshev distance as the distance function d (z, z k ).
  • Figure 4 is a diagram illustrating the concept of processing the current statistics estimating unit 204 calculates the distance r k.
  • the current statistic estimation unit 204 calculates distances r 1 to r 6 between the six parameter sets z 1 to z 6 held by the evaluation value storage unit 203 and the current parameter set z.
  • An example is shown.
  • the weight function w (r) determined by the distance r is, for example, a decreasing function for r, and is a function in which r is infinite and w (r) converges to 0.
  • FIG. 5 shows an example in which 1 / r ⁇ ⁇ (where ⁇ is a real number larger than 1) is used as the weighting function w (r).
  • w (r) 1 / r ⁇ ⁇ is a self-similar function and does not have a characteristic size. Therefore, the current statistic estimation unit 204 does not need to perform an operation of calculating the average radius of z k by using the above-described function to calculate the weight as in the case of using the function described later in FIG. Therefore, the processing amount can be reduced.
  • the current statistic estimation unit 204 performs an estimated value calculation process for calculating A * (z) (S302). Specifically, the current statistic estimation unit 204 calculates a total sum W of L weights w 1 to w L in the estimated value calculation process. Subsequently, the current statistic estimation unit 204 calculates the statistic estimation value A * (z) in the current parameter set z by summing up the relative weights w k / W corresponding to x k, respectively. .
  • the current statistic estimation unit 204 obtains the estimated value A * (z) of the statistic in the current parameter set z by performing the above process, that is, using a value obtained by weighting the evaluation value x k in the parameter set z k . Can be calculated.
  • FIG. 3 shows an example in which the statistic is an average value. However, when calculating an estimated value of another statistic, the formula in step S302 is changed to a formula for calculating the weighted statistic. Change it.
  • FIG. 6 shows another example of the statistic estimation process in step S213 performed by the current statistic estimation unit 204.
  • the preconditions such as information held by the evaluation value storage unit 203 are the same as those of the example of FIG.
  • FIG. 6 shows an example in which the statistics are average values.
  • the current statistic estimation unit 204 calculates an average radius r m of L parameter sets z 1 to z L (S601). Specifically, the current statistic estimation unit 204 calculates, for example, centroids z m of L parameter sets. Subsequently, the current statistics estimator 204, z m and each parameter set z k (k is a natural number 1 or more L or less) by calculating the mean square of the distance between, calculating the average radius r m.
  • Figure 7 is a diagram illustrating the concept of center of gravity z m and the average radius r m of the plurality of parameter sets. Each white point in FIG. 7 indicates each of L parameter sets, and each black point indicates the center of gravity z m .
  • the current statistics estimating unit 204 calculates the respective distances r k in the same manner as in FIG. 3. Further, the current statistic estimation unit 204 calculates each of the weights w k (S602).
  • the weight w k in the example of FIG. 6 depends not only on r k but also on the average radius r m , that is, the function for calculating the weight takes the form of w (r k ; r m ).
  • the current statistic estimation unit 204 performs an estimated value calculation process for calculating A * (z) by the same method as in step S302 (S603).
  • z 1 to z L include a parameter set that is exactly the same as or very close to the given parameter set z. That is, even when r is 0 or very close to 0, the statistic estimation process can be performed stably.
  • FIG. 9 shows another example of the statistic estimation process in step S213 performed by the current statistic estimation unit 204.
  • the preconditions such as information held by the evaluation value storage unit 203 are the same as those of the example of FIG.
  • the current statistic estimation unit 204 directly calculates the estimated value A * (z) of the statistic in the current parameter set z from the evaluation results x 1 to x L in the L parameter sets. Instead, first, an estimated distribution function F * (x, z) of the attention index X at z is calculated. The current statistic estimation unit 204 calculates A * (z) using the calculated F * (x, z).
  • the current statistic estimation unit 204 for example, in the same manner as in step S301, the distance r k between the given parameter set z and each of the L parameter sets z k held by the evaluation value storage unit 203. And the weights w k are calculated from the distance r k (S901).
  • the current statistic estimation unit 204 calculates the total sum W of each weight w k and calculates F * (x, z) using the relative weight w k / W (S902). Specifically, the current statistic estimation unit 204 calculates F * (x, z) as a weighted sum of the step function U (x ⁇ x k ) using the evaluation value x k as a threshold value.
  • U (x) is a unit step function.
  • FIG. 10 is a diagram for explaining the concept of distribution function estimation processing.
  • the evaluation value storage unit 203 holds six parameter sets z 1 to z 6 and evaluation values x 1 to x 6 of the attention index of each parameter set.
  • FIG. 10 shows an example of the estimated distribution function F * (x; z) when the magnitude relationship from x 1 to x 6 is x 3 ⁇ x 1 ⁇ x 6 ⁇ x 2 ⁇ x 5 ⁇ x 4 .
  • F * (x, z) has a step of height w k / W at each x k .
  • the distribution function estimation processing described here is obtained by adding weighting processing using the weight w k / W in the estimation of the empirical distribution function.
  • the current statistic estimation unit 204 uses a function having a characteristic scale (size) such as the Gaussian function described in FIG. 6 as a weight function instead of the weight shown in FIG. It may be estimated.
  • the current statistics estimator 204 for example, as described in FIG. 6 may be used an average radius r m as the scale.
  • the current statistic estimation unit 204 calculates an estimated value A * (z) of the statistic from the estimated distribution function F * (x, z) in the parameter z estimated in the distribution function estimation process (S903).
  • the current statistic estimation unit 204 calculates a statistic A (z) from the true distribution function F (x, z), for example, a distribution estimated instead of the true distribution function F (x, z).
  • a * (z) may be calculated by using the function F * (x, z).
  • the current statistic estimation unit 204 obtains an estimated distribution function F * (x, z) in a given parameter set z and calculates A * (z) from F * (x, z) in the method described in FIG. Calculated. Therefore, even if the specific implementation method for directly estimating the statistic from the weighted evaluation value (for example, the mathematical formula for directly estimating the average shown in step S302) is not known, the current statistic estimation unit 204 is A * (Z) can be calculated.
  • a method in which the current statistic estimation unit 204 calculates A * (z) using the approximate function F * (x, z) of the distribution function is, for example, that the statistic A (z) is the mode of the attention index x. In the case of a value (mode), the accuracy is higher than the method of directly estimating A * (z).
  • the explanation is read as the explanation of the new statistic estimation process in step S216.
  • the current statistic estimation unit 204 may be read as a new statistic estimation unit 206
  • the current parameter set z may be read as a new parameter set candidate zN.
  • FIG. 11 shows a case where a conventional optimization method, that is, a known optimization method such as a hill-climbing method, a quasi-Newton method, a differential evolution method, or a particle swarm optimization method is applied to optimization of a parameter set in a stochastic system as it is.
  • a conventional optimization method that is, a known optimization method such as a hill-climbing method, a quasi-Newton method, a differential evolution method, or a particle swarm optimization method is applied to optimization of a parameter set in a stochastic system as it is.
  • An example of the index evaluation history is shown. “Count” in the history indicates the total number of index evaluation processes, “Point Count” indicates the number of evaluations in the same parameter set, “z1” and “z2” indicate values of elements of the parameter set z, and “EvaluatedVal” indicates the value of the evaluation value x z of the attention index.
  • the computer sets each parameter set in order to calculate the statistic A (z) related to the attention index with sufficient accuracy. It is necessary to repeat the evaluation process many times.
  • the history includes evaluation values evaluated 100 times for the same parameter set. Further, the history includes an average value calculated from 100 evaluation results, and the calculated average value is used as an estimated value A * (z) of the statistic in the parameter set.
  • FIG. 12 shows an example of an index evaluation history when the optimization method of this embodiment is used.
  • the history is output to the output device 106, for example.
  • the history of FIG. 12 includes Count, z1, z2, EvaluatedVal, and EstimatedVal indicating the estimated value A * (z) of the statistic in the evaluation value xz of the target index.
  • Information indicated by Count, z1, z2, and Evaluated Val is the same as that in FIG.
  • the parameter set optimization system 100 performs evaluation for each parameter set once (or a smaller number of times compared to the case where the conventional optimization method is applied as it is).
  • the example of the history in FIG. 12 is that one A * (z) is displayed for one evaluation value in each parameter set, and that the parameter set changes each time the count is performed. Different from history.
  • FIG. 13 is an example of a user interface of the parameter set optimization processing system in the present embodiment.
  • the user interface 1300 is displayed on the output device 106, for example, and includes an optimization target setting section 1310 for designating an optimization target and an optimization condition setting section 1320 for displaying optimization processing conditions. .
  • the user inputs an optimization target and conditions in each section via the input device 105.
  • the optimization target setting section 1310 includes, for example, an optimization target model specifying section 1311, an attention index specifying section 1312, a check box 1313, a parameter set specifying section 1314, and a statistic specifying section 1315.
  • the optimization target model designation section 1311 accepts designation of a simulation model that is an optimization target.
  • the attention index designation section 1312 accepts designation of a method for calculating the actual value x of the optimization attention index X from the simulation result.
  • the parameter set specification section 1314 accepts specification of a parameter set z that is one or more parameters that are targets of optimization.
  • a check box 1313 is a check box for designating all parameters included in the optimization target model as optimization targets.
  • Statistic specification section 1315 accepts specification of the type of statistic A (z) calculated from the distribution of attention index X.
  • the expected value, the mode value, the value at risk, or the like is an example of the type of the statistic specified in the statistic specifying section 1315.
  • the statistic specification section 1315 may accept, for example, an input of a mathematical formula for calculating a statistic index from the distribution of the attention index X.
  • the optimization condition setting section 1320 includes, for example, an optimization method specifying section 1321, a model evaluation number specifying section 1322, a calculation time specifying section 1323, a reliability specifying section 1324, and a confidence interval radius specifying section 1325.
  • the optimization method designation section 1321 accepts designation of methods such as a hill-climbing method, a quasi-Newton method, a differential evolution method, and a particle swarm optimization method.
  • the optimization method designation section 1321 may accept designation of a program or the like in which the optimization method is described.
  • the model evaluation count designation section 1322 accepts specification of the model in the entire optimization process, that is, designation of the total number of simulations.
  • the calculation time designation section 1323 accepts designation of the maximum time for the optimization process. Since the number of model evaluations and the calculation time are in a proportional relationship, when one of them is specified, the other is automatically determined. Therefore, the user can designate only one value of the model evaluation number designation section 1322 or the calculation time designation section 1323, and the other section may display the value calculated by the parameter set optimization system 100. .
  • the reliability specification section 1324 and the confidence interval radius specification section 1325 accept specification of information for determining the target accuracy of optimization.
  • the confidence interval radius designated in the confidence interval radius designation section 1325 that is, 10 ⁇ 5 . This indicates a condition that the probability that the optimum parameter set exists is the reliability specified in the reliability specification section 1324, that is, 95% or more.
  • the other set of sections may display a guide value automatically calculated by the parameter set optimization system 100.
  • the parameter set optimization system 100 uses different parameter sets in which the statistic A (z) of the attention index that is an optimization target in the parameter set z necessary in the course of the optimization process is evaluated in the past.
  • the evaluation value of the attention index By using the evaluation value of the attention index at, the number of evaluations of the attention index for each parameter set candidate is sufficient.
  • the parameter set optimization system 100 according to the present embodiment significantly reduces the total number of evaluations of the attention index in the entire optimization process while maintaining the accuracy in the optimization process, and performs a high-speed optimization process. It can be realized.
  • a parameter set optimization unit is applied to a design that takes into account manufacturing variations in an electronic circuit of a semiconductor integrated circuit in a probabilistic model having a large number of parameters.
  • the circuit designer needs to optimize the design parameters so as to optimize the characteristics in consideration of variations in the designed circuit.
  • the design parameters in each transistor include about 10 related to variations, power, layout area, etc., such as gate width W, gate length L, diffusion layer width LOD, and inter-transistor distance PDX. Therefore, in general, the number of design parameters of the circuit block is about 10 times the number of transistors constituting the circuit. Since the design parameters in a complicated circuit block composed of a large number of transistors can be enormous, it is difficult to manually optimize individual design parameters. In this embodiment, design efficiency can be greatly improved by automatically obtaining design parameters that optimize characteristics that take into account circuit variations, such as expected performance values, yield, or power consumption. .
  • FIG. 14 shows an example of an SRAM cell circuit composed of six transistors.
  • the SRAM cell needs to satisfy mutually contradicting characteristics that the value stored in the SRAM cell is not lost in normal times and that the stored value of the SRAM cell is properly rewritten to the intended value when the memory is rewritten.
  • the actual parameter values of the individual transistors in the manufactured integrated circuit do not become values specified at the time of design due to variations in manufacturing of the integrated circuit, but are distributed according to a certain probability distribution, for example. As a result, for example, a value that is normally stored in the SRAM cell may be lost, or when the memory is rewritten, the stored value of the SRAM cell may not be properly rewritten to the intended value.
  • the circuit designer needs to optimize the design parameters so as to minimize the defect rate of the actually manufactured SRAM cell circuit by performing a Monte Carlo simulation by changing the design parameter values to various values. is there.
  • the optimization of the parameter set optimization method in the stochastic system of the first embodiment is described.
  • the parameter vector z in this embodiment is composed of transistor design parameters. For example, when there are 10 design parameters for each transistor, the parameter vector z in an SRAM cell circuit composed of 6 transistors is a 60-dimensional vector.
  • the characteristic variation of the SRAM circuit is caused by the fact that the actual parameter value of the transistor varies at the time of manufacture. That is, for example, a 60-dimensional parameter y is generated with respect to a 60-dimensional design parameter z that determines the characteristics of the transistor due to variations in manufacturing.
  • the index evaluation unit 202 can determine the behavior x (t) of the SRAM cell circuit deterministically by a normal circuit simulation if the actual parameter y after manufacture is determined. Therefore, the index evaluation unit 202 can determine whether the SRAM circuit is a good product or a defective product based on the parameter y. The index evaluation unit 202 outputs 0 as the evaluation result if the SRAM circuit is a non-defective product and 1 if the SRAM circuit is defective. At this time, if the statistic A (z) of the evaluation result is the expected value E [x] of x, A (z) indicates the defective rate of the SRAM cell.
  • the current statistic estimation unit 204 and the new statistic estimation unit 206 are the non-defective items of the SRAM circuit output from the index evaluation unit 202 or output from the index evaluation unit 202 in the past and stored in the evaluation value storage unit 203.
  • the expected value of the determination result in the given parameter set z, that is, the defect rate is estimated from the determination result of the defective product. As described above, it is possible to optimize the design parameter that minimizes the defective rate of the SRAM circuit by using the parameter set optimization system 100 in the first embodiment.
  • the parameter set optimization system 100 can efficiently obtain the optimum design parameter value in consideration of manufacturing variations in an electronic circuit of a semiconductor integrated circuit composed of a large number of transistors. it can.
  • This embodiment will explain an example in which the parameter set optimizing means in a probabilistic system is applied to the profit optimization of a financial field, particularly a bank.
  • Financial institutions usually formulate business plans for the future transaction volume targets of the financial products they handle.
  • the purpose of a for-profit company, not just a financial institution, is to generate as much revenue as possible based on limited assets or other resources. It is an optimization problem that determines where to allocate assets or other resources.
  • FIG. 15 shows an example of the balance plan table in the bank.
  • the leftmost column of the income and expenditure schedule shows the items of financial products handled by the bank.
  • Actual banks may have several thousand financial product subjects.
  • Each row of the table shows the transaction amount for each item of the financial product in the period shown in the top row. For example, if the current time is the end of 2Q in 2014, the handling volume for '14 / 1Q and '14 / 2Q will show the actual value, and the handling volume after '14 / 3Q will be the plan at the current time (end of 2Q in 2014) Indicates the value.
  • FIG. 15 an example of a plan for a total of eight periods in a quarter unit is shown. However, in an actual bank, for example, a plan for about five years may be made on a monthly or week basis.
  • the balance plan table includes several hundred periods.
  • the relationship between transaction volume and revenue in each subject depends mainly on, for example, bank funding interest rates, that is, spot rates.
  • spot rates The relationship between the spot rate and the profit can be modeled with a certain degree of accuracy for each subject, whereas the future spot rate is uncertain and can only be probabilistically predicted.
  • the expected value and dispersion of earnings are simulated by Monte Carlo simulation, and the validity of the business plan is judged.
  • a random spot is used to generate a future spot rate realization path, calculate the revenue value based on the planned transaction volume of each item, and total the revenues of all subjects.
  • the process of calculating the profit value is performed many times. Through this multiple processing, the expected value and variability of the overall bank profit under the given business plan is estimated.
  • the parameter vector z in the present embodiment is, for example, a planned value of the handling amount in each future period for all subjects. For example, when the number of subjects is about several thousand and the period is several hundred periods, the parameter vector z is a vector of about 100,000 dimensions.
  • the index evaluation unit 202 Each time the evaluation is performed, the index evaluation unit 202 generates a new random number internally and generates one path for realizing a future spot rate.
  • the index evaluation unit 202 generates the realization path using a probabilistic model such as a Full-White model, a CIR model, or a BDT model, for example.
  • the spot rate at time t + 1 is determined based on the spot rate at time t and a random number (newly generated at time t).
  • the profit of the entire bank is calculated and output from the generated path of the future spot rate and the current parameter set z, that is, the planned value of the handling amount of about 100,000 items in total.
  • the current statistic estimation unit 204 and the new statistic estimation unit 206 are given based on the revenue value output by the index evaluation unit 202 or output in the past by the index evaluation unit 202 and stored in the evaluation value storage unit 203.
  • the expected value or the value at risk of the profit value in the obtained parameter set z is estimated.
  • FIG. 16 shows an example of a probability distribution of bank profits.
  • Value at risk (VaR) represents an estimated value of risk of loss of asset value over a certain period.
  • the example of FIG. 16 indicates that the probability that the maximum loss is equal to or lower than VaR is 95%.
  • the parameter set optimization system 100 of this embodiment can improve the efficiency of the business planning process in the financial field, particularly a bank.
  • this invention is not limited to the above-mentioned Example, Various modifications are included.
  • the above-described embodiments have been described in detail for easy understanding of the present invention, and are not necessarily limited to those having all the configurations described.
  • a part of the configuration of a certain embodiment can be replaced with the configuration of another embodiment, and the configuration of another embodiment can be added to the configuration of a certain embodiment.
  • each of the above-described configurations, functions, processing units, processing means, and the like may be realized by hardware by designing a part or all of them with, for example, an integrated circuit.
  • Each of the above-described configurations, functions, and the like may be realized by software by interpreting and executing a program that realizes each function by the processor.
  • Information such as programs, tables, and files that realize each function can be stored in a memory, a hard disk, a recording device such as an SSD (Solid State Drive), or a recording medium such as an IC card, an SD card, or a DVD.
  • control lines and information lines indicate what is considered necessary for the explanation, and not all the control lines and information lines on the product are necessarily shown. Actually, it may be considered that almost all the components are connected to each other.

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Abstract

L'invention concerne un système : qui conserve des informations d'évaluation qui comprennent des ensembles de paramètres évalués et la valeur d'évaluation de l'indice d'intérêt de chacun des ensembles de paramètres évalués ; qui sélectionne, relativement aux ensembles de paramètres d'un premier ensemble d'ensembles de paramètres, un premier ensemble d'ensembles de paramètres évalués et les valeurs d'évaluation correspondantes de l'indice d'intérêt dans les informations d'évaluation ; qui calcule, sur la base des distances entre les ensembles de paramètres évalués respectifs du premier ensemble d'ensembles de paramètres évalués, des premiers poids correspondant aux valeurs d'évaluation de l'indice d'intérêt des ensembles de paramètres du premier ensemble d'ensembles de paramètres évalués ; sur la base des valeurs d'évaluation sélectionnées de l'indice d'intérêt et du premier poids, qui calcule une valeur estimée d'une valeur statistique de l'indice d'intérêt des ensembles de paramètres du premier ensemble d'ensembles de paramètres.
PCT/JP2015/065588 2015-05-29 2015-05-29 Système de recherche d'ensemble de paramètres dans lequel une valeur statistique d'indice d'intérêt de système stochastique est réduite à un minimum WO2016194051A1 (fr)

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WO2019235614A1 (fr) * 2018-06-07 2019-12-12 日本電気株式会社 Dispositif d'analyse de relation, procédé d'analyse de relation et support d'enregistrement
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JPWO2019235603A1 (ja) * 2018-06-07 2021-07-08 日本電気株式会社 関係性分析装置、関係性分析方法およびプログラム
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WO2020196866A1 (fr) * 2019-03-28 2020-10-01 株式会社 東芝 Dispositif de traitement d'informations, système de traitement d'informations, procédé de traitement d'informations, support de stockage et programme
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EP4379594A1 (fr) 2022-12-02 2024-06-05 Hitachi, Ltd. Système et procédé de simulation

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