Information processing device, information processing method, and information processing program

Abstract

The present invention provides an information processing device, an information processing method, and an information processing program that can reduce the possibility of adverse effects on decision-making due to dependence on the pattern of the probability distribution. [Solution] The information processing device, information processing method, and information processing program use a controller connected to an input unit and an output unit. The controller obtains input data relating to the probability density function followed by a random variable and a confidence coefficient via the input unit, calculates a range for the random variable where the probability density function is greater than or equal to a threshold, and is set based on a threshold where the difference between the integral amount and the confidence coefficient over the range of the probability density function is less than a predetermined standard value, based on the input data, and outputs output data relating to the range via the output unit.

Description

Technical Field

[0001] The present disclosure relates to an information processing apparatus, an information processing method, and an information processing program.

Background Art

[0002] Patent Document 1 discloses a technique related to a method for outputting measurement values and a display device. The technique acquires measurement values obtained by multiple measurements, calculates upper and lower boundaries regarding the confidence interval of the measurement values based on the average and standard deviation of the measurement values, and displays the upper and lower boundaries on a display.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] According to the technique described in Patent Document 1, only a pattern in which the probability distribution of the measurement values has a single peak is assumed in the interval sandwiched by the upper and lower boundaries. Depending on the pattern of the probability distribution, such as a pattern in which the probability distribution has two or more peaks in the interval, there may be measurement values with a low probability of being taken in the interval, and in this case, there is a problem that it may adversely affect decision-making based on the probability distribution. 7]

[0005] The present disclosure has been made in view of the above problems. An object thereof is to provide an information processing apparatus, an information processing method, and an information processing program capable of reducing the possibility of adversely affecting decision-making depending on the pattern of the probability distribution.

Means for Solving the Problems

[0006] The information processing device, information processing method, and information processing program relating to this disclosure use a controller connected to an input unit and an output unit. The controller obtains input data relating to the probability density function followed by a random variable and a confidence coefficient via the input unit, calculates a range for the random variable where the probability density function is greater than or equal to a threshold, and is set based on a threshold where the difference between the integral amount and the confidence coefficient over the range of the probability density function is less than a predetermined standard value, based on the input data, and outputs output data relating to the range via the output unit.

[0007] The probability density function may have multiple peaks.

[0008] The range may be divided into sections based on the peaks.

[0009] The output unit may output an interval of possible values ​​for at least one variable that constitutes the random variable, based on the output data.

[0010] The controller may calculate the range by changing the threshold so that the integrated quantity approaches the confidence coefficient.

[0011] The controller may increase the threshold when the integral is greater than the confidence coefficient, and decrease the threshold when the integral is less than the confidence coefficient.

[0012] The controller calculates a solution where the probability density function equals the threshold, and expresses the range based on the solution. It may also be something that represents something.

[0013] The controller may estimate the probability density function by performing parametric or nonparametric estimation based on the input data.

[0014] The random variable may include at least one of the following: a predicted value for the quantity of goods shipped, and a predicted value for the quantity of parts ordered. [Effects of the Invention]

[0015] According to the present disclosure, it is possible to provide an information processing apparatus, an information processing method, and an information processing program that can reduce the possibility of adversely affecting decision-making depending on the pattern of the probability distribution.

Brief Description of the Drawings

[0016] [Figure 1] It is a block diagram showing the configuration of an information processing apparatus according to an embodiment of the present disclosure. [Figure 2] It is a flowchart showing the processing procedure of the information processing apparatus. [Figure 3] It is a diagram showing an example of a probability density function having a plurality of peaks. [Figure 4A] It is a diagram showing an example of setting a range related to a random variable. [Figure 4B] It is a diagram showing a comparative example of setting a range related to a random variable. [Figure 5A] It is a diagram showing an example of setting a range related to a random variable in time series prediction. [Figure 5B] It is a diagram showing a comparative example of setting a range related to a random variable in time series prediction.

Embodiments for Carrying Out the Invention

[0017] Hereinafter, several exemplary embodiments will be described with reference to the drawings. In the drawings, the same reference numerals are given to common parts, and redundant descriptions are omitted.

[0018] [Configuration of Information Processing Apparatus] FIG. 1 is a block diagram showing the configuration of an information processing apparatus according to an embodiment of the present disclosure. The information processing apparatus 20 includes an input unit 21, an output unit 23, and a controller 25. The information processing apparatus 20 may include an operation unit 27. The controller 25 is connected so as to be communicable with the input unit 21, the output unit 23, and the operation unit 27.

[0019] In addition, the input unit 21, the output unit 23, and the operation unit 27 may be provided in the information processing apparatus 20 itself, or may be arranged outside the information processing apparatus 20 and connected to the information processing apparatus 20.

[0020] The input unit 21 acquires input data regarding a probability density function followed by a random variable.

[0021] A "random variable" is a variable that takes values (for example, real numbers or integers) assigned to possible events in the probability theory of statistics. Each event has a probability, and the random variable randomly takes values according to the proportion thereof. The random variable may be a discrete random variable that takes discrete values, or may be a continuous random variable that takes continuous values within a predetermined range. The random variable may be a one-variable real number or a multi-variable real number of two or more. The probability determined based on the random variable is called a probability distribution.

[0022] A "probability density function" is a function that describes the probability density of an event that a continuous random variable takes a certain value. It is defined such that the probability that the random variable takes values within a certain range can be obtained by integrating the probability density function over that range. The value range of the probability density function is a non-negative real number, and the integral over the entire domain of the random variable is 1. Note that for a discrete random variable, the "probability density function" may be read as a probability mass function that associates the probability of the random variable taking that value.

[0023] "Input data" is data that characterizes the probability density function. The input data may be values (sampling values) actually taken by the random variable, or may be statistical quantities (mean, variance, kurtosis, skewness, etc.) of the values taken by the random variable. The input data may be data indicating the probability density function itself followed by the random variable. The data characterizing the probability density function is not limited to the examples given here. [[ID=第十九]]

[0024] Furthermore, probability distributions can be of various types. For example, the probability density function that a random variable follows may have one peak or two or more peaks. A probability density function with only one peak is called "unimodal," and a probability density function with two or more peaks is called "multimodal."

[0025] For example, the probability distribution may be a normal distribution, exponential distribution, gamma distribution, beta distribution, uniform distribution, Cauchy distribution, log-normal distribution, Pareto distribution, Weibull distribution, hypergeometric distribution, binomial distribution, Bernoulli distribution, Poisson distribution, etc. The probability distribution may also be represented by a superposition of these distributions. The probability distribution is not limited to the examples given here. Furthermore, the input data may include type data indicating which of these distributions the probability distribution belongs to.

[0026] Next, let's look at an example of a "random variable." In recent years, there has been a growing demand for decision-making based on data-driven estimation and forecasting (hereinafter collectively referred to as "estimation"), such as determining appropriate inventory levels and staffing based on shipment volume forecasts in logistics warehouses. A "random variable" may include at least one of the following: a predicted value for the shipment volume of goods, or a predicted value for the order volume of parts. Random variables are not limited to the examples given here.

[0027] The input unit 21 may be connected to a computer (not shown) that performs estimations related to random variables, such as predicted values ​​for the quantity of goods shipped and predicted values ​​for the quantity of parts ordered. The input unit 21 may also acquire input data related to the probability density function followed by the random variable from the computer that performs the estimations related to the random variable.

[0028] For sound decision-making, it is crucial not only to improve the accuracy of estimates regarding the quantity of goods shipped or the quantity of parts ordered, but also to provide users with more information to guide their decisions. For example, for random variables, "interval estimation" can be used instead of "point estimation." Point estimation presents only one specific estimated value. Interval estimation, on the other hand, estimates and presents the range of high-probability values ​​(also called a confidence interval) that the random variable can take. Compared to point estimation, using interval estimation makes it easier for users to make decisions that take into account the reliability and uncertainty of the data and estimation model.

[0029] To indicate the range of probabilities that a random variable can take, the input unit 21 obtains a confidence coefficient. Here, the "confidence coefficient" is a parameter that determines the range of the random variable used when integrating the probability density function. For example, the confidence coefficient is a real number in the range of 0 to 1.

[0030] The range for the random variable includes the values ​​of the random variable corresponding to the peak of the probability density function, and as the confidence coefficient approaches 0, the range for the random variable narrows to a narrower range near the values ​​of the random variable corresponding to the peak of the probability density function. If the probability density function has multiple peaks, the range for the random variable may be divided according to each peak. As the confidence coefficient approaches 1, the range of the random variable becomes wider, and this range approaches the domain of the random variable. How to calculate the range of the random variable based on the confidence coefficient will be explained later.

[0031] The output unit 23 outputs output data generated by the controller 25, which will be described later. The "output data" is data relating to the range of a random variable.

[0032] Furthermore, the output unit 23 may output the range of possible values ​​for at least one variable constituting the random variable, based on the output data. More specifically, if the random variable is composed of univariate real numbers, it may output the range of possible values ​​for that univariate real number. Also, if the random variable is composed of multivariate real numbers, it may output the range of possible values ​​for any one of the multivariate real numbers.

[0033] For example, the output unit 23 may be connected to a display device (not shown) and output to the user of the information processing device 20, via the display device, an interval of possible values ​​for at least one variable constituting the random variable. Alternatively, the output unit 23 may be connected to a computer (not shown) that performs subsequent processing using the interval related to the random variable.

[0034] The operation unit 27 is an input device that allows the user of the information processing device 20 to perform operations. For example, the operation unit 27 may be a keyboard, mouse, trackball, touch panel, etc. The operation unit 27 is not limited to the examples given herein. The user's operations entered via the operation unit 27 are transmitted to the controller 25.

[0035] For example, the operation unit 27 may acquire input data relating to the probability density function followed by a random variable based on user operations. Alternatively, the operation unit 27 may acquire confidence coefficients based on user operations. In this case, the operation unit 27 functions as an input unit 21. The input data relating to the probability density function followed by the random variable, and the confidence coefficients, may be acquired via the input unit 21 or via the operation unit 27.

[0036] The controller 25 is a general-purpose computer equipped with a CPU (Central Processing Unit), memory, and an input / output unit. The controller 25 has a computer program (information processing program) installed on it that allows it to function as an information processing device 20. By executing the computer program, the controller 25 functions as one of the multiple information processing circuits (251, 253, 255, 257, 259) provided by the information processing device 20.

[0037] This disclosure provides an example of implementing multiple information processing circuits (251, 253, 255, 257, 259) using software. However, it is also possible to configure the information processing circuits (251, 253, 255, 257, 259) by preparing dedicated hardware for each of the information processing operations described below. Alternatively, the multiple information processing circuits (251, 253, 255, 257, 259) may be configured using separate hardware.

[0038] As shown in Figure 1, the controller 25 comprises a plurality of information processing circuits (251, 253, 255, 257, 259), including a generation unit 251, a threshold setting unit 253, a calculation unit 255, a determination unit 257, and an output generation unit 259.

[0039] The generation unit 251 obtains input data and confidence coefficients related to the probability density function followed by the random variable via the input unit 21. Then, the generation unit 251 generates the probability density function followed by the random variable based on the input data.

[0040] For example, based on the input data, parametric estimation or non-parametric estimation The probability density function may be estimated by performing estimation. Specifically, the generation unit 251 may generate a probability density function by aggregating multiple sample values. Alternatively, the generation unit 251 may select a type of probability distribution to reproduce the statistical quantity of the value taken by the random variable, set parameters that define the shape of the probability density function related to the selected probability distribution, and generate a probability density function.

[0041] If the input data is the probability density function that the random variable follows, the generation unit 251 may use that probability density function instead of generating a probability density function itself.

[0042] Figure 3 shows an example of a probability density function with multiple peaks. Figure 3 shows the probability density function F(X) obeyed by the random variable X. For example, the probability density function may have two or more peaks. In Figure 3, peaks P1 and P2 are shown, and the probability density function F(X) takes its maximum value at the peak locations.

[0043] The threshold setting unit 253 sets a threshold for defining a range for a random variable. The threshold setting unit 253 may also modify the set threshold. The threshold setting unit 253 sets a range for a random variable in which the probability density function is greater than or equal to the threshold.

[0044] For example, the threshold setting unit 253 may divide the domain of the random variable into a grid of predetermined fineness. For each of the multiple cells constituting the grid, the threshold setting unit 253 may determine whether the probability density function is greater than or equal to a threshold. Then, it may extract the cells in which the probability density function is greater than or equal to the threshold, and set a range for the random variable whose probability density function is greater than or equal to the threshold by combining the extracted cells. The method for setting a range for the random variable whose probability density function is greater than or equal to a threshold is not limited to the examples given here.

[0045] Furthermore, the threshold setting unit 253 may calculate a solution in which the probability density function is equal to the threshold and express a range based on the calculated solution. For example, the threshold setting unit 253 may calculate a solution in which the probability density function is equal to the threshold using Newton's method or Newton-Raphson's method. In particular, considering the case where there are multiple solutions in which the probability density function is equal to the threshold, the threshold setting unit 253 may change the initial value of the random variable used in Newton's method or Newton-Raphson's method in various ways. The method for calculating a solution in which the probability density function is equal to the threshold is not limited to the examples given herein.

[0046] FIG. 4A is a diagram showing an example of setting a range related to a random variable. FIG. 4B is a diagram showing a comparative example of setting a range related to a random variable. In FIGS. 4A and 4B, it is shown that when the random variable X becomes X11, X12, X21, X22, the probability density function F(X) is equal to the threshold value TH.

[0047] Also, in FIG. 4A, in the range RG1 where “X11 ≦ X ≦ X12” and the range RG2 where “X21 ≦ X ≦ X22”, it is shown that the probability density function F(X) is equal to or greater than the threshold value TH. The range RG1 is a range near the peak P1, and the range RG2 is a range near the peak P2. Therefore, if the ranges RG1 and RG2 can be presented to the user, it can be recognized that the probability density function F(X) has the peaks P1 and P2. As a result, it becomes easy for the user to make a decision considering the reliability and uncertainty of the data and the estimation model.

[0048] Regarding the confidence interval, when only showing the interval sandwiched by the upper and lower boundaries, for example, it shows the range RGC where “X11 ≦ X ≦ X22” shown in FIG. 4B. The range RGC includes the range where the probability density function F(X) is less than the threshold value TH, that is, “X12 < X < X21”. That is, the range where the probability that the probability density function F(X) can take is small is shown without being distinguished from the ranges near the peaks P1 and P2. Therefore, there is a risk of adversely affecting the decision-making based on the probability distribution. Therefore, it is required to determine the threshold value TH corresponding to the confidence coefficient, and calculate and output the ranges RG1 and RG2 related to the random variable as shown in FIG. 4A.

[0049] Therefore, it is required to determine the threshold value TH corresponding to the confidence coefficient, and calculate and output the ranges RG1 and RG2 related to the random variable as shown in FIG. 4A.

[0050] The threshold setting unit 253 may also calculate a range for the random variable by changing the threshold in a direction that brings the integral amount calculated by the calculation unit 255 (described later) closer to the confidence coefficient. For example, the threshold setting unit 253 may increase the threshold when the integral amount is greater than the confidence coefficient, and decrease the threshold when the integral amount is less than the confidence coefficient.

[0051] The calculation unit 255 calculates the integral of the probability density function over a range of random variables where the probability density function is equal to or greater than a threshold. Specifically, it calculates the integral of the probability density function using the range of random variables set by the threshold setting unit 253 as the integration range.

[0052] For example, the threshold setting unit 253 calculates the integral of the probability density function by numerical integration. The threshold setting unit 253 may divide the integration range into a grid of predetermined fineness and calculate a value for each of the multiple cells constituting the grid by multiplying the measure of the cell (an index for measuring the size of the cell, such as length, area, or volume) by the value of the probability density function in that cell. The threshold setting unit 253 may then calculate the sum of the multiplied values ​​across the cells included in the integration range to calculate the integral of the probability density function.

[0053] In addition, the threshold setting unit 253 may calculate the integral of the probability density function using the Monte Carlo method. The method for calculating the integral of the probability density function is not limited to the examples given herein.

[0054] The integral obtained by the calculation unit 255 represents the probability of an event occurring that corresponds to a random variable whose probability density function is above a threshold. The integral obtained by the calculation unit 255 does not include the probability of an event occurring that corresponds to a random variable whose probability density function is below a threshold.

[0055] The determination unit 257 determines whether the difference between the integral quantity calculated by the calculation unit 255 and the confidence coefficient is less than a predetermined threshold value. The predetermined threshold value is a value that can be arbitrarily selected. The smaller the predetermined threshold value, the more accurate the calculation of the range of the random variable determined in relation to the confidence coefficient becomes.

[0056] If the difference between the integral and the confidence coefficient is not less than a predetermined threshold value, the threshold setting unit 253 changes the threshold in a direction that brings the integral closer to the confidence coefficient and recalculates the range for the random variable. In other words, the predetermined threshold value serves as the criterion for determining convergence when changing the threshold so that the integral converges to the confidence coefficient.

[0057] As described above, the controller 25 calculates the integral of the probability density function over a range of random variables where the probability density function is greater than or equal to a threshold, and obtains a threshold where the difference between the integral and the confidence coefficient is less than a predetermined standard value. Then, the controller 25 calculates a range to be set based on the threshold where the difference between the integral and the confidence coefficient is less than a predetermined standard value.

[0058] The output generation unit 259 outputs output data via the output unit 23 regarding a range set based on a threshold value when the difference between the integral quantity and the confidence coefficient is less than a predetermined reference value.

[0059] The "output data" is data relating to the range of a random variable, calculated based on the probability density function and confidence coefficient that the random variable follows. For example, the output data may be data that specifies the ranges RG1 and RG2 shown in Figure 4A. In particular, the output data includes data that specifies the range for each peak.

[0060] Specifically, if the random variable consists of univariate real numbers, the output data may include data representing the lower and upper limits of the range for each peak, namely "X11,X12" and "X21,X22".

[0061] Furthermore, if the random variable is composed of multiple real numbers, it may include data indicating the lower and upper limits of the range for each peak among the possible values ​​of any one of the multiple real numbers.

[0062] In addition, the output generation unit 259 may generate output data corresponding to each time step for a time-varying probability density function.

[0063] Figure 5A shows an example of setting a range for a random variable in time series forecasting. Figure 5B shows a comparison example of setting a range for a random variable in time series forecasting.

[0064] Figures 5A and 5B show how the positions of peaks P1 and P2 in the probability density function change with time T. By calculating the range for each peak, as shown in the ranges RG1 and RG2 in Figure 5A, and outputting it as output data, users can more easily recognize the trends in the probability distribution in time series forecasting. As a result, users can more easily make decisions that take into account the reliability and uncertainty of the data and estimation model.

[0065] As shown in Figure 5B, when range RGCs are output without distinguishing between peak ranges, it becomes difficult for users to recognize the trends in the probability distribution in time series forecasting. As a result, decision-making may be negatively affected.

[0066] For example, in the operation and management of a logistics warehouse, the predicted values ​​of the shipment volume of goods and the predicted values ​​of the order volume of parts can fluctuate depending on the time of day and other conditions. By making it easier to recognize the trends in the probability distribution in time series forecasts, users can determine appropriate inventory levels and staffing levels. Therefore, this can contribute to improving the efficiency of logistics warehouse operation and management. Furthermore, when applied to the forecasting of the order volume of spare parts for a plant, it can also contribute to improving the efficiency of spare parts management for the plant. For example, it can be applied when a predicted distribution of future order volumes is generated using historical data on order volumes or lifespan data of parts. By applying this disclosure to the predicted distribution of future order volumes, it is possible to generate a confidence interval for order volumes with a high probability.

[0067] [Processing Procedure of Information Processing Device] Figure 2 is a flowchart showing the processing procedure of an information processing device.

[0068] In step S101, the generation unit 251 obtains input data relating to the probability density function followed by the random variable, as well as a confidence coefficient, via the input unit 21.

[0069] In step S103, the generation unit 251 generates a probability density function that the random variable follows, based on the input data.

[0070] In step S105, the threshold setting unit 253 sets a threshold to define the range for the random variable.

[0071] In step S107, the threshold setting unit 253 sets a range for random variables whose probability density function is greater than or equal to a threshold.

[0072] In step S109, the calculation unit 255 calculates the integral of the probability density function over the range of random variables for which the probability density function is greater than or equal to a threshold.

[0073] In step S111, the determination unit 257 determines whether the difference between the integral and the confidence coefficient is less than a predetermined standard value.

[0074] If the difference between the integral and the confidence coefficient is not less than a predetermined standard value (the result is NO in step S111), in step S115, the threshold setting unit 253 changes the threshold so that the integral approaches the confidence coefficient. Then, the process proceeds to step S107.

[0075] On the other hand, if the difference between the integral and the confidence coefficient is less than a predetermined standard value (if the answer is YES in step S111), the output generation unit 259 outputs the output data in step S113.

[0076] [Effects of the Embodiment] As described in detail above, the information processing device, information processing method, and information processing program related to this disclosure use a controller connected to an input unit and an output unit. The controller obtains input data relating to the probability density function followed by a random variable and a confidence coefficient via the input unit, calculates a range for the random variable where the probability density function is greater than or equal to a threshold, and is set based on a threshold where the difference between the integral amount and the confidence coefficient over the range of the probability density function is less than a predetermined standard value, based on the input data, and outputs output data relating to the range via the output unit.

[0077] This reduces the likelihood that decisions may be negatively influenced by the pattern of the probability distribution. Users can more easily make decisions that take into account the reliability and uncertainty of the data and estimation models.

[0078] Specifically, as the confidence coefficient approaches 0, the range of the random variable becomes narrower, converging near the peak value of the random variable in the probability density function. Conversely, as the confidence coefficient approaches 1, the range of the random variable becomes wider, and this range approaches the domain of the random variable. In other words, within this range, the probability density function never falls below the threshold determined by the confidence coefficient. Therefore, situations where the range includes regions with a low probability of realization are avoided, and the negative impact on decision-making is suppressed.

[0079] Furthermore, the method can output regions that do not contain areas with low probability of realization, not only in the case where the probability density function has two or more peaks ("multimodal"), but also in the case where the probability density function has only one peak ("unimodal"). The method disclosed herein has the advantage of being able to handle both the "multimodal" and "unimodal" cases.

[0080] A probability density function may have multiple peaks. This allows users to make decisions that take into account the tendencies of the probability distribution when dealing with probability density functions with multiple peaks.

[0081] The range may be divided by peak. This allows the trends of the probability distribution to be output separately for each peak. As a result, users can make decisions that correspond to the trends of each peak.

[0082] The output unit may output the range of possible values ​​for at least one variable that constitutes the random variable, based on the output data. This allows the user to make decisions corresponding to the trend at each peak by focusing on at least one variable that constitutes the random variable. In particular, even when the random variable is composed of multivariate real numbers, focusing on a portion of the variables... Because the output is limited to a specific type, the burden on the user in recognizing the tendencies of the probability distribution can be reduced.

[0083] The controller may calculate the range by changing the threshold so that the integral quantity approaches the confidence coefficient. This allows for accurate determination of the range for a random variable based on the confidence coefficient.

[0084] The controller may increase the threshold when the integral is greater than the confidence coefficient and decrease the threshold when the integral is less than the confidence coefficient. This allows the threshold to be modified so that the integral converges to the confidence coefficient.

[0085] The controller may calculate a solution where the probability density function equals a threshold, and then express the range based on that solution. This allows for accurate determination of the range for a random variable based on the confidence coefficient. Furthermore, it ensures reliable calculation of the range for a random variable.

[0086] The controller may estimate the probability density function by performing parametric or nonparametric estimation based on the input data. This makes it possible to determine the probability density function corresponding to various probability distributions. The method of this disclosure can be applied to various probability distributions.

[0087] The random variable may include at least one of the following: a predicted value for the quantity of goods shipped, and a predicted value for the quantity of parts ordered. This allows the user to determine appropriate inventory levels and staffing levels for the operation and management of the logistics warehouse. Therefore, it can contribute to improving the efficiency of logistics warehouse operation and management. Furthermore, when applied to predicting the order quantity of spare parts for a plant, it can also contribute to improving the efficiency of managing spare parts for the plant. For the predicted value for the quantity of goods shipped and the predicted value for the quantity of parts ordered, a confidence interval for the predicted value with a high probability can be generated.

[0088] Each of the functions described in the embodiments above may be implemented by one or more processing circuits. These processing circuits may include programmed processors, electrical circuits, and other devices such as application-specific integrated circuits (ASICs), or circuit components arranged to perform the described functions.

[0089] Although several embodiments have been described, it is possible to modify or transform the embodiments based on the above disclosure. All components of the above embodiments, and all features described in the claims, may be taken individually and combined, provided that they do not conflict with each other. [Explanation of Symbols]

[0090] 20 Information Processing Device 20 21 Input section 21 23 Output section 23 25 Controller 25 27 Operation section 27 251 Generation section 251 253 Threshold setting unit 253 255 Calculation Unit 255 257 Judgment section 257 259 Output generation unit 259 P1, P2 peaks RG1, RG2, RGC range TH threshold

Claims

1. An information processing apparatus comprising an input unit, an output unit, and a controller, The aforementioned controller, Through the aforementioned input unit, input data relating to the probability density function followed by the random variable, and the confidence coefficient are obtained. The range relating to the random variable in which the probability density function is greater than or equal to a threshold, The range set based on the threshold value at which the difference between the integral of the probability density function over the range and the confidence coefficient is less than a predetermined reference value is calculated based on the input data. Output data relating to the range is output via the output unit. Information processing device.

2. The information processing apparatus according to claim 1, wherein the probability density function has multiple peaks.

3. The information processing apparatus according to claim 2, wherein the range is divided into the peaks.

4. The information processing apparatus according to claim 1, wherein the output unit outputs an interval of possible values ​​for at least one variable constituting the random variable based on the output data.

5. The information processing apparatus according to claim 1, wherein the controller changes the threshold in a direction that brings the integral amount closer to the confidence coefficient, and calculates the range.

6. The aforementioned controller, If the integral amount is greater than the confidence coefficient, the threshold is increased. If the integral amount is smaller than the confidence coefficient, the threshold is reduced. The information processing apparatus according to claim 5.

7. The aforementioned controller, A solution is calculated in which the probability density function is equal to the threshold. Based on the above solution, the range is expressed as follows: The information processing apparatus according to claim 1.

8. The information processing apparatus according to claim 1, wherein the controller estimates the probability density function by performing parametric estimation or nonparametric estimation based on the input data.

9. The information processing apparatus according to any one of claims 1 to 8, wherein the random variable includes at least one of a predicted value for the shipment quantity of goods and a predicted value for the order quantity of parts.

10. An information processing method for controlling a controller connected to an input unit and an output unit, The aforementioned controller, Through the aforementioned input unit, input data relating to the probability density function followed by the random variable, and the confidence coefficient are obtained. The range relating to the random variable in which the probability density function is greater than or equal to a threshold, The range set based on the threshold value at which the difference between the integral of the probability density function over the range and the confidence coefficient is less than a predetermined reference value is calculated based on the input data. Output data relating to the range is output via the output unit. Information processing methods.

11. An information processing program to be executed in a controller connected to an input unit and an output unit, The aforementioned controller, The steps include obtaining input data relating to the probability density function followed by the random variable, and the confidence coefficient, via the aforementioned input unit. The range relating to the random variable in which the probability density function is greater than or equal to a threshold, A step of calculating the range based on the input data, where the difference between the integral of the probability density function over the range and the confidence coefficient is less than a predetermined reference value is a threshold value, The steps include outputting output data relating to the range via the output unit, An information processing program that includes this.

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