Information processing device, information processing method, and program

Abstract

This information processing device acquires an acquisition function using the kernel mean embedding of conditional distribution that is estimated from a dataset obtained through data sampling. The information processing device determines, on the basis of the acquisition function, a sampling point at which to acquire data. The information processing device acquires data at the determined sampling point.

Description

[Technical Field]

[0001] This disclosure relates to an information processing device, an information processing method, and program Regarding. [Background technology]

[0002] Bayesian optimization is known as one method for efficiently acquiring data. For example, Patent Document 1 describes using a Bayesian optimization method to search for parameters, with the voltage applied to a liquid chromatograph-mass spectrometer as the parameter. Furthermore, Patent Document 1 describes that in Bayesian optimization, under the assumption that the model under investigation follows a Gaussian process, the mean and variance of the posterior distribution of the model function are calculated based on the acquired observational data, and the next experimental conditions are determined based on these calculated values. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] International Publication No. 2019 / 244474 [Overview of the project] [Problems that the invention aims to solve]

[0004] When determining the sampling points for acquiring data, it is preferable that the assumed probability distribution for the values ​​of the data to be acquired is not limited to a specific type of distribution.

[0005] One example of the purpose of this disclosure is to provide an information processing device, an information processing method, and that can solve the above-mentioned problems. program The objective is to provide. [Means for solving the problem]

[0006] According to a first aspect of this disclosure, the information processing device includes: an acquisition function acquisition means for acquiring an acquisition function using a kernel mean embedding of a conditional distribution estimated from a data set obtained by sampling data; a sampling point determination means for determining sampling points for acquiring data based on the acquisition function; and a data acquisition means for acquiring data at the sampling points determined by the sampling point determination means.

[0007] According to a second aspect of this disclosure, the information processing method includes a computer obtaining an acquisition function using a kernel mean embedding of a conditional distribution estimated from a data set obtained by sampling data, determining sampling points for acquiring data based on the acquisition function, and acquiring data at the determined sampling points.

[0008] According to a third aspect of this disclosure, program This is a program that causes a computer to perform the following actions: obtain an acquisition function using a kernel mean embedding of a conditional distribution estimated from a data set obtained by sampling data; determine sampling points for acquiring data based on the acquisition function; and acquire data at the determined sampling points. That is . [Effects of the Invention]

[0009] According to this disclosure, when determining the sampling points from which to acquire data, the probability distribution assumed for the values ​​of the data to be acquired is not limited to a specific type of distribution. [Brief explanation of the drawing]

[0010] [Figure 1] This figure shows an example of the configuration of an information processing device according to some embodiments of this disclosure. [Figure 2] This figure shows examples of multiple Gaussian kernel functions. [Figure 3] This figure shows an example of the superposition of multiple Gaussian kernel functions. [Figure 4]This figure shows an example of the integral of a Gaussian kernel function. [Figure 5] This figure shows an example of the relationship between the approximation function of the PI acquisition function and the bandwidth. [Figure 6] This figure shows an example of the relationship between the approximation function of the EI acquisition function and the bandwidth. [Figure 7] This figure shows an example of a processing procedure for performing a solution search using an information processing device according to some embodiments of the present disclosure. [Figure 8] This figure shows another example of the configuration of an information processing device according to some embodiments of the present disclosure. [Figure 9] This figure shows an example of the configuration of a system according to some embodiments of this disclosure. [Figure 10] This figure shows an example of a processing procedure in an information processing method according to some embodiments of the present disclosure. [Figure 11] This is a schematic block diagram showing the configuration of a computer according to at least one embodiment. [Modes for carrying out the invention]

[0011] The embodiments described below are not intended to limit the claims of the invention. Furthermore, not all combinations of features described in the embodiments are necessarily essential to the solution of the invention. Figure 1 is a diagram showing an example of the configuration of an information processing device according to some embodiments of the present disclosure. In the configuration shown in Figure 1, the information processing device 100 comprises a communication unit 110, a display unit 120, an operation input unit 130, a storage unit 180, and a processing unit 190. The processing unit 190 comprises a data acquisition unit 191, an acquisition function acquisition unit 192, and a sampling point determination unit 193.

[0012] The information processing device 100 acquires data. In particular, the information processing device 100 samples data in order to determine one or more of the following: the maximum value or the largest possible value of the data to be sampled, the conditions for the data to be sampled to take the maximum value or the largest possible value, the minimum value or the smallest possible value of the data to be sampled, and the conditions for the data to be sampled to take the minimum value or the smallest possible value. When sampling data, the information processing device 100 determines the next sampling point based on the data already obtained. The information processing device 100 may be configured using a computer such as a personal computer (PC) or a workstation (WS).

[0013] In this context, data sampling refers to determining the conditions under which data will be acquired and then acquiring the data under those conditions. The data to be sampled is the data being acquired. The act of acquiring data is also referred to as data observation. The conditions under which data is acquired are also called sampling points or observation points. The data that links a sampling point to the data to be sampled at that sampling point is also called sample data. The set of sample data is called the sample data set, or simply the data set.

[0014] For example, if the information processing device 100 wants to determine the parameter values ​​to set on a device that produces a certain product in order to maximize (faster) its production speed, the parameter values ​​can be used as sampling points, and the production speed can be used as the data to be sampled. In this case, determining the parameter values ​​for data acquisition, setting the determined parameter values ​​on the device, and measuring the production speed of the product by the device when those parameter values ​​are set are examples of data sampling.

[0015] Increasing values ​​such as production speed as much as possible is also referred to as maximizing those values. The information processing device 100 may automatically set the acquired parameter values, which are intended to maximize the production speed, into the device. Alternatively, the information processing device 100 may present the acquired parameter values, which are intended to maximize the production speed, to the user.

[0016] Alternatively, if the information processing device 100 determines parameter values ​​to be set in the communication system in order to minimize the error rate (e.g., the code error rate) of the communication system, the parameter values ​​can be used as sampling points and the error rate as the data to be sampled. In this case, determining the parameter values ​​for data acquisition, setting the determined parameter values ​​in the communication system, and measuring the error rate in the communication system when those parameter values ​​are set are examples of data sampling.

[0017] Minimizing values ​​such as the error rate is also referred to as reducing those values. The information processing device 100 may automatically set the acquired parameter values, which are intended to minimize the error rate, into its communication system. Alternatively, the information processing device 100 may present the acquired parameter values, which are intended to minimize the error rate, to the user.

[0018] The process of finding one or more of the following: the maximum value or the largest possible value of the data to be sampled, the conditions under which the data to be sampled takes the maximum value or the largest possible value, the minimum value or the smallest possible value of the data to be sampled, or the conditions under which the data to be sampled takes the minimum value or the smallest possible value, is also called solution search or sampling point search.

[0019] The following explanation will use an example where the information processing device 100 seeks (searches for) a sampling point that maximizes the amount of data to be sampled. However, the data search performed by the information processing device 100 is not limited to this. As described above, the information processing device 100 may seek the largest possible value of the data to be sampled. Alternatively, the information processing device 100 may seek a sampling point that results in the smallest possible data to be sampled. Alternatively, the information processing device 100 may seek the smallest possible value of the data to be sampled. Furthermore, the information processing device 100 may determine multiple pieces of the above data, such as determining the largest possible value of the data to be sampled and the sampling point at that time.

[0020] The information processing device 100 obtains an acquisition function using kernel mean embeddings, determines sampling points using the obtained acquisition function, and performs data sampling. The solution search performed by the information processing device 100 can be viewed as Bayesian optimization using kernel mean embeddings as a surrogate model. Here, the surrogate model is a model constructed based on sample data.

[0021] The communication unit 110 communicates with other devices. For example, if the information processing device 100 determines a parameter value to be set on the device to be acquired as a sampling point for acquiring data to be sampled, the communication unit 110 may transmit the determined parameter value to the device to be acquired for it to set. Alternatively, the communication unit 110 may receive data to be sampled from the device to be acquired. Furthermore, if the information processing device 100 automatically sets the acquired parameter value as a parameter value to maximize the value of the data to be sampled on the data acquisition target device, the communication unit 110 may transmit that parameter value to the data acquisition target device for it to set.

[0022] The display unit 120 has a display screen such as a liquid crystal panel or an LED (Light Emitting Diode) panel, and displays various images. For example, the display unit 120 may display the value obtained as the largest possible value of the data to be sampled, the sampling point from which that value was obtained, or either one of these. Furthermore, the display unit 120 may display the processing status while the information processing device 100 is searching for data. For example, the display unit 120 may display the probability distribution of the sampled data for each sampling point in a graph or the like.

[0023] The operation input unit 130 is configured to include, for example, input devices such as a keyboard and a mouse, and accepts user operations. For example, the operation input unit 130 may accept user operations to specify the data search range, such as the domain for defining the sampling points and the value range of the data to be sampled. The operation input unit 130 may also accept user operations to specify the sampling termination conditions, such as the number of sampling repetitions.

[0024] The storage unit 180 stores various types of data. The storage unit 180 is configured using the storage devices provided by the information processing device 100. The processing unit 190 controls various parts of the information processing device 100 to perform various processes. The functions of the processing unit 190 are performed, for example, by the CPU (Central Processing Unit) of the information processing device 100 reading a program from the storage unit 180 and executing it.

[0025] The data acquisition unit 191 acquires sample data. Specifically, the data acquisition unit 191 acquires the initial values ​​of the data set. The data acquisition unit 191 also acquires the data to be sampled at the sampling points determined by the sampling point determination unit 193 and updates the data set. The data acquisition unit 191 is an example of a data acquisition means. The data set acquired and updated by the data acquisition unit 191 is used by the acquisition function acquisition unit 192 to estimate the kernel mean embedding when acquiring the acquisition function. The kernel mean embedding acquired by the data acquisition unit 191 can be considered as a surrogate model of the probability distribution of the sampled data. By updating the data set by the data acquisition unit 191, the acquisition function acquisition unit 192 can improve the estimation accuracy of the kernel mean embedding, and is expected to obtain a more accurate acquisition function.

[0026] The initial values ​​of the data set are used by the acquisition function unit 192 to perform the initial estimation of the kernel mean embedding. The number of sample data points included in the initial values ​​of the data set can be one or more, and is not limited to a specific number.

[0027] In obtaining the initial values ​​of the data set, the data acquisition unit 191 or the sampling point determination unit 193 may select one or more sampling points from the domain of the sample points. The data acquisition unit 191 may then acquire the data to be sampled for each selected sampling point. The method of selecting the sampling points in this case is not limited to any particular method. For example, the data acquisition unit 191 or the sampling point determination unit 193 may select sampling points that evenly divide the domain of the sampling points. Alternatively, the data acquisition unit 191 may randomly select the sampling points. Alternatively, the sampling points to be adopted as the initial values ​​of the data set may be specified in advance. Alternatively, the storage unit 180 may store initial values ​​for the data set in advance. The data acquisition unit 191 may then read the initial values ​​for the data set from the storage unit 180.

[0028] In updating the data set, the data acquisition unit 191 generates sample data that links the sampling points determined by the sampling point determination unit 193 with the data to be sampled obtained at those sampling points. The data acquisition unit 191 then updates the data set by adding the generated sample data to the data set.

[0029] In data sampling, the information processing device 100 may be configured to automatically perform data sampling. For example, when the data acquisition unit 191 or the sampling point determination unit 193 determines a parameter value to be set as a sampling point on the device to be acquired, the data acquisition unit 191 may transmit the determined parameter value to the device to be acquired via the communication unit 110 for it to set. The data acquisition unit 191 may also receive the data to be sampled from the device to be acquired via the communication unit 110.

[0030] Alternatively, the information processing device 100 may present sampling points to the user, allowing the user to set the sampling points. For example, the data acquisition unit 191 or the sampling point determination unit 193 may determine the sampling points, which are then displayed on the display unit 120 to the user.

[0031] In acquiring the data to be sampled, the data acquisition unit 191 may acquire the data to be sampled from the device to be data acquired or from the sensor that measures the data to be sampled via the communication unit 110. Alternatively, the user may input the data to be sampled using the operation input unit 130, and the data acquisition unit 191 may acquire the input data to be sampled.

[0032] The acquisition function acquisition unit 192 acquires the acquisition function. Specifically, the acquisition function acquisition unit 192 estimates the kernel mean embedding based on the data set and calculates the acquisition function using the estimated kernel mean embedding. The acquisition function acquisition unit 192 is an example of an acquisition function acquisition means.

[0033] The sampling point determination unit 193 determines the sampling points at which the data acquisition unit 191 will sample data. The sampling point determination unit 193 determines the sampling points based on the acquisition function acquired by the acquisition function acquisition unit 192. The sampling point determination unit 193 is an example of a sampling point determination means. For example, the sampling point determination unit 193 may select sampling points where the value of the acquisition function is as large as possible, such as sampling points where the acquisition function takes its maximum value, as sampling points for which the data acquisition unit 191 will sample data. Alternatively, depending on the acquisition function, the sampling point determination unit 193 may select sampling points where the value of the acquisition function is as small as possible, such as sampling points where the acquisition function takes its minimum value, as sampling points for which the data acquisition unit 191 will sample data. The sampling point determination unit 193, the acquisition function acquisition unit 192, and the data acquisition unit 191 repeatedly determine sampling points, acquire acquisition functions, and acquire data until the termination condition for solution search by the information processing device 100 is met.

[0034] The acquisition function acquired by the acquisition function acquisition unit 192 will be explained further. Let Y be a probability space * Let Y be F, P. * represents the sample set (sample space). F is the sample set Y * This represents a sigma-algebra. P represents a probability measure. sample set Y * Let Y be a random variable whose values ​​are the elements of μ. Then, the kernel mean embeddings (KME) μ Y This can be expressed as shown in equation (1).

[0035]

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[0036] The ":=" sign indicates that the right-hand side is the definition of the left-hand side. In equation (1), the kernel mean embedding μ Y is, E Y[k Y* is defined as (·, Y). E represents the expected value. E Y represents the expected value with respect to the random variable Y. k Y* (·, Y) is a measurable positive definite kernel function on the sample set Y * . k Y* The "·" in (·, Y) is a wildcard, indicating that the argument is undetermined. y represents the value of the random variable Y. Thus, as in Equation (2), y represents an element of the sample set Y * .

[0037]

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[0038] H in Equation (1) represents the Reproducing Kernel Hilbert Space (RKHS). When the kernel function k Y* (·, Y) is characteristic, the kernel mean embedding μ Y : P * → H is injective. Here, the probability measure P is the set of values that can be taken on the sample set Y * and is denoted as P * .

[0039] When the kernel mean embedding μ Y : P * → H is injective, the kernel mean embedding μ Y is a class sufficient to represent all moments of the probability distribution. From this, it can be said that the information of the probability distribution is preserved by the kernel mean embedding μ Y . Assuming a conditional distribution conditioned on a certain realization value x of a random variable X with elements of a sample set X * as its values, the kernel mean embedding μ Y|x of the conditional distribution can be expressed as in Equation (3) based on Equation (1).

[0040]

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[0041] dataset {(x i ,y i )} i=1 n Given μ^, estimate the kernel mean embedding of the empirical conditional distribution. Y|x This can be expressed as shown in equation (4).

[0042]

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[0043] Sometimes, characters with a circumflex accent (^), such as "μ^", are represented by adding "^" after the character. Equation (4) can be used as an approximation of equation (3). weight w i (x) can be expressed as shown in equation (5).

[0044]

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[0045] The superscript T represents the transpose of a vector or matrix. ε is a constant for normalization, and ε > 0. I n This represents an n x n identity matrix. k X* (x) is the sample set X * The above is a measurable positive definite kernel function, which can be expressed as shown in equation (6).

[0046]

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[0047] R n This represents the n-dimensional real number space. In equation (5), G is an n x n matrix, and the elements of matrix G are G ij This can be expressed as shown in equation (7).

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[0049] Furthermore, if g(Y) is a function on the reproducing kernel Hilbert space H, then the conditional expectation value E of g(Y) is Y|x [g(Y)] is expressed as shown in equation (8).

[0050]

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[0051] <·,·> H This represents the inner product on the reproducing kernel Hilbert space H.

[0052] As an example of an acquisition function acquired by the acquisition function acquisition unit 192, we will explain the case where the acquisition function for PI (Probability of Improvement) or the acquisition function for EI (Expected Improvement) is constructed using kernel mean embedding.

[0053] (PI acquisition function) The acquisition function α of PI PI This means that the random variable Y has a certain value y + It is defined as the probability of taking one of the above values ​​and is expressed as shown in equation (9).

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[0055] Given dataset {(x i ,y i )} i=1 n The largest y i The value of y +When used in this way, according to PI, the x that has the highest probability of updating the maximum value y of the random variable Y can be selected as the next sampling point. u is the unit step function (or heaviside step function) represented by equation (10).

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[0057] As shown in equation (9), the acquisition function α of PI PI This is expressed as the expected value of the unit step function u(Y) in the conditional distribution P(Y|x). In the acquisition function, the function whose expected value is taken is also called the integrand. In the case of PI, the unit step function u is the integrand g in PI. PI It is also called the integrand g. PI This can be expressed as shown in equation (11).

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[0059] If the integrand g belongs to the reproducing kernel Hilbert space H, then the integrand g and the estimated kernel mean embedding μ^ are as shown in equations (8) and (4). Y|x The expected value E is obtained by the inner product with Y|x [g(Y)] can be calculated. Therefore, the kernel function k used in the kernel mean embedding is chosen so that the integrand g belongs to the reproducing kernel Hilbert space H. y Let's consider approximating the integrand with a linear combination of .

[0060] Here, using the Gaussian kernel function, we define the integrand g in PI. PI Let's explain using the example of representing a unit step function u. However, the kernel function used in the acquisition function acquired by the acquisition function acquisition unit 192 is not limited to a Gaussian kernel function, but can be any kernel function that can represent or approximate the integrand. For example, the acquisition function acquisition unit 192 may use the acquisition function α of PI as the acquisition function. PI When obtaining the unit step function u, various kernel functions that can represent or approximate it are used as the acquisition function α of PI. PI It can be used as part of something. Note that the kernel function used for representing or approximating the integrand and the kernel function k used for kernel mean embedding are also included. Y* (·,Y) are assumed to be the same kernel function.

[0061] The Gaussian kernel function is also called the Radial Basis Function or Squared Exponential. y (y i ,y j ) can be expressed as shown in equation (12).

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[0063] exp represents the exponential function. h is a constant representing the bandwidth, and h > 0. C is a constant, and here we use the C shown in equation (13).

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[0065] When using C as shown in equation (13), the Gaussian kernel function k y (y i ,y jThe symbol ) represents the shape of the Gaussian distribution. The Gaussian kernel function is positive definite and characteristic. By using the Gaussian kernel function as the kernel function, as described above, information about the probability distribution is preserved by kernel mean embedding.

[0066] The integrand g in PI PI This is obtained by using the integral of the Gaussian kernel function, and the g^ of equation (14) PI It can be approximated as follows.

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[0068] h is a constant where h > 0. h is also called the bandwidth. The error function erf is expressed as shown in equation (15).

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[0070] e represents Napier's constant. The closer the value of the bandwidth h approaches 0, the more the approximation function g^ PI is the integrand g PI Approaching.

[0071] The integral of the Gaussian kernel function will be further explained with reference to Figures 2 through 5. Figure 2 shows examples of several Gaussian kernel functions. Figure 2 shows the Gaussian kernel function k shown in equation (14). Y* This shows examples of multiple (r,y) values ​​arranged with varying values ​​of r. In the graph in Figure 2, the horizontal axis represents the value of the argument r. The vertical axis represents the Gaussian kernel function k Y* The values ​​of (r,y) are shown. Each of the lines L111, L112, L113, ... represents the Gaussian kernel function k Y* This indicates (r,y).

[0072] Figure 3 shows an example of the superposition of multiple Gaussian kernel functions. Figure 3 shows an example of superimposing multiple Gaussian kernel functions as shown in Figure 2. In other words, Figure 3 shows an example of summing the values ​​of multiple Gaussian kernel functions as shown in Figure 2. The horizontal axis of the graph in Figure 3 represents the value of the argument r. The vertical axis represents the Gaussian kernel function k. Y* This shows the sum of (r,y).

[0073] In the graph in Figure 3, the Gaussian kernel function k increases as the value of the argument r increases. Y* After the sum of (r,y) is greater than 0, the Gaussian kernel function k Y* The sum of (r,y) repeatedly increases and decreases. The smaller the spacing between multiple Gaussian kernel functions, the smaller the magnitude of this increase and decrease becomes, and the closer it approaches a constant value.

[0074] Figure 4 shows an example of the integral of a Gaussian kernel function. In Figure 4, the horizontal axis of the graph shows the value of the argument r. The vertical axis shows the Gaussian kernel function k. Y* The integral value of (r,y) is shown. In the graph in Figure 4, the Gaussian kernel function k increases as the value of the argument r increases. Y* After the integral of (r,y) becomes greater than 0, the Gaussian kernel function k Y* The integral of (r,y) is set to a constant value. Gaussian kernel function k Y* The slope at which the integral of (r,y) rises depends on the magnitude of the bandwidth h in equation (14).

[0075] Figure 5 shows the approximation function g^ PI This figure shows an example of the relationship between (y) and the bandwidth h. As in equation (14) above, the approximation function g^ PI Let (y) be the Gaussian kernel function k Y* We use the integral of the integral of (r,y). In the graph in Figure 5, the horizontal axis represents the value of the argument y. The vertical axis represents the approximation function g^ PI The value of (y) is shown.

[0076] Each of the lines L211, L212, L213, and L214 indicates the value of the approximation function g^ PI (y) for each value of the argument y. In the case of line L211, the value of the bandwidth h is the largest, and the value of the bandwidth h decreases in the order of lines L212, L213, and L214. In line L214, the value of the bandwidth h is close to 0, and it has the same shape as the graph of the integrand function g PI , that is, the same shape as the graph of the unit step function. As in the example of FIG. 5, as the value of the bandwidth h is decreased (approached to 0), the rising slope of the approximation function g^ PI (y) becomes steeper, and it can approach the shape of the graph of the integrand function g PI .

[0077] The acquisition function α of PI PI can be approximated as α^ PI in Equation (16).

[0078]

Equation

[0079] As the value of the bandwidth h is decreased (approached to 0), the approximation function α^ PI can be made closer to the acquisition function α of PI PI . By the acquisition function acquisition unit 192 acquiring (calculating) the approximation function α^ PI as the acquisition function, the sampling point determination unit 193 can select, as the next sampling point, the sampling point with the highest possibility of updating the maximum value of the sampling target data.

[0080] (Acquisition function of EI) The acquisition function α of EI EI is defined as the expected value that the random variable Y takes a value greater than or equal to a certain value y + and is expressed as in Equation (17).

[0081]

Equation

[0082] For the given dataset \(\{(x i , y i )}\ i=1 n Among them, if the value of the largest \(y\) is used as \(y i \), according to EI, the \(x\) with the highest expected value of updating the maximum value of the value \(y\) of the random variable \(Y\) can be selected as the next sampling point. +

[0083] As shown in Equation (17), the acquisition function \(\alpha EI \) of EI is expressed as the expected value of the product of the difference obtained by subtracting a certain value \(y + \) from the value \(y\) of the random variable in the conditional distribution \(P(Y|x)\) and the unit step function \(u(Y)\). In the case of EI, the product of the difference obtained by subtracting a certain value \(y + \) from the value \(y\) of the random variable and the unit step function \(u\) is also called the integrand \(g EI \) in EI. The integrand \(g EI \) is expressed as shown in Equation (18).

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[0085] Here, taking the case of expressing \(g EI \) in EI using the Gaussian kernel function, that is, \(g=(y - y + )u(y)\) as an example for explanation. However, as described above, the kernel function used in the acquisition function obtained by the acquisition function acquisition unit 192 is not limited to the Gaussian kernel function, and can be various kernel functions that can represent or approximate the integrand. For example, when the acquisition function acquisition unit 192 acquires the acquisition function \(\alpha EI \) of EI, various kernel functions that can represent or approximate \((y - y + )u(y)\) can be used as part of the acquisition function \(\alpha EI \) of EI.

[0086] The integrand g in EI EI This is obtained by using the integral of the Gaussian kernel function, and the g^ of equation (19) EI It can be approximated as follows.

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[0088] In equation (19), as the value of the bandwidth h approaches 0, the approximation function g^ EI is the integrand g EI Approaching. Figure 6 shows the approximation function g^ EI This figure shows an example of the relationship between (y) and bandwidth. In the graph in Figure 6, the horizontal axis represents the value of the argument y. The vertical axis represents the approximation function g^ EI The value of (y) is shown.

[0089] Lines L311, L312, L313, and L314 each represent the approximation function g^ for each value of argument y. EI This shows the value of (y). In the case of line L311, the bandwidth h value is the largest, and the bandwidth h value decreases in the order of lines L312, L313, and L314. In line L314, the bandwidth h value is close to 0, and the integrand g EI The graph is similar to the graph shown. Note that the integrand g EI The graph is obtained by translating the graph of the ramp function (normalized linear function, Rectified Linear Function (ReLU)) along the horizontal axis (y-axis in Equation 18). As shown in the example in Figure 6, the smaller the value of the bandwidth h (the closer it gets to 0), the more the approximation function g^ EI The rise of (y) from value 0 becomes steep, and the integrand g EI The graph of this function, that is, the graph of the ramp function, can be made to approximate a graph obtained by translating it.

[0090] EI's acquisition function α EI α^ EI It can be approximated as follows.

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[0092] The smaller the value of the bandwidth h (the closer it gets to 0), the more the approximation function α^ EI The acquisition function α of EI EI It can be brought closer to that. The acquisition function acquisition unit 192 approximates the function α^ as the acquisition function. EI By obtaining (calculating) this, the sampling point determination unit 193 can select the sampling point as the next sampling point that has the largest expected value for updating the maximum value of the data to be sampled.

[0093] However, the acquisition function acquired by the acquisition function acquisition unit 192 is not limited to the acquisition function of PI or the acquisition function of EI. The kernel mean embedding μ^ of the conditional distribution estimated from the data set. Y|x Various acquisition functions obtained using this method can be used as the acquisition functions acquired by the acquisition function acquisition unit 192. The kernel mean embedding μ^ of the conditional distribution estimated from the data set. Y|x Obtaining the acquisition function using μ^ Y|x This can be understood as using a surrogate model that represents the probability distribution of the sampled data, and obtaining an acquisition function based on the probability distribution of the sampled data.

[0094] Note that the weight w in equation (4) i (x) may be normalized. Weight w i The normalization of (x) is shown in equation (21).

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[0096] weight w iIf (x) is normalized, the possibility that the sampling point selected as the next point to be explored will be localized can be reduced. Here, weight w i If (x) is not normalized, and the next candidate sampling point is far from a sampling point where data has already been sampled, then the weight w of that candidate i The value of (x) becomes extremely small, which may make it difficult to select candidate sampling points that are far from the sampling points where the data has already been sampled. In contrast, the weight w i If (x) is normalized, it is expected that the sampling point determination unit 193 will be able to select candidate sampling points that are far from sampling points where data has already been sampled. On the other hand, the weight w i (x) does not need to be normalized. In this case, the weight w i The computational complexity is relatively low because normalization of (x) is not required.

[0097] Figure 7 shows an example of a processing procedure in which the information processing device 100 performs a solution search. In the process shown in Figure 7, the data acquisition unit 191 acquires initial values ​​for the data set (step S101). Next, the acquisition function acquisition unit 192 acquires the acquisition function (step S102). As described above, the acquisition function acquisition unit 192 estimates the kernel mean embedding based on the data set and acquires the acquisition function based on the estimated kernel mean embedding.

[0098] Next, the sampling point determination unit 193 determines the sampling points (step S103). The sampling point determination unit 193 selects sampling points that maximize the value of the acquisition function, such as the sampling point where the acquisition function takes its maximum value. Alternatively, depending on the acquisition function, the sampling point determination unit 193 may select sampling points that minimize the value of the acquisition function, such as the sampling point where the acquisition function takes its minimum value.

[0099] Next, the data acquisition unit 191 acquires the sample target data at the sampling point determined by the sampling point determination unit 193 (step S104). Then, the data acquisition unit 191 updates the data set by adding the sample data, which is linked to the sampling point determined by the sampling point determination unit 193 and the sample target data obtained at that sampling point, to the data set (step S105).

[0100] Next, the processing unit 190 determines whether or not the termination condition for the solution search by the information processing device 100 has been met (step S106). The termination conditions for the solution search performed by the information processing device 100 are not limited to specific conditions. For example, the termination condition for the solution search by the information processing device 100 may be that sample data satisfying a predetermined threshold has been obtained. Furthermore, for example, if the goal is to make the sample data as large as possible, the termination condition for the solution search by the information processing device 100 may be that sample data equal to or greater than a predetermined threshold has been obtained. Alternatively, if the goal is to make the sample data as small as possible, the termination condition for the solution search by the information processing device 100 may be that sample data equal to or less than a predetermined threshold has been obtained.

[0101] Alternatively, the termination condition for the solution search by the information processing device 100 may be that the magnitude of the variation in the sampled data between samples becomes smaller than a predetermined condition. Furthermore, for example, the termination condition for the solution search by the information processing device 100 may be the condition shown in equation (22).

[0102]

number

[0103] y t This shows the sampled data obtained in the t-th sampling. || || represents a norm. The norm here is not limited to any particular one. For example, the norm here may be the L1 norm, but is not limited to that. ε is a constant such that ε>0 represents a predetermined threshold. Equation (22) is given by the sampling target data y obtained in the tth sampling. t From this, the sampling target data y obtained in the t-1 sampling. t-1 This shows the condition that the magnitude (norm) of the difference obtained by subtracting is less than the threshold ε. Alternatively, the termination condition for the solution search by the information processing device 100 may be the condition shown in equation (23).

[0104]

number

[0105] Equation (23) is given by the sampling target data y obtained in the tth sampling. t From this, the sampling target data y obtained in the t-1 sampling. t-1 The magnitude of the difference (norm) obtained by subtracting this is the sampled data y obtained in the tth sampling. t We show the condition that the quotient obtained by dividing by the magnitude (norm) is less than the threshold ε.

[0106] If the processing unit 190 determines in step S106 that the termination condition for the solution search by the information processing device 100 has not been met (step S106: NO), the process returns to step S102. On the other hand, if the processing unit 190 determines in step S106 that the termination condition for the solution search by the information processing device 100 is met (step S106: YES), the information processing device 100 terminates the process shown in Figure 7.

[0107] As described above, the acquisition function acquisition unit 192 acquires the acquisition function using the kernel mean embedding of the conditional distribution estimated from the data set obtained by sampling the data. The sampling point determination unit 193 determines the sampling points for acquiring data based on the acquisition function acquired by the acquisition function acquisition unit 192. The data acquisition unit 191 acquires the data at the sampling points determined by the sampling point determination unit 193.

[0108] According to the information processing device 100, the acquisition function is obtained using a kernel mean embedding of a conditional distribution estimated from the data set. Therefore, when determining the sampling points for acquiring data, the probability distribution assumed for the values ​​of the data to be acquired is not limited to a specific type of distribution.

[0109] In Bayesian estimation using Gaussian process regression, a known method for finding the sampling point that maximizes or minimizes the data, a Gaussian distribution is assumed as the conditional probability distribution of the data (the probability distribution of data for each sampling point). Therefore, in Bayesian estimation using Gaussian process regression, if the probability distribution of the data follows a distribution other than Gaussian, the accuracy of the probability distribution estimation decreases, which in turn can lead to a decrease in the accuracy of the sampling point search.

[0110] For example, assuming a Gaussian distribution as a probability distribution is equivalent to representing the probability distribution using the second-order moments of the mean and variance, and it is possible that distributions with third-order or higher moments cannot be represented in detail. Furthermore, if a Gaussian distribution is assumed as a probability distribution, it is possible that distributions asymmetric with respect to the mean cannot be represented with high accuracy.

[0111] In contrast, with kernel mean embedding, the assumed probability distribution is not limited to a specific type of distribution, and various distributions can be assumed depending on the data being sampled. For example, in equation (3) above, various distributions can be assumed as the distribution of the conditional probability P(x|y) depending on the data being sampled, and for example, a distribution with moments of any order can be assumed. According to the information processing device 100, in this respect, it is expected that the conditional distribution of the data to be sampled can be represented with relatively high accuracy, and sampling points can be searched with relatively high accuracy.

[0112] Furthermore, the acquisition function acquisition unit 192 acquires an acquisition function that is expressed as the inner product of an equation represented by a linear combination of kernel functions and an equation that shows the kernel mean embedding of the conditional distribution estimated from the data set. According to the information processing device 100, the acquisition function can be calculated using relatively simple calculations such as the calculation of the dot product, and the computational load on the acquisition function is relatively small. For example, in the information processing device 100, the integral calculation in the calculation of the acquisition function can be replaced with the calculation of the dot product, as shown in the examples of equations (8) and (9).

[0113] Furthermore, the acquisition function acquisition unit 192 acquires an acquisition function that is expressed as the inner product of an approximation formula for a unit step function, which is represented by the integral of the kernel function, a two-variable function, with respect to one variable, and a formula that shows the kernel mean embedding of the conditional distribution estimated from the data set. According to the information processing device 100, the acquisition function of PI can be obtained, and the sampling point with the highest probability of updating the maximum or minimum value of the sampled data can be selected as the next sampling point. According to the information processing device 100, in this respect, it is expected that the solution search can be performed efficiently.

[0114] Furthermore, the acquisition function acquisition unit 192 acquires an acquisition function expressed as the inner product of an expression representing the integral of the product of the difference between a variable and a predetermined value and a kernel function that takes that variable as input, and an expression representing the kernel mean embedding of the conditional distribution estimated from the data set. According to the information processing device 100, the acquisition function of EI can be obtained, and the sampling point can be selected as the next sampling point, which has the largest expected value for the update range of the maximum or minimum value of the data to be sampled. According to the information processing device 100, in this respect, it is expected that the solution search can be performed efficiently.

[0115] Furthermore, the acquisition function unit 192 normalizes the weight coefficients calculated for each sampling point using a kernel function for the sampling point, and calculates the kernel mean embedding of the conditional distribution estimated from the data set by summing the product of the normalized weight coefficients and the kernel function for the data to be sampled for each sampling point included in the data set. According to the information processing device 100, by normalizing the weight coefficients, it is expected that even when a candidate for the next sampling point is far from a sampling point where data has already been sampled, the value of the weight wi(x) for that candidate will not become extremely small. As a result, the information processing device 100 can reduce the possibility that the sampling point selected by the sampling point determination unit 193 will be localized.

[0116] Figure 8 shows another example of the configuration of an information processing apparatus according to some embodiments of the present disclosure. In the configuration shown in Figure 8, the information processing apparatus 610 comprises an acquisition function acquisition unit 611, a sampling point determination unit 612, and a data acquisition unit 613. In this configuration, the acquisition function acquisition unit 611 acquires an acquisition function using a kernel mean embedding of a conditional distribution estimated from the data set obtained by sampling the data. The sampling point determination unit 612 determines the sampling points for acquiring data based on the acquisition function acquired by the acquisition function acquisition unit 611. The data acquisition unit 613 acquires data at the sampling points determined by the sampling point determination unit 612. The acquired function acquisition unit 611 is an example of an acquired function acquisition means. The sampling point determination unit 612 is an example of a sampling point determination means. The data acquisition unit 613 is an example of a data acquisition means.

[0117] According to the information processing device 610, the acquisition function is obtained using a kernel mean embedding of a conditional distribution estimated from the data set. Therefore, when determining the sampling points for acquiring data, the probability distribution assumed for the values ​​of the data to be acquired is not limited to a specific type of distribution.

[0118] As mentioned above, Bayesian estimation using Gaussian process regression, a known method for finding the sampling point that maximizes or minimizes the data, assumes a Gaussian distribution as the conditional probability distribution of the data (the probability distribution of data for each sampling point). Therefore, in Bayesian estimation using Gaussian process regression, if the probability distribution of the data follows a distribution other than Gaussian, the accuracy of the probability distribution estimation decreases, and in this respect, the accuracy of searching for sampling points may decrease.

[0119] For example, assuming a Gaussian distribution as a probability distribution is equivalent to representing the probability distribution using the second-order moments of the mean and variance, and it is possible that distributions with third-order or higher moments cannot be represented in detail. Furthermore, if a Gaussian distribution is assumed as a probability distribution, it is possible that distributions asymmetric with respect to the mean cannot be represented with high accuracy.

[0120] In contrast, with kernel mean embedding, the assumed probability distribution is not limited to a specific type of distribution; various distributions can be assumed depending on the data being sampled. For example, a distribution with moments of any order can be assumed. According to the information processing device 610, in this respect, it is expected that the conditional distribution of the data to be sampled can be represented with relatively high accuracy, and that sampling points can be searched with relatively high accuracy.

[0121] The acquisition function acquisition unit 611 can be implemented, for example, using the functions of the acquisition function acquisition unit 192 in Figure 1. The sampling point determination unit 612 can be implemented, for example, using the functions of the sampling point determination unit 193 in Figure 1. The data acquisition unit 613 can be implemented, for example, using the functions of the data acquisition unit 191 in Figure 1.

[0122] Figure 9 shows an example of the configuration of a system according to some embodiments of the present disclosure. In the configuration shown in Figure 9, the system 620 comprises an information processing device 621 and a parameter setting target 626. The information processing device 621 comprises a data acquisition unit 622, an acquisition function acquisition unit 623, a sampling point determination unit 624, and a parameter setting unit 625.

[0123] The parameter setting target 626 is a system or device that operates based on the setting of parameter values. The parameter setting target 626 is not limited to a specific type of system or device, but can be various systems or devices. For example, the parameter setting target 626 may be a system or device that produces some kind of product. Alternatively, the parameter setting target 626 may be a communication system or communication device.

[0124] The information processing device 621 performs the same processing as the information processing device 100 in Figure 1 to determine the parameter values ​​to be set in the parameter setting target 626, and sets the determined parameter values ​​in the parameter setting target 626. In the information processing device 621, the method of setting parameter values ​​is limited to automatically setting the parameter values ​​in the parameter setting target 626 without user intervention. The information processing device 621 uses an objective function that shows the evaluation of the processing performed by the parameter setting target 626 to search for parameter values ​​that will result in the best possible evaluation shown by the objective function. In all other respects, the information processing device 621 is the same as the information processing device 100.

[0125] The data acquisition unit 622 is the same as the data acquisition unit 191 in Figure 1, and acquires the initial values ​​of the data set, and also acquires the data to be sampled at the sampling points determined by the sampling point determination unit 624 and updates the data set. The acquisition function acquisition unit 623 is similar to the acquisition function acquisition unit 192 in Figure 1, and estimates the kernel mean embedding based on the data set, and calculates the acquisition function using the estimated kernel mean embedding.

[0126] The sampling point determination unit 624 is similar to the sampling point determination unit 193 in Figure 1, and determines the sampling points where the data acquisition unit 622 will sample data, based on the acquisition function acquired by the acquisition function acquisition unit 192. The sampling point determination unit 624 determines the parameter values ​​of the parameter setting target 626 as the sampling points.

[0127] The parameter setting unit 625 is similar to the communication unit 110 in Figure 1, and sets parameter values ​​for the parameter setting target 626. Specifically, the parameter setting unit 625, like the communication unit 110 in Figure 1, transmits parameter values ​​to the parameter setting target 626, causing the parameter setting target 626 to set the transmitted parameter values.

[0128] In particular, the parameter setting unit 625, along with the data acquisition unit 622, the acquisition function acquisition unit 623, and the sampling point determination unit 624, repeatedly perform data sampling and data set updating, acquire an acquisition function using kernel mean embedding estimated based on the acquired data set, and determine sampling points using the acquired acquisition function until the parameter value search termination condition is met, and set the determined parameter values ​​to the parameter setting target 626.

[0129] According to system 620, the search for parameter values ​​to be set in the parameter setting target 626 is performed automatically without requiring user operation, and the parameter values ​​obtained through the search can be set in the parameter setting target 626.

[0130] Figure 10 shows an example of the processing steps in an information processing method according to some embodiments of the present disclosure. The information processing method shown in Figure 10 includes obtaining an acquisition function (step S611), determining sampling points (step S612), and acquiring data (step S613).

[0131] In obtaining the acquisition function (step S611), the computer obtains the acquisition function using a kernel mean embedding of the conditional distribution estimated from the data set obtained by sampling the data. In determining the sampling points (step S612), the computer determines the sampling points from which to acquire data based on the obtained acquisition function. In acquiring data (step S613), the computer acquires data at the determined sampling points.

[0132] According to the information processing method shown in Figure 10, the acquisition function is obtained using a kernel mean embedding of a conditional distribution estimated from the data set. Therefore, when determining the sampling points for acquiring data, the probability distribution assumed for the values ​​of the data to be acquired is not limited to a specific type of distribution.

[0133] As mentioned above, Bayesian estimation using Gaussian process regression, a known method for finding the sampling point that maximizes or minimizes the data, assumes a Gaussian distribution as the conditional probability distribution of the data (the probability distribution of data for each sampling point). Therefore, in Bayesian estimation using Gaussian process regression, if the probability distribution of the data follows a distribution other than Gaussian, the accuracy of the probability distribution estimation decreases, and in this respect, the accuracy of searching for sampling points may decrease.

[0134] For example, assuming a Gaussian distribution as a probability distribution is equivalent to representing the probability distribution using the second-order moments of the mean and variance, and it is possible that distributions with third-order or higher moments cannot be represented in detail. Furthermore, if a Gaussian distribution is assumed as a probability distribution, it is possible that distributions asymmetric with respect to the mean cannot be represented with high accuracy.

[0135] In contrast, with kernel mean embedding, the assumed probability distribution is not limited to a specific type of distribution; various distributions can be assumed depending on the data being sampled. For example, a distribution with moments of any order can be assumed. According to the information processing device 610, in this respect, it is expected that the conditional distribution of the data to be sampled can be represented with relatively high accuracy, and that sampling points can be searched with relatively high accuracy.

[0136] Figure 11 is a schematic block diagram showing the configuration of a computer according to at least one embodiment. In the configuration shown in Figure 11, the computer 700 comprises a CPU 710, a main memory 720, an auxiliary memory 730, an interface 740, and a non-volatile recording medium 750.

[0137] One or more of the above-described information processing devices 100, 610, and 621, or parts thereof, may be implemented in the computer 700. In that case, the operation of each processing unit described above is stored in the auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, expands it in the main memory 720, and executes the above-described processing according to the program. The CPU 710 also allocates memory areas in the main memory 720 corresponding to each of the above-described memory units according to the program. Communication between each device and other devices is performed by the interface 740 having a communication function and performing communication according to the control of the CPU 710. The interface 740 also has a port for the non-volatile recording medium 750 and reads information from the non-volatile recording medium 750 and writes information to the non-volatile recording medium 750.

[0138] When the information processing device 100 is implemented in a computer 700, the operation of the processing unit 190 and each of its parts is stored in auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from auxiliary storage device 730, loads it into main memory device 720, and executes the above processing according to the program.

[0139] Furthermore, the CPU 710 reserves a memory area for the memory unit 180 in the main memory 720 according to the program. Communication with other devices by the communication unit 110 is performed by the interface 740 having a communication function and operating under the control of the CPU 710. Display of images by the display unit 120 is performed by the interface 740 having a display device and displaying various images under the control of the CPU 710. Acceptance of user operations by the operation input unit 130 is performed by the interface 740 having an input device and accepting user operations under the control of the CPU 710.

[0140] When the information processing device 610 is implemented in the computer 700, the operation of each part of it is stored in auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from auxiliary storage device 730, loads it into main memory device 720, and executes the above processing according to the program.

[0141] Furthermore, the CPU 710 reserves memory in the main memory 720 for the information processing device 610 to perform processing according to the program. Communication between the information processing device 610 and other devices is performed by the interface 740 having communication functions and operating under the control of the CPU 710. Interaction between the information processing device 610 and the user is performed by the interface 740 equipped with input / output devices such as a display device, controller, mouse, and keyboard, and operating under the control of the CPU 710.

[0142] When the information processing device 621 is implemented in the computer 700, the operation of each part of it is stored in the auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main memory 720, and executes the above processing according to the program.

[0143] Furthermore, the CPU 710 reserves memory in the main memory 720 for the information processing device 621 to perform processing according to the program. Communication between the information processing device 621 and other devices is performed by the interface 740 having a communication function and operating under the control of the CPU 710. Interaction between the information processing device 621 and the user is performed by the interface 740 being equipped with input / output devices such as a display device, controller, mouse, and keyboard and operating under the control of the CPU 710.

[0144] One or more of the above-mentioned programs may be recorded on the non-volatile recording medium 750. In this case, the interface 740 may read the program from the non-volatile recording medium 750. The CPU 710 may then either directly execute the program read by the interface 740, or temporarily save it in the main memory 720 or auxiliary memory 730 before executing it.

[0145] Alternatively, the processing of each part may be performed by recording a program for executing all or part of the processing performed by the information processing device 100 and the information processing device 610 on a computer-readable recording medium, and then loading and executing the program recorded on this recording medium into a computer system. The term "computer system" here includes hardware such as the OS (Operating System) and peripheral devices. Furthermore, "computer-readable recording media" refers to portable media such as flexible disks, magneto-optical disks, ROMs (Read Only Memory), CD-ROMs (Compact Disc Read Only Memory), and storage devices such as hard disks built into computer systems. The above-mentioned program may be intended to implement only a part of the functions described above, and may also be able to implement the above-mentioned functions in combination with programs already recorded in the computer system.

[0146] While embodiments of this invention have been described in detail above with reference to the drawings, the specific configurations are not limited to these embodiments and include designs and the like that do not depart from the spirit of this invention.

[0147] Some or all of the above embodiments may also be described as follows, but are not limited to the following:

[0148] (Note 1) An acquisition function acquisition means that obtains an acquisition function using a kernel mean embedding of a conditional distribution estimated from a data set obtained by sampling data, A sampling point determination means for determining sampling points for acquiring data based on the aforementioned acquisition function, A data acquisition means that acquires data at the sampling point determined by the sampling point determination means, An information processing device equipped with the following features.

[0149] (Note 2) The acquisition function acquisition means acquires an acquisition function that is expressed as the inner product of an equation represented by a linear combination of kernel functions and an equation representing the kernel mean embedding of the conditional distribution estimated from the data set. The information processing device described in Appendix 1.

[0150] (Note 3) The acquisition function acquisition means acquires the acquisition function which is expressed as the inner product of an approximation formula for a unit step function, which is expressed as an integral of a kernel function that is a two-variable function with respect to one variable, and a formula that shows the kernel mean embedding of the conditional distribution estimated from the data set. The information processing device described in Appendix 2.

[0151] (Note 4) The information processing device described in Appendix 2, wherein the acquisition function acquisition means acquires the acquisition function which is expressed as the inner product of an expression that represents the integral of the product of the difference between a variable and a predetermined value and a kernel function that takes that variable as input, and an expression that shows the kernel mean embedding of the conditional distribution estimated from the data set.

[0152] (Note 5) The acquisition function means normalizes the weight coefficients calculated for each sampling point using a kernel function for the sampling point, and calculates the kernel mean embedding of the conditional distribution estimated from the data set by summing the product of the normalized weight coefficients and the kernel function for the data to be sampled for each sampling point included in the data set. An information processing device described in any one of the appendices 1 to 4.

[0153] (Note 6) Computers The acquisition function is obtained using the kernel mean embedding of the conditional distribution estimated from the data set obtained by sampling the data. Based on the acquisition function described above, the sampling points for acquiring data are determined. Obtain data at the determined sampling points. Information processing methods that include the following.

[0154] (Note 7) On the computer, The acquisition function is obtained using the kernel mean embedding of the conditional distribution estimated from the data set obtained by sampling the data, and Based on the aforementioned acquisition function, the sampling points for acquiring data are determined, To acquire data at the determined sampling points, A recording medium that stores a program to execute.

[0155] This application claims priority based on Japanese Patent Application No. 2022-164055, filed on 12 October 2022, and incorporates all of its disclosures herein. [Industrial applicability]

[0156] This disclosure may be applied to information processing devices, information processing methods, and recording media. [Explanation of Symbols]

[0157] 100, 610, 621 Information Processing Devices 110 Communications Department 120 Display section 130 Operation Input Section 180 Storage section 190 Processing Unit 191, 613, 622 Data acquisition unit 192, 611, 623 Acquisition function acquisition unit 193, 612, 624 Sampling point determination unit 625 Parameter setting section

Claims

1. An acquisition function acquisition means that obtains an acquisition function using a kernel mean embedding of a conditional distribution estimated from a data set obtained by sampling data, A sampling point determination means for determining sampling points for acquiring data based on the aforementioned acquisition function, A data acquisition means that acquires data at the sampling point determined by the sampling point determination means, An information processing device equipped with the following features.

2. The acquisition function acquisition means acquires an acquisition function that is expressed as the inner product of an equation represented by a linear combination of kernel functions and an equation representing the kernel mean embedding of the conditional distribution estimated from the data set. The information processing apparatus according to claim 1.

3. The acquisition function acquisition means acquires the acquisition function which is expressed as the inner product of an approximation formula for a unit step function, which is expressed as an integral of a kernel function that is a two-variable function with respect to one variable, and a formula that shows the kernel mean embedding of the conditional distribution estimated from the data set. The information processing apparatus according to claim 2.

4. The acquisition function acquisition means acquires the acquisition function which is expressed as the inner product of an expression that represents the integral with respect to the variable of the product of the difference between the variable and a predetermined value and a kernel function which is a two-variable function that takes the variable as input, and an expression that shows the kernel mean embedding of the conditional distribution estimated from the data set. The information processing apparatus according to claim 2.

5. The acquisition function means normalizes the weight coefficients calculated for each sampling point using a kernel function for the sampling point, and calculates the kernel mean embedding of the conditional distribution estimated from the data set by summing the product of the normalized weight coefficients and the kernel function for the data to be sampled for each sampling point included in the data set. An information processing apparatus according to any one of claims 1 to 4.

6. Computers The acquisition function is obtained using the kernel mean embedding of the conditional distribution estimated from the data set obtained by sampling the data. Based on the acquisition function described above, the sampling points for acquiring data are determined. Obtain data at the determined sampling points. Information processing methods that include the following.

7. On the computer, The acquisition function is obtained using the kernel mean embedding of the conditional distribution estimated from the data set obtained by sampling the data, and Based on the aforementioned acquisition function, the sampling points for acquiring data are determined, To acquire data at the determined sampling points, A program to execute.

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