JP6047476B2 - SAMPLE DATA PROCESSING DEVICE, METHOD, AND PROGRAM - Google Patents

Description

  The present invention relates to a sample data processing apparatus, method, and method for estimating population characteristic values of the entire spatio-temporal based on sample data sampled in a part of the spatio-temporal by a sensor carried by the user, for example, during the movement of the user Regarding the program.

  In the course of a user's movement, user-participation-type environmental sensing that collects and uses spatio-temporal data sampled by a sensor carried by the user, that is, sample data, has attracted attention (for example, see Non-Patent Document 1). ). In user-participation-type environmental sensing, only spatio-temporal data is sampled along the trajectory of a user moving with a sensor. For this reason, in order to obtain the characteristic value of the entire spatio-temporal, the data characteristic value of the entire spatio-temporal (population characteristic value) from a part of the spatio-temporal data (sample data) sampled along the user's trajectory. Need to be estimated.

  As a method for estimating a population characteristic value from sampled sample data, a sample survey method is known (see, for example, Non-Patent Document 2). In the sampling survey method, the probability that the elements constituting the population are included in the sample is set in advance, the sample data actually obtained by sampling according to the set probability, and the reciprocal of the preset probability, Is used to estimate the population characteristic value, and the characteristic value of the entire spatio-temporal can be estimated without bias. It should be noted that there is no bias in the estimation results of population characteristic values based on the premise that actual sampling is performed according to preset probability.

Shinichi Kiso, Satoshi Sezaki, “Real World Sensing in Urban Life”, The Institute of Electrical Engineers of Japan, Vol.129, No.3, pp.156-159 (2009). Takahiro Tsuchiya, “Outline Specimen Survey Method”, pp.5-25, Asakura Shoten (2009).

  However, in user-participation-type environmental sensing, the sampled portion of the entire space-time changes depending on the user carrying the sensor and moving. For this reason, when the sample survey method is applied to user-participation-type environmental sensing, actual sampling is not always performed according to the preset probability, but the inverse of the preset probability and the actually sampled sample. There is a problem that the estimation results of population characteristic values using data are biased.

  For example, when estimating the average daily temperature at a certain place, even if it was assumed in advance that the data would be sampled with equal probability in any time zone, the data was actually sampled in the daytime when the temperature was high In some cases, the average temperature will be overestimated. On the other hand, when data is sampled biased at night when the temperature is low, the average temperature is underestimated.

  The present invention has been made paying attention to the above circumstances, and the object of the present invention is to make it possible to estimate the population characteristic value of the entire spatio-temporal from the sample data sampled in a part of the spatio-temporal. A sample data processing apparatus, method, and program are provided.

In order to achieve the above object, the present invention comprises the following aspects.
(1) In a sample data processing apparatus for estimating a population characteristic value from accumulated sample data, a spatio-temporal range for defining a population for which the characteristic value is to be estimated, and the population Means for accepting designation of a spatio-temporal unit for defining an element, a sensor type to be estimated, and a type of characteristic value to be estimated; and the designated spatio-temporal range as a population of the designated spatio-temporal unit Means for retrieving and storing sample data corresponding to the specified sensor type from the accumulated sample data for each element of the divided population, and elements of the population A sample corresponding to the specified sensor type and the reciprocal of the probabilities estimated after the posterior estimation of the probability that the element of the population is included in the sample data from the sample data stored for each And a means for estimating a population characteristic value corresponding to the specified characteristic value type based on the data, and a means for outputting an estimated value of the estimated population characteristic value. It is.

  (2) The aspect described in (1) further includes means for acquiring, as auxiliary data, sample data other than the designated sensor type, in which the correct value of the population characteristic value is known. The means for estimating the population characteristic value includes, after the posterior estimation means, from the sample data stored for each element of the population, the probability that the element of the population is included in the sample data; The means for correcting the reciprocal of the estimated probability based on the acquired auxiliary data, the reciprocal of the corrected probability, and the sample data corresponding to the specified sensor type, Means for estimating a population characteristic value corresponding to the specified characteristic value type.

  (3) In the aspect described in (1) or (2), the means for estimating the population characteristic value uses a regression model to estimate the probability that the elements of the population are included in the sample data. It is what I did.

  (1) The probability that the elements constituting the population are included in the sample is estimated after the actual sampled sample data, and the reciprocal of the estimated probability and the actually sampled sample data are used. Population characteristic values are estimated. For this reason, even if it is not always possible to control which part of the entire space-time data is sampled, such as user-participated environmental sensing, the spatio-temporal from the sampled data of a part of the space-time sampled. It is possible to estimate the entire data characteristic value, that is, the population characteristic value without deviation or with a small error.

  (2) The reciprocal of the probability estimated after the fact is corrected based on auxiliary data for which the correct value of the population characteristic value is known. For this reason, the estimation error of the population characteristic value can be further reduced.

  (3) The estimation of the probability that the elements of the population are included in the sample data is efficiently performed using the regression model.

  That is, according to each aspect of the present invention, there is provided a sample data processing apparatus, method, and program that can estimate the population characteristic value of the entire spatiotemporal from the sample data sampled in a part of the spatiotemporal without any deviation. be able to.

The block diagram which shows the structure of the system containing the population characteristic value estimation apparatus which is 1st Embodiment of the sample data processing apparatus which concerns on this invention. The figure which shows an example of the sensing data stored in a sensor database apparatus. The figure which shows an example of the spatio-temporal range designated from an application execution apparatus as one parameter of the estimation request | requirement of a population characteristic value. The figure which shows an example of the space-time unit designated from an application execution apparatus as one parameter of the estimation request | requirement of a population characteristic value. The figure which shows an example of the sensor classification designated from an application execution apparatus as one parameter of the estimation request | requirement of a population characteristic value. The figure which shows an example of the characteristic value classification designated from an application execution apparatus as one parameter of the estimation request | requirement of a population characteristic value. The figure which shows an example of the spatio-temporal data arrangement | sequence produced | generated by the spatiotemporal division part of the population characteristic value estimation apparatus shown in FIG. The flowchart which shows the process sequence and the processing content in the characteristic value estimation part of the population characteristic value estimation apparatus shown in FIG. The figure which shows an example of the spatiotemporal binary arrangement | sequence produced | generated by the characteristic value estimation process shown in FIG. The figure which shows an example of the spatiotemporal probability array produced | generated by the characteristic value estimation process shown in FIG. The figure which shows an example of the spatio-temporal weight arrangement | sequence produced | generated by the characteristic value estimation process shown in FIG. The flowchart which shows the process sequence and the processing content in the characteristic value estimation part of the population characteristic value estimation apparatus which is 2nd Embodiment of the sample data processing apparatus which concerns on this invention. The figure which shows an example of the spatio-temporal data arrangement | sequence used as assistance used in the specific value estimation process shown in FIG. The figure which shows an example of the spatiotemporal weight arrangement | sequence after correction | amendment produced | generated by the specific value estimation process shown in FIG.

Embodiments according to the present invention will be described below with reference to the drawings.
[First Embodiment]
FIG. 1 is a block diagram showing a configuration of an environment sensing system including a population characteristic value estimation device which is a first embodiment of a sample data processing device according to the present invention.
This system includes a population characteristic value estimation apparatus 1 as a sample data processing apparatus, and an application execution apparatus 2 and a sensor database apparatus 3 that can be connected to the population characteristic value estimation apparatus 1 via a network (not shown). ing.

  The sensor database device 3 is provided on a database server, for example, and accumulates sensor data sampled in time series by a sensor carried by the user for each user. FIG. 2 shows an example of the sensor data. Each record includes date / time data, position data represented by latitude and longitude, data representing a sensor type, and measurement data of the sensor. For example, the record in the first line has the measurement data “26.0” of the sensor type “temperature” at the position (latitude “35.738157”, longitude “139.565407”) at the date and time “2013-08-20 09:15:00”. Means that it was sampled.

  The application execution device 2 is composed of, for example, a personal computer used by a service provider, and gives an estimation request to the population characteristic value estimation device 1 and receives an estimation result by the population property value estimation device 1 for this request. used. In the estimation request, a spatiotemporal range, a spatiotemporal unit, a sensor type, and a characteristic value type are inserted as parameters.

  The population characteristic value estimation device 1 is composed of, for example, a server computer provided in a cloud system, and includes a processing unit 11 having a CPU (Central Processing Unit), a storage unit having a buffer unit 12, the sensor database device 3 and application execution. A communication interface unit (not shown) that performs data transmission with the apparatus 2 is provided.

  The processing unit 11 includes a request reception unit 111, a characteristic value estimation unit 112, an estimation result response unit 113, and a space-time division unit 114 as processing functions necessary for carrying out the first embodiment of the present invention. ing. Note that these processing units 111 to 114 are realized by causing the CPU to execute a program stored in a program memory (not shown).

  The request reception unit 111 receives the estimation request transmitted from the application execution device 2, and among the parameters inserted in the received estimation request, represents data representing a spatiotemporal range, a spatiotemporal unit, and a sensor type. Processing for giving the space-time division unit 114 and the characteristic value type to the characteristic value estimation unit 112 is performed.

  The spatio-temporal division unit 114 first divides the spatio-temporal range into elements of the spatio-temporal unit based on the spatio-temporal range, spatio-temporal unit, and sensor type given from the request receiving unit 111. Is created on the buffer unit 12. Next, for each of the divided space-time elements, a record corresponding to the input sensor type is searched from the sensor database device 3, and the measurement data included in the search result record is stored in the space-time data array of the buffer unit 12. Process to store in. When there are a plurality of search result records, representative values (for example, average value and median value) of the measurement data are stored, and when there are no search result records, NA is stored.

  The characteristic value estimator 112 is based on the characteristic type given from the request receiver 111 and the spatiotemporal data array stored in the buffer unit 12 to store the spatiotemporal data stored in the buffer unit 12. Processing to create a space-time binary array from an array, processing to create a space-time probability array from the created space-time binary array, and processing to create a space-time weight array from the created space-time probability array And processing for estimating the characteristic value from the created spatiotemporal weight array and the spatiotemporal data array.

  The estimation result response unit 113 performs processing for returning information representing the characteristic value created by the characteristic value estimation unit 112 to the application execution apparatus 2 that is a request source.

(Operation)
Next, the operation of the population characteristic value estimation apparatus 1 configured as described above will be described.
(1) Collection of sample data A user is carrying a portable terminal equipped with a GPS (Global Positioning System) sensor and a temperature sensor, and the portable terminal measures the GPS sensor and the temperature sensor in this movement process. The obtained position data and temperature data are transmitted to the sensor database device 3 at a preset cycle. The sensor database device 3 receives each sensor data transmitted from the portable terminal for each user and stores it in the database. FIG. 2 shows an example of sensor data stored in a database. Each record is composed of position data represented by date, latitude, and longitude, sensor type, and measurement data. In this example, the case where the sensor data transmitted from the portable terminal at a cycle of 15 minutes is stored is shown.

(2) Estimation of population characteristic values in the entire space-time (2-1) Specification of parameters for estimation When requesting the population characteristic value estimation device 1 to estimate the population characteristic values in the entire space-time, In the application execution apparatus 2, the operator designates and inputs the spatiotemporal range, spatiotemporal unit, sensor type, and characteristic value type to be estimated as parameters. Then, the application execution apparatus 2 sends an estimation request including the designated and input spatiotemporal range, spatiotemporal unit, sensor type, and characteristic value type to the population characteristic value estimating apparatus 1.

  FIGS. 3 and 4 show examples of spatiotemporal ranges and spatiotemporal units, respectively. This example shows the date and time “2013-08-20 08:00:00” to “2013-08-20 12:00:00”, location (latitude “35.722000” to “35.738000”, longitude “139.560000” to “139.566000” ) Is defined as the population for estimating the characteristic value, and the space-time unit defined by the date and time interval "01:00:00" and the position (latitude) interval "0.004" It means to make it a constituent element. As will be described later, the spatio-temporal division unit 114 divides the spatio-temporal range shown in FIG. 3 into spatio-temporal elements shown in FIG.

  5 and 6 show examples of sensor types and characteristic value types, respectively. This example means that the sensor type to be estimated is “temperature” and the characteristic value type to be estimated is “average”.

(2-2) Receiving process of estimation request In the population characteristic value estimation apparatus 1, when an estimation request is sent from the application execution apparatus 2, a parameter is extracted from the estimation request by the request reception unit 111, and among these parameters, The spatiotemporal range, spatiotemporal unit, and sensor type are given to the spatiotemporal division unit 114, and the characteristic value type is given to the characteristic value estimation unit 112, respectively.

(2-3) Spatio-temporal division processing In the spatio-temporal division unit 114, based on the spatio-temporal range, spatio-temporal unit, and sensor type given from the request receiving unit 111, first, the designated spatio-temporal range is converted to the A spatio-temporal data array divided into elements of a designated spatio-temporal unit is created on the buffer unit 12. Next, for each of the divided space-time elements, a record corresponding to the input sensor type is read from the sensor database device 3, and the measurement data included in the read record is stored in the buffer unit 12. Stored in a spatial data array. If there are a plurality of read records, representative values of those data, for example, average value or median value are stored, and if there is no read record, NA is stored.

  FIG. 7 shows an example of a spatio-temporal data array. A spatio-temporal data array was created according to the spatio-temporal range shown in FIG. 3, the spatio-temporal unit shown in FIG. 4, and the sensor type shown in FIG. The case is shown. That is, the date and time interval “01” shown in FIG. 4 is from the start date “2013-08-20 08:00:00” to the end date “2013-08-20 12:00:00” shown in FIG. 00:00 ”is divided into four, and the position (latitude) interval“ 0.004 ”shown in FIG. 4 from the start (35.722000) of the position (latitude) shown in FIG. 3 to the end“ 35.738000 ”of the position (latitude) shown in FIG. Is divided into four. Further, the sensor type “temperature” data shown in FIG. 5 is stored for each of the divided space-time elements.

Here, the population U for estimating the characteristic value is a whole set of divided space-time elements, and U = {(j, k) | j = 1,2,3,4, k = 1,2, 3,4}. The sample s from which data of the sensor type “temperature” is sampled is a subset of the population U, and s = {(1,2), (2,2), (2,3), (3 , 2)}. As will be described later, the characteristic value estimation unit 112 uses the data y_i (i∈s⊆U) of the element i of the sample s stored in the spatiotemporal data array to generate the data y_i of the element i of the population U. A characteristic value summarizing (i∈U) is estimated.
In FIG. 7, the time axis is a one-dimensional and the spatial axis is a two-dimensional array. However, when the position (longitude) interval is also specified in FIG. It becomes a three-dimensional array with one dimension and a two-dimensional space axis.

(2-4) Characteristic Value Estimation Processing The characteristic value estimation unit 112 is based on the characteristic type given from the request receiving unit 111 and the spatiotemporal data array held in the buffer unit 12 as follows. Spatio-temporal characteristic value estimation processing is performed. FIG. 8 is a flowchart showing the processing procedure and processing contents.

に示すように、母集団Uの要素iが標本sに含まれる場合、つまり母集団Uの要素iのデータy_iがNAでない場合にはz_i=1、母集団Uの要素iが標本sに含まれない場合、つまり母集団Uの要素iのデータy_iがNAである場合にはz_i=0となる、二値z_iを格納した時空間二値配列（z_i）が作成され、バッファ部１２に保存される。 In the characteristic value estimation unit 112, first, in step S1, a spatiotemporal data array is read from the buffer unit 12, and a process of creating a spatiotemporal binary array from the spatiotemporal data array is performed as follows. That is, if the spatiotemporal data array is (y_i),

As shown in, z_i = 1 if the element i of the population U is included in the sample s, that is, if the data y_i of the element i of the population U is not NA, and the element i of the population U is included in the sample s. If not, that is, if the data y_i of the element i of the population U is NA, a spatiotemporal binary array (z_i) storing binary z_i with z_i = 0 is created and stored in the buffer unit 12 Is done.

  FIG. 9 shows an example of a spatiotemporal binary array. In this example, the spatiotemporal data array is as shown in FIG. Among the elements of the population U = {(j, k) | j = 1,2,3,4, k = 1,2,3,4}, the sample s = {(1,2), (2,2 ), (2,3), (3,2)} are only 1 and other elements are 0.

に示すように、母集団Uの要素iが標本sに含まれるか否かを示す二値z_iを目的変数、母集団Uの要素iの日時と位置（緯度）からなるベクトルx_iを説明変数として、ロジスティック回帰モデルに当てはめ、尤度L(β)を最大化するパラメータベクトルβを推定する処理が行われる。 In the characteristic value estimation unit 112, subsequently, in step S2, processing for creating a spatiotemporal probability array from the spatiotemporal binary array created in step S1 is performed as follows. That is, if the space-time binary array stored in the buffer unit 12 is (z_i),

As shown in Fig. 2, binary z_i indicating whether or not element i of population U is included in sample s is an objective variable, and vector x_i consisting of the date, time and position (latitude) of element i of population U is used as an explanatory variable Then, a process for estimating the parameter vector β that maximizes the likelihood L (β) is performed by applying to the logistic regression model.

に示すように、そのパラメータベクトルの推定値β^と説明変数のベクトルx_iとを用いて、母集団Uの要素iが標本sに含まれる確率の推定値π^_iが計算され、その計算結果が時空間確率配列（π^_i）としてバッファ部１２に保存される。なお、式（２）及び式（３）において、Tは転置ベクトルを表す。
図１０は、以上のように作成された時空間確率配列（π^_i）の一例を示すもので、時空間二値配列が図９に示した場合に得られるものである。 next,

The estimated value π ^ _i of the probability that the element i of the population U is included in the sample s is calculated using the parameter vector estimate β ^ and the explanatory variable vector x_i, as shown in Fig. Is stored in the buffer unit 12 as a spatiotemporal probability array (π ^ _i). In Expressions (2) and (3), T represents a transposed vector.
FIG. 10 shows an example of the spatiotemporal probability array (π ^ _i) created as described above, and is obtained when the spatiotemporal binary array is shown in FIG.

  In the above example, the case where the logistic regression model is used to estimate the probability that the elements constituting the population are included in the sample is described. However, other regression models such as a probit regression model and a kernel regression model can also be used. Moreover, the case where date and time and position (latitude) are used as the explanatory variable vector is illustrated, but if there are other variables that can be used to explain the probability that the elements constituting the population are included in the sample, the date and time described above Other variables may be used instead of or in addition to the position (latitude).

に示すように、母集団Uの要素iが標本sに含まれる確率の推定値π^_iの逆数である重みw_iが算出され、この算出された重みw_iにより表される時空間重み配列（w_i）がバッファ部１２に保存される。
図１１にこのようにして作成された時空間重み配列（w_i）の一例を示す。この例は、時空間確率配列（π^_i）が図１０に示した場合に対応するものである。 Next, in step S3, the characteristic value estimation unit 112 performs processing for creating a spatiotemporal weight array from the spatiotemporal probability array created in step S2. That is, when the spatiotemporal probability array held in the buffer unit 12 is (π ^ _i) as described above,

As shown, a weight w_i that is the reciprocal of the estimated value π ^ _i of the probability that the element i of the population U is included in the sample s is calculated, and the spatio-temporal weight array (w_i) represented by the calculated weight w_i ) Is stored in the buffer unit 12.
FIG. 11 shows an example of the spatiotemporal weight array (w_i) created in this way. This example corresponds to the case where the spatiotemporal probability array (π ^ _i) is shown in FIG.

  Next, in step S4, the characteristic value estimation unit 112 and the spatiotemporal weight array (w_i) created in step S3 and the spatiotemporal space previously created by the spatiotemporal division unit 114 and stored in the buffer unit 12 are stored. Based on the data array (y_i), the process of estimating the spatio-temporal characteristic value is performed as follows.

に示すように、標本sの要素iの重みw_iとデータy_i、および母集団サイズ｜U｜を用いて、平均の推定値μ^が計算され、その結果がバッファ部１２に格納される。例えば、時空間重み配列（w_i）が図１１に示したようになっており、時空間データ配列（y_i）が図７に示したようになっていたとすると、平均の推定値μ^は
(2.5*30.1+3.3*33.0+3.3*31.7+5.0*35.7)/16=29.2
となる。 That is, if the characteristic value type specified by the estimation request is “average” as shown in FIG.

As shown in FIG. 4, an average estimated value μ ^ is calculated using the weight w_i of the element i of the sample s, the data y_i, and the population size | U |, and the result is stored in the buffer unit 12. For example, if the spatiotemporal weight array (w_i) is as shown in FIG. 11 and the spatiotemporal data array (y_i) is as shown in FIG. 7, the average estimated value μ ^ is
(2.5 * 30.1 + 3.3 * 33.0 + 3.3 * 31.7 + 5.0 * 35.7) /16=29.2
It becomes.

  In the above example, the case where the characteristic value type to be estimated is “average” has been described. However, for other characteristic value types, such as ratio and variance, “average (or the total based on the average)” is basically used. Therefore, it can be estimated using a spatiotemporal weight array and a spatiotemporal data array.

(2-5) Estimation Result Output Processing When the characteristic value estimation unit 112 notifies that the population characteristic value estimation has been completed, the estimation result response unit 113 displays information indicating the estimation result of the characteristic value in the buffer unit 12. The estimated value of the read characteristic value is transmitted to the application execution apparatus 2 as a result of population characteristic value estimation.

(Effects of the first embodiment)
As described in detail above, in the first embodiment, the probability that the elements constituting the population are included in the sample from each record (sample data) of the actually sampled sensor data is estimated using the logistic regression model, The population characteristic value is estimated using the reciprocal of the probability estimated after this fact and the sample data actually sampled.

  Therefore, even if it is not always possible to control which part of the whole space-time is sampled, such as user-participated environmental sensing, the entire space-time can be obtained from the sampled data of a part of the space-time. It is possible to estimate the data characteristic value of the above, that is, the population characteristic value without deviation or with a small error.

[Second Embodiment]
In the second embodiment of the present invention, when data for which the correct value of a population characteristic value is known, that is, when data of a sensor type that is not an estimation target obtained by sampling all elements of a population is available, the data is used as auxiliary data. Is used to correct the spatio-temporal weight array, and the corrected spatio-temporal weight array is used to estimate the population characteristic value of the sensor type that was originally the estimation target.

FIG. 12 is a flowchart showing an estimation processing procedure and processing contents in the characteristic value estimation unit of the population characteristic value estimation apparatus which is the second embodiment of the sample data processing apparatus according to the present invention. In the figure, the same parts as those in FIG.
Further, here, it is assumed that auxiliary data other than the sensor type to be estimated is stored in the buffer unit 12 as a spatio-temporal data array (y′_i) similarly to the data of the sensor type to be estimated. I do.

  In the characteristic value estimation unit 112, when the process of creating the spatiotemporal weight array (w_i) in step S3 is completed, the process proceeds to step S5, where the spatiotemporal weight array (w_i) is used as another auxiliary data. Correction processing is performed based on the spatio-temporal data array (y′_i) depending on the sensor type.

に示すように、母集団Uの要素iの補助データy’_iの総計の正解値（分子）と、標本sの要素iの重みw_iと補助データy’_iから推定される総計の推定値（分母）との比を用いて重みw_iが補正され、この補正された重みw’_iを格納した時空間重み配列（w’_i）がバッファ部１２に保存される。 In particular,

As shown, the correct value (numerator) of the sum of auxiliary data y'_i of element i of population U, and the estimated value of the total estimated from weight w_i of element i of sample s and auxiliary data y'_i ( The weight w_i is corrected using the ratio to the denominator), and the spatio-temporal weight array (w′_i) storing the corrected weight w′_i is stored in the buffer unit 12.

For example, assume that the spatiotemporal weight array (w_i) is as shown in FIG. 11 and the spatiotemporal data array (y′_i) as auxiliary data is as shown in FIG. In this case, the ratio between the correct value and the estimated value of the sum of the auxiliary data y'_i is
(75.3 + 70.7 +… + 64.2 + 62.2) / (2.5 * 70.7 + 3.3 * 71.5 + 3.3 * 65.4 + 5.0 * 70.8) = 1.1
It becomes. For this reason, the spatiotemporal weight array (w_i) is corrected to 1.1 times, and the corrected spatiotemporal weight array (w′_i) is stored in the buffer unit 12. FIG. 14 shows an example of the spatio-temporal weight array (w′_i) corrected in this way.

  Subsequently, in step S4, the characteristic value estimation unit 112 and the corrected spatiotemporal weight array (w′_i) generated in step S5 and the spatiotemporal division unit 114 previously generated and stored in the buffer unit 12 are stored. Based on the spatiotemporal data array (y_i), the process of estimating the spatiotemporal characteristic value is performed as follows.

に示すように、標本sの要素iの補正された重みw’_iと計測データy_i、および母集団サイズ｜U｜を用いて、平均の推定値μ^’が計算され、この計算結果μ^’がバッファ部１２に保存される。 That is, if the characteristic value type specified by the estimation request is “average” as shown in FIG.

As shown in Fig. 4, the average estimated value μ ^ 'is calculated using the corrected weight w'_i of the element i of the sample s, the measurement data y_i, and the population size | U |. 'Is stored in the buffer unit 12.

For example, the corrected spatiotemporal weight array (w′_i) is as shown in FIG. 14, and the spatiotemporal data array (y_i) of the sensor type to be estimated is as shown in FIG. Then the average estimate μ ^ '
(2.8 * 30.1 + 3.6 * 33.0 + 3.6 * 31.7 + 5.5 * 35.7) /16=32.1
It becomes.

  When there are a plurality of auxiliary data other than the estimation target sensor type that can be used to correct the spatiotemporal weight array, the auxiliary data having the highest correlation with the estimation target sensor type data is used. .

  As described above, according to the second embodiment, the spatio-temporal weight array (w_i) used for estimating the population characteristic value is determined based on the sensor type other than the estimation target for which the correct value of the population characteristic value is known in advance. By correcting the spatio-temporal data array as auxiliary data, the estimation error of the population characteristic value can be further reduced.

[Other Embodiments]
The present invention is not limited to the above embodiments. For example, in the embodiment, the case where the population characteristic value estimation device 1 is configured as a device different from the application execution device 2 and the sensor database device 3 has been described as an example. However, the present invention is not limited thereto, and the function of the population characteristic value estimation device 1 may be provided in one of the application execution device 2 or the sensor database device 3, or the function of the population characteristic value estimation device 1 and the application execution device The function 2 and the function of the sensor database device 3 may be provided in the same device.

  In addition, the configuration of the population characteristic value estimation apparatus, the center type to be estimated, the type and configuration of sample data, the procedure of the characteristic value estimation process and the contents of the process, and the like are variously within the scope of the present invention. It can be implemented with modifications.

  In short, the present invention is not limited to the above-described embodiments as they are, and can be embodied by modifying the components without departing from the scope of the invention in the implementation stage. Moreover, various inventions can be formed by appropriately combining a plurality of constituent elements disclosed in the above embodiments. For example, some components may be deleted from all the components shown in the embodiment. Furthermore, you may combine suitably the component covering different embodiment.

  DESCRIPTION OF SYMBOLS 1 ... Population characteristic value estimation apparatus, 2 ... Application execution apparatus, 3 ... Sensor database apparatus, 11 ... Processing unit, 12 ... Buffer part, 111 ... Request reception part, 112 ... Characteristic value estimation part, 113 ... Estimation result response part 114 Space-time division unit.

Claims (7)

A sample data processing device that estimates population characteristic values from accumulated sample data,
The spatio-temporal range for defining the population from which the characteristic value is to be estimated, the spatio-temporal unit for defining the elements constituting the population, the sensor type to be estimated, and the type of characteristic value to be estimated Means to accept the designation of,
The designated spatio-temporal range is divided into population elements of the designated spatio-temporal unit, and the designated sensor type is determined from the accumulated sample data for each of the divided population elements. Means for retrieving and storing sample data corresponding to
From the sample data stored for each element of the population, the probability that the element of the population is included in the sample data is estimated after the fact, and the reciprocal of the probability estimated after the fact and the specified sensor type Means for estimating a population characteristic value corresponding to the specified characteristic value type based on corresponding sample data;
A sample data processing apparatus comprising: means for outputting an estimated value of the estimated population characteristic value. The correct value of the population characteristic value is known, further comprising means for acquiring sample data other than the designated sensor type as auxiliary data,
The means for estimating the population characteristic value is:
Means for posteriorly estimating the probability that an element of the population is included in the sample data from the sample data stored for each element of the population;
Means for correcting the inverse of the probability estimated after the fact based on the acquired auxiliary data;
Means for estimating a population characteristic value corresponding to the specified characteristic value type based on the reciprocal of the corrected probability and the sample data corresponding to the specified sensor type. The specimen data processing apparatus according to claim 1.   3. The sample data processing apparatus according to claim 1, wherein the means for estimating the population characteristic value estimates a probability that an element of the population is included in the sample data using a regression model. A population characteristic value estimation apparatus comprising a computer and a storage medium is a sample data processing method for executing a process of estimating a population characteristic value from accumulated sample data,
The computer estimates a spatio-temporal range for defining a population for which the characteristic value is to be estimated, a spatio-temporal unit for defining elements constituting the population, and a sensor type to be estimated A process of accepting specification of a characteristic value type;
The computer divides the designated spatio-temporal range into elements of a population of the designated spatio-temporal unit, and for each divided element of the population, the designation is made from the accumulated sample data. Retrieving sample data corresponding to the sensor type and storing it in the storage medium;
From the sample data stored for each element of the population, the computer estimates the probability that the element of the population is included in the sample data after the fact, and is designated as the reciprocal of the probability estimated after the fact. Estimating a population characteristic value corresponding to the specified characteristic value type based on sample data corresponding to the sensor type,
A sample data processing method comprising: a step of outputting an estimated value of the estimated population characteristic value by the computer. The computer further comprises a step of obtaining sample data other than the specified sensor type as auxiliary data, in which the correct value of the population characteristic value is known,
The process of estimating the population characteristic value includes:
From the sample data stored for each element of the population, a process for estimating the probability that the element of the population is included in the sample data after the fact;
Correcting the reciprocal of the probability estimated after the fact based on the acquired auxiliary data;
A step of estimating a population characteristic value corresponding to the specified characteristic value type based on the reciprocal of the corrected probability and the sample data corresponding to the specified sensor type. The sample data processing method according to claim 4.   6. The sample data processing method according to claim 4, wherein in the process of estimating the population characteristic value, the probability that the elements of the population are included in the sample data is estimated afterwards using a regression model.   The program which makes the computer with which the said sample data processing apparatus performs the process which each means with which the sample data processing apparatus in any one of Claim 1 thru | or 3 has is provided.

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