ESTIMATION APPARATUS, ESTIMATION SYSTEM, ESTIMATION METHOD AND PROGRAM

1 . An estimation apparatus comprising:

a memory; and

a processor configured to execute:

taking a set of observation points representing events observed in a space region of a predetermined dimensionality in an observation, an observation count representing the number of times the observation is performed, a first function satisfying a predetermined condition, and a parameter of the first function as inputs, and

analytically estimating a rate function for obtaining occurrence rates of the events in the space region.

2 . The estimation apparatus according to claim 1 , wherein the predetermined condition is that the first function is a symmetric function and an eigenvalue is 0 or greater and 1/R or less when the observation count is R and the first function is used as a kernel function of an integral operator.

3 . The estimation apparatus according to claim 1 , wherein the processor is further configured to execute:

taking a set of estimation target points representing points, the points being in the space region and being estimation targets for the occurrence rates of the events, and the rate function as inputs, and

estimating occurrence rates of events at the estimation target points.

4 . The estimation apparatus according to claim 1 , wherein the analytically estimating of the rate function estimates the rate function including the observation count, a parameter representing a square root of an average value of the rate function, a second function obtained by integrating the first function in the space region, a vector representing values of the first function at the observation points, and a vector representing reciprocals of square roots of estimated values of the rate function at the observation points.

5 . An estimation system comprising:

a first apparatus including a memory and a processor; and

a second apparatus including a memory and a processor, and being different from the first apparatus,

wherein the processor of the first apparatus is configured to take a set of observation points representing events observed in a space region of a predetermined dimensionality in an observation, an observation count representing the number of times the observation is performed, a first function satisfying a predetermined condition, and a parameter of the first function as inputs, and analytically estimate a rate function for obtaining occurrence rates of the events in the space region, and

wherein the processor of the second apparatus is configured to take a set of estimation target points representing points, which are in the space region and are estimation targets for the occurrence rates of the events, and the rate function as inputs, and estimate occurrence rates of events at the estimation target points.

6 . An estimation method executed by a computer including a memory and a processor, the estimation method comprising:

taking a set of observation points representing events observed in a space region of a predetermined dimensionality in an observation, an observation count representing the number of times the observation is performed, a first function satisfying a predetermined condition, and a parameter of the first function as inputs, and

analytically estimating a rate function for obtaining occurrence rates of the events in the space region.

7 . A non-transitory computer-readable recording medium having computer-readable instructions stored thereon, which when executed, cause a computer to operate as the estimation apparatus according to claim 1 .