Parameter estimation system, parameter estimation method, and parameter estimation program recording medium for estimating parameter and kernel functions by incorporating machine learning

A parameter estimation method in a parameter estimation system for estimating a parameter θ of a function, the parameter estimation method being for determining, by repetitive learning, the parameter θ to be set to the function, from samples of the parameter θ, using the function for producing data y, the method comprising:

• acquiring N (where N represents an integer which is not less than two) samples θi, (1≤i≤N) of the parameter θ from a prior distribution P;
• acquiring N data yi from the function by successively supplying the N samples θi, to the function, respectively;
• calculating N degrees of similarity wi between the N data yi and correct data y* using a kernel function k;
• constructing a kernel mean μ of a posterior distribution based on the N degrees of similarity wi, the N samples θi, and the kernel function k;
• acquiring T (where T represents an integer which is not less than two) new samples θt (1≤t≤T) of the parameter θ based on the kernel mean μ and the kernel function k;
• and
• determining whether a difference ∥yk−y*I| between new data yk and the correct data y* is less than a predetermined threshold value ε, the new data yk being obtained from the function by supplying the function with one sample Ok selected from the T new samples θt;
• wherein the selected sample θk is estimated and produced as the parameter θ when it is determined that the difference ∥yk−y*I| is less than the predetermined threshold value ε and
• wherein the N samples θi are acquired while adjusting a hyper parameter η of the prior distribution P.

A non-transitory recoding medium recording a parameter estimation program causing, in a parameter estimation system for estimating a parameter θ of a function, a computer to determine, by repetitive learning, the parameter θ to be set to the function, from samples of the parameter θ, using the function for producing data y, wherein the parameter estimation program causes the computer to execute:

• a first sample acquisition step of acquiring N (where N represents an integer which is not less than two) samples θi(1≤i≤N) of the parameter θ from a prior distribution P;
• a function execution step of acquiring N data yi from the function by successively supplying the N samples θi to the function, respectively;
• a degree-of-similarity calculation step of calculating N degrees of similarity wi between the N data yi and correct data y* using a kernel function k;
• a kernel mean construction step of constructing a kernel mean μ of a posterior distribution based on the N degrees of similarity wi, the N samples θi, and the kernel function k;
• a second sample acquisition step of acquiring T (where T represents an integer which is not less than two) new samples θt (1≤t≤T) of the parameter θ based on the kernel mean μ and the kernel function k;
• and
• a sample evaluation step of determining whether a difference ∥yk−y*I| between new data yk and the correct data y* is less than a predetermined threshold value ε, the new data yk being obtained from the function by supplying the function with one sample θk selected from the T new samples θt;
• wherein the sample evaluation step causes the computer to estimate and produce the selected sample θk as the parameter θ when it is determined that the difference ∥yk−y*I| is less than the predetermined threshold value ε and
• wherein the first sample acquisition step causes the computer to acquire the N samples θi while adjusting a hyper parameter η of the prior distribution P.