genetic algorithm combined for non-linear regression
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Hi,
I was suggested and I believe that is really a good idea, that by using a genetic algorithm to determine my initial guesses for a non-linear regression could minimize ill-conditioned initial guesses. However, I am really struggling to implement this idea.
So my purpose is use the genetic algorithm to find some good initial guesses for a non-linear regression (nlinfit).
The function that I use for the non-linear regression is the following
function y = objective(ksiz,x)
y=exp(x*ksiz);
ksiz are coefficients to be found by the non-linear regression, calling it as follows:
I call the non-linear regression as follows:
ksi1 = nlinfit(X(1:T-1,:),ex1','objective',ksi10);
where ksi1, are the optimum choice (coefficients) for the fit, and ksi0 the corresponding guesses.
X is the matrix of the explanatory variables, and ex1 is the data of the dependent variable. The matrix X is for example defined as:
X = [ones(T-1,1) log(kh(1:T-1,1)) log(zh(T:T-1,1)) log((A(1:T-1,1)))]
where T is the length of sample, and kh, zh, A are my data. As you notice I also include a constant term, captured by the vector of ones. I attach for you the sample with those data
UPDATE
My algorithm essentially is trying to find a fixed point, of some parameters that I use to approximate an unknown function through a simple polynomial. The fixed point involves a loop over which the data are generated and uses a regression to minimize the errors between the approximated function and the true one. The data sample to be used in the regression are determined endogenously through my models equations.
I start with a guess for the parameters:
%% Guess of the coefficients to be used in the polynomial
be1=[1.9642; 0.5119; 0.0326; -2.5694];
be2=[1.8016; 1.3169; 0.0873; -2.6706];
be3=[1.9436; 0.5082; 0.0302; -2.5742];
be4=[0.6876; 0.5589; 0.0330; -2.6824];
be5=[2.0826; 0.5509; 0.0469; -2.5404];
%% My guess for the initial values to be used in the non-linear regression
ksi1=be1;
ksi2=be2;
ksi3=be3;
ksi4=be4;
ksi5=be5;
In the "sample.mat" file I include the initialization for the variables used in the polynomial.
In my loop anything that does not change within the loop is a parameter already assigned a value.
%%% Loop to find the fixed point through homotopy
while dif> crit
for t=1:T
%%basis points of the polynomial of Degree 1
X(t,:) = Ord_Polynomial_N([log(kh(t,1)) log(zh(t,1)) log((A(t,1))) ], D);
%%the function that I approximate
psi1(t)=exp((X(t,:)*be1));
ce(t)=psi1(t)^(1/(1-gamma));
if eps == 1
v(t)=((1-beta)^(1-beta))*(beta*ce(t))^(beta);
u(t)=1-beta;
else
v(t)=(1+beta^(eps)*ce(t)^(eps-1))^(1/(eps-1));
u(t)=v(t)^(1-eps);
end
% approximate some other functions
psi2(t)=exp(X(t,:)*be2);
psi3(t)=exp(X(t,:)*be3);
psi4(t)=exp(X(t,:)*be4);
psi5(t)=exp(X(t,:)*be5);
%%%Generate the sample
kh(t+1)= psi2(t)/psi3(t);
kh(t+1)= kh(t+1)*(kh(t+1)>khlow)*(kh(t+1)<khup)+khlow*(kh(t+1)<khlow)+khup*(kh(t+1)>khup);
theta(t+1) = 1/(1+kh(t+1));
phi(t+1) = psi4(t)/psi5(t);
zh(t+1) = (phi(t+1)/(1-phi(t+1)))*(1-theta(t+1));
zh(t+1) = zh(t+1)*(zh(t+1)>zhlow)*(zh(t+1)<zhup)+zhlow*(zh(t+1)<zhlow)+zhup*(zh(t+1)>zhup);
end
%%%Using the sample before, generate the 'true' function
for t=1:T
Rk(t) = 1+A(t)*alpha*kh(t)^(alpha-1)-delta1;
Rh(t) = 1+A(t)*(1-alpha)*kh(t)^(alpha)-delta1+eta(t);
R(t) = 1 + A(t)*ai(t)*(1-alpha)*(q)^(alpha)-delta2;
Rx(t) = (Rk(t)*(1-theta(t)) + Rh(t)*theta(t))*(1-phi(t))+ phi(t)*R(t);
end
for t=1:T-1
%%This was approximated by psi1
ex1(t)=v(t+1)^(1-gamma)*Rx(t+1)^(1-gamma);
%%This was approximated by psi2
ex2(t)=v(t+1)^(1-gamma)*Rx(t+1)^(-gamma)*Rk(t+1)*(kh(t+1)) ;
% This was approximated by psi3
ex3(t)=v(t+1)^(1-gamma)*Rx(t+1)^(-gamma)*Rh(t+1);
% This was approximated by psi4
ex4(t)=v(t+1)^(1-gamma)*Rx(t+1)^(-gamma)*Rk(t+1)*phi(t+1);
this was approximated by psi5
ex5(t)=v(t+1)^(1-gamma)*Rx(t+1)^(-gamma)*R(t+1);
end
W_new=[kh zh];
%%Convergent criterion
dif= mean(mean(abs(1-W_new./W_old))) ;
disp(['Difference: ' num2str(dif)])
%%%Update of the coefficients through regressions
opts = statset('MaxIter',60000);
ksi1 = nlinfit(X(1:T-1,:),ex1','objective',ksi1,opts);
ksi2 = nlinfit(X(1:T-1,:),ex2','objective',ksi2,opts);
ksi3 = nlinfit(X(1:T-1,:),ex3','objective',ksi3,opts);
ksi4 = nlinfit(X(1:T-1,:),ex4','objective',ksi4,opts);
ksi5 = nlinfit(X(1:T-1,:),ex5','objective',ksi5,opts);
%%Homotopy
be1 = update*ksi1 + (1-update)*be1;
be2 = update*ksi2 + (1-update)*be2;
be3 = update*ksi3 + (1-update)*be3;
be4 = update*ksi4 + (1-update)*be4;
be5 = update*ksi5 + (1-update)*be5;
W_old=W_new;
end
I would really appreciate your assistance on how to use the genetic algorithm. I am confused by the mathwork documentation as my problem here seems much simpler than the available examples I found.
댓글 수: 1
dmr
2020년 8월 13일
can i ask how you found your sets of beta? is it via parameter estimation like maximum likelihood? i want to use genetics algorithm too and i have my parameters estimated by mle but of course i only got one set (except if you add other sets from the iterations).
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