多核学习方法

这是一份非常有效的多核学习程序，效率比较高

function [fgradhessianinvcholetalambda2da_dsigmad2a_dsigma2] = all_derivatives（Ksylossalphadslambdamu）;
m=Ks.m;
[fgradhessianinvcholetalambda2] = objective_function（Ksylossalphadslambdamu）;


psi2 = psi2_loss（lambda * alpha y loss）;
psi3 = psi3_loss（lambda * alpha y loss）;
da_dlambda = alpha .* psi2;
da_dlambda = - hessianinvchol * （ hessianinvchol‘ * da_dlambda ）;
temp11 = hessianinvchol * （ hessianinvchol‘ * （ psi2 .* alpha ） ） ;
temp22 = kernel_operation（Ks1temp11）;
temp3 = kernel_operation（Ks1alpha）;
temp3 = hessianinvchol * （ hessianinvchol‘ * temp3 ）;

temp4 = （  2 * psi2 + 2 * lambda * psi3 .* alpha ） .* temp11 - alpha .* alpha .* psi3 ;
d2a_dlambda2 = hessianinvchol * （ hessianinvchol‘ * temp4 ）;

for j=1:m
    temp44 = sum（ alpha.*temp22（:j） ）;
    d2a_dlambda2 = d2a_dlambda2 - 2/mu*eta（j）^2 * temp44 * hessianinvchol * （ hessianinvchol‘ * temp22（:j） ）;
    d2a_dlambda2 = d2a_dlambda2 - 2/mu*eta（j）^2 * temp44 * hessianinvchol * （ hessianinvchol‘ * temp22（:j） ）;
    d2a_dlambda2 = d2a_dlambda2 - 8*eta（j）^3/mu/mu * temp44 * temp44 * temp3（:j）;
    d2a_dlambda2 = d2a_dlambda2 - 2/mu*eta（j）^2 * sum（ temp11 .* temp22（:j） ） * temp3（:j）;
end
d2a_dlambda2 = d2a_dlambda2 - lambda^2 * hessianinvchol * （ hessianinvchol‘ * （ psi3 .* temp11 .* temp11 ） ）;     


da_dsigma = da_dlambda * （ -lambda ）;
d2a_dsigma2 = d2a_dlambda2 * lambda * lambda +  da_dlambda * （ lambda ）;



% switch loss_type
%     case ‘regression‘
%         da_dlambda = alpha .* psi2_regression（lambda * alpha y ）;
%         da_dlambda = - hessianinvchol * （ hessianinvchol‘ * da_dlambda ）;
%         temp1 = hessianinvchol * （ hessianinvchol‘ * alpha ） ;
%         temp2 = kernel_operation（Ks1temp1）;
%         temp3 = kernel_operation（Ks1alpha）;
%         temp3 = hessianinvchol * （ hessianinvchol‘ * temp3 ）;
%         
%         
%         d2a_dlambda2 = 2 * hessianinvchol * （ hessianinvchol‘ * temp1 ）;
%         for j=1:m
%             temp4 = sum（ alpha.*temp2（:j） ）;
%             d2a_dlambda2 = d2a_dlambda2 - 4/mu*eta（j）^2 * temp4 * hessianinvchol * （ hessianinvchol‘ * temp2（:j） ）;
%             d2a_dlambda2 = d2a_dlambda2 - 8*eta（j）^3/mu/mu * temp4^2 * temp3（:j）;
%             d2a_dlambda2 = d2a_dlambda2 - 2/mu*eta（j）^2 * sum（ temp1 .* temp2（:j） ） * temp3（:j）;
%         end
%         
%     case ‘logistic‘
%         psi2 = psi2_logistic（lambda * alpha y ）;
%         psi3 = psi3_logistic（lambda * alpha y ）;
%         da_dlambda = alpha .* psi2;
%         da_dlambda = - hessianinvchol * （ hessianinvchol‘ * da_dlambda ）;
%         temp11 = hessianinvchol * （ hessianinvchol‘ * （ psi2 .* alpha ） ） ;
%         temp22 = kernel_operation（Ks1temp11）;
%         temp3 = kernel_operation（Ks1alpha）;
%         temp3 = hessianinvchol * （ hessianinvchol‘ * temp3 ）;
%         
%         temp4 = （  2 * psi2 + 2 * lambda * psi3 .* alpha ） .* temp11 - alpha .* alpha .* psi3 ;
%         d2a

 属性            大小     日期    时间   名称
----------- ---------  ---------- -----  ----
     文件        5089  2004-08-19 10:37  multi-kernel-path-1.0\all_derivatives.m
     文件       56912  2004-10-25 15:08  multi-kernel-path-1.0\boston.mat
     文件         649  2004-12-24 16:33  multi-kernel-path-1.0\build_efficient_Ks.asv
     文件         784  2004-12-24 16:36  multi-kernel-path-1.0\build_efficient_Ks.m
     文件         482  2004-10-25 13:55  multi-kernel-path-1.0\build_efficient_Ks_test.m
     文件         510  2004-12-25 08:33  multi-kernel-path-1.0\compute_ds.asv
     文件         596  2004-12-25 08:34  multi-kernel-path-1.0\compute_ds.m
     文件        1283  2004-11-01 20:50  multi-kernel-path-1.0\compute_newlambda2.m
     文件        5390  2004-12-25 08:53  multi-kernel-path-1.0\create_path_kernel_matrices.asv
     文件        5634  2004-12-25 09:00  multi-kernel-path-1.0\create_path_kernel_matrices.m
     文件        5735  2004-11-02 07:49  multi-kernel-path-1.0\cv_general_script.m
     文件        3434  2004-12-24 22:28  multi-kernel-path-1.0\demo_script_1.m
     文件        3441  2004-12-24 22:28  multi-kernel-path-1.0\demo_script_2.m
     文件        7164  2004-12-24 22:28  multi-kernel-path-1.0\demo_script_3.asv
     文件        7060  2004-12-24 22:29  multi-kernel-path-1.0\demo_script_3.m
     文件         457  2004-08-17 12:01  multi-kernel-path-1.0\devectorize.c
     文件        6144  2004-08-17 12:01  multi-kernel-path-1.0\devectorize.dll
     文件       13095  2004-12-24 14:57  multi-kernel-path-1.0\follow_entire_path.asv
     文件       13245  2004-12-24 15:15  multi-kernel-path-1.0\follow_entire_path.m
     文件        1055  2004-12-25 08:23  multi-kernel-path-1.0\generate_random_problem.asv
     文件        1071  2004-12-25 08:27  multi-kernel-path-1.0\generate_random_problem.m
     文件       96416  2004-10-26 08:48  multi-kernel-path-1.0\ionosphere.mat
     文件         831  2004-08-17 15:14  multi-kernel-path-1.0\kernel_operation.m
     文件         864  2004-08-19 10:01  multi-kernel-path-1.0\kernel_operation_test.m
     文件       17496  2004-08-24 16:17  multi-kernel-path-1.0\liver.mat
     文件        2912  2004-11-09 13:36  multi-kernel-path-1.0\newton_method.m
     文件        1627  2004-10-27 12:05  multi-kernel-path-1.0\objective_function.m
     文件        1799  2004-11-08 13:46  multi-kernel-path-1.0\predictor_step.m
     文件         233  2004-08-19 10:43  multi-kernel-path-1.0\problem_type.m
     文件         220  2004-10-25 14:39  multi-kernel-path-1.0\psi1_loss.m
     文件         231  2004-10-25 14:39  multi-kernel-path-1.0\psi2_loss.m
............此处省略10个文件信息