BEST LAMBDA

Choose the best value for the Tikhonov regularization parameter lambda

Contents

Function of MOBY-DIC TOOLBOX.

Description

Consider the following regularized least squares optimization problem:

$$ \min_w || G w \textrm{--} d ||^2 + || \lambda L w ||^2 $$

subject to:

$$A w <= B$$

$$Aeq w = Beq$$

Call H = G'G, Q = L'L, y = G'd. If a test set matrix Gt and a test vector dt are not null, lambda is found in order to minimize $|| Gt w \textrm{--} dt ||^2$. If they are null, $\lambda$ is chosen with a generalized cross validation technique (see function GCVcost). This function uses a nested function 'solve' which determines the cost associated to a given value of $\lambda$, by solving the optimization problem. A handle to this function is passed to Matlab function fmincon which finds the value of lambda minimizing the cost.

Syntax

lambda = bestLambda(H,Q,y,G,d,Gt,dt,constraints,solver)

H, Q, y, G are the matrices defining the cost functional. Gt and dt are the matrices used as test set. constraints is a structure with fields A, B, Aeq, Beq representing the constraints matrices. solver is a string specifying the solver you want to use to solve the QP problem (this is necessary only in presence of constraints. Possible choices are 'quadprog' (default), 'cvx', 'cplex', 'yalmip', 'clp'.

Acknowledgements

Contributors:

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Published with MATLAB® 7.8