Optimization module

Optimization module for PCM toolbox with main functionality for model fitting. @author: jdiedrichsen

optimize.best_algorithm(M, algorithm=None)

Parameters:

optimize.mcmc(th0, likelihood_fcn, proposal_sd=0.1, burn_in=100, n_samples=1000, verbose=1): Implement Markov Chain Monte Carlo sampling for PCM models Metropolis-Hastings algorithm with adaptive proposal distribution

optimize.newton(theta0, lossfcn, max_iter=80, thres=0.0001, hess_reg=0.0001, regularization='sEig', verbose=0, fit_param=None)

Minimize a loss function using Newton-Raphson with automatic regularization

Parameters:

theta (np.array) – Vector of parameter starting values
lossfcn (fcn) – Handle to loss function that needs to return a) Loss (Negative log-likelihood) b) First derivative of the Loss c) Expected second derivative of the loss
max_iter (int) – Maximal number of iterations (default: 80)
thres (float) – Threshold for change in Loss function (default: 1e-4)
hess_reg (float) – starting regulariser on the Hessian matrix (default 1e-4)
regularization (string) – ‘L’: Levenberg ‘LM’: Levenberg-Marquardt ‘sEig’:smallest Eigenvalue (default)
verbose (int) – 0: No feedback, 1:Important warnings 2:full feedback regularisation
fit_param (Logical) – If provided, it will only fit the parameters indicated

Returns: