 function [s_hat,e_hat,W_hat,de_hat,Fx_hat,Fs_hat] = estimate_mAR_IPA(x,mAR,ICA,ISA,unknown_dimensions,de)
%Estimates the mARIPA model. Method: mAR identification + ISA on the estimated innovation.
%
%INPUT:
% x: x(:,t) is the observation at time t.
% mAR: mAR estimator, see 'estimate_mAR.m'.
% ICA: solver for independent component analysis, see 'estimate_ICA.m'.
% ISA: solver for independent subspace analysis (=clustering of the ICA elements). ISA.cost_type, ISA.cost_name, ISA.opt_type: cost type, cost name, optimization type. Example: ISA.cost_type = 'sumH', ISA.cost_name = 'Renyi_kNN_1tok', ISA.opt_type = 'greedy' means that we use an entropy sum ISA formulation ('sumH'), where the entropies are estimated Renyi entropies via kNN methods ('Renyi_kNN_1tok') and the optimization is greedy; see also 'demo_ISA.m'
% unknown_dimensions: '0' means 'the subspace dimensions are known'; '1' means 'the number of the subspaces are known' (but the individual dimensions are unknown).
% de:
% 1)in case of 'unknown_dimensions = 0': 'de' contains the subspace dimensions.
% 2)in case of 'unknown_dimensions = 1': the length of 'de' must be equal to the number of subspaces, but the coordinates of the vector can be arbitrary.
%OUTPUT:
% s_hat: estimated source, s_hat(:,t) corresponds to time t
% e_hat: estimated driving noise, e_hat(:,t) corresponds to time t
% W_hat: estimated demixing matrix.
% de_hat: estimated subspace dimensions.
% Fx_hat: estimated observation dynamics.
% Fs_hat: estimated source dynamics.
%
%REFERENCE:
% Zoltan Szabo. Autoregressive Independent Process Analysis with Missing Observations. European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN), pp. 159164, 2010.
%
%Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "szzoli (at) cs (dot) elte (dot) hu")
%
%This file is part of the ITE (Information Theoretical Estimators) Matlab/Octave toolbox.
%
%ITE is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by
%the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
%
%This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
%MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
%
%You should have received a copy of the GNU General Public License along with ITE. If not, see <http://www.gnu.org/licenses/>.
%mAR fit to x:
[x_innovation_hat,Fx_hat,SBCs] = estimate_mAR(x,mAR);
%ISA on the estimated innovation of x:
[e_hat,W_hat,de_hat] = estimate_ISA(x_innovation_hat,ICA,ISA,unknown_dimensions,de,size(x_innovation_hat,1));
%estimated source(s_hat) and its dynamics:
s_hat = W_hat * x;
Fs_hat = basis_transformation_AR(Fx_hat,W_hat,inv(W_hat));
