[nPOE, vPOE, uPOE] = ccl_error_poe_alpha (f_proj, X, NS_t) Compute the normalised projection observation error (nPOE) with state dependant projections. To evaluate the fit without the true nullspace policy, an alternative criterion must be used. This indicates the quality of the learnt projection matrix in capturing the image space of the observations. i.e., how well the learnt N satisfy Nu = u Input: f_proj State dependent prediction of the projection matrix X True state NS_t True observed null-space component Output: nPOE Normalised projected observation error vPOE Variance of the nullspace policy uPOE Projected observation error
0001 function [nPOE, vPOE, uPOE] = ccl_error_poe_alpha (f_proj, X, NS_t) 0002 % [nPOE, vPOE, uPOE] = ccl_error_poe_alpha (f_proj, X, NS_t) 0003 % Compute the normalised projection observation error (nPOE) with state dependant projections. 0004 % To evaluate the fit without the true nullspace policy, an alternative criterion must be used. 0005 % This indicates the quality of the learnt projection matrix in capturing the image space of 0006 % the observations. i.e., how well the learnt N satisfy Nu = u 0007 % 0008 % Input: 0009 % 0010 % f_proj State dependent prediction of the projection matrix 0011 % X True state 0012 % NS_t True observed null-space component 0013 % 0014 % Output: 0015 % 0016 % nPOE Normalised projected observation error 0017 % vPOE Variance of the nullspace policy 0018 % uPOE Projected observation error 0019 0020 0021 0022 0023 % CCL: A MATLAB library for Constraint Consistent Learning 0024 % Copyright (C) 2007 Matthew Howard 0025 % Contact: matthew.j.howard@kcl.ac.uk 0026 % 0027 % This library is free software; you can redistribute it and/or 0028 % modify it under the terms of the GNU Lesser General Public 0029 % License as published by the Free Software Foundation; either 0030 % version 2.1 of the License, or (at your option) any later version. 0031 % 0032 % This library is distributed in the hope that it will be useful, 0033 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0034 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 0035 % Lesser General Public License for more details. 0036 % 0037 % You should have received a copy of the GNU Library General Public 0038 % License along with this library; if not, write to the Free 0039 % Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. 0040 0041 dim_n = size(NS_t,2) ; 0042 NS_p = zeros(size(NS_t)) ; 0043 for n = 1:dim_n 0044 NS_p(:,n) = f_proj(X(:,n)) * NS_t(:,n) ; 0045 end 0046 uPOE = mean (sum((NS_t-NS_p).^2,1) ) ; 0047 vPOE = var(NS_t, 0, 2); 0048 nPOE = uPOE / sum(vPOE); 0049 end