On Mon, Oct 22, 2012 at 10:33 AM, <josef.p...@gmail.com> wrote: > On Mon, Oct 22, 2012 at 10:05 AM, federico vaggi > <vaggi.feder...@gmail.com> wrote: >> Hi Gael, >> >> I took the time to dig a little bit, and found some MATLAB code >> written by Diego di Bernardo. >> >> http://dibernardo.tigem.it/wiki/index.php/Network_Inference_by_Reverse-engineering_NIR >> >> He has a closed form result (the formula is in calc_cov.m), but the >> formula is really weird, and I can't really figure out where it comes >> from. >> >> function covA = calc_cov(A,X,sX,P,sP,RIDGE,W); >> >> % covA = calc_cov(A,X,sX,P,sP [, RIDGE, W]); >> % X,sX,P,SP are N x M, where N=number of genes, M=number of expts. >> % RIDGE is an optional ridge regression parameter >> % W is an optional weight parameter. >> >> [rows,N]=size(A); >> covA=zeros(N,N,rows); >> [N,M] = size(X); >> >> if 1~=exist('RIDGE') >> RIDGE = 0; >> end >> if 1~=exist('W') >> W = eye(M); >> end >> >> Q = W*W'; >> >> for g=1:rows >> idx = find(A(g,:)~=0); >> vEta = sP(g,:).^2 + A(g,:).^2 * sX.^2; >> % vEta = sP(g,g).^2 + A(g,:).^2 * sX.^2; % Deigo's way >> Z=X(idx,:); >> T=inv(Z*Q*Z'+RIDGE*eye(length(idx)))*Z*Q'; >> covA(idx,idx,g) = T*diag(vEta)*T'; >> end >> >> I'm not really sure how exactly the formula was derived though. > > I don't know about L1 penalization, but for Ridge there is a > literature on Ridge Regression with heteroscedastic or autocorrelated > errors, or general error covariance matrix. > > W looks like it's just a weight matrix, combined with ridge, Q is the > error covariance.
Also calculating Q is not very efficient in this case. If you know W, then you can just calculate new data by whitening or transforming x_new = W * X for the estimation. Josef > > Your problem is a bit different from standard Ridge regression because > you have several dependent/outcome variables. > > Josef > > >> >> Note - while the code is free to download, he specifically says that >> he doesn't want the code used for commercial purposes without >> permission. I presume reproducing it is ok? >> >> Federico >> >> >> >> On Mon, Oct 22, 2012 at 3:34 PM, Gael Varoquaux >> <gael.varoqu...@normalesup.org> wrote: >>> On Fri, Oct 19, 2012 at 01:09:21PM +0200, federico vaggi wrote: >>>> Assuming that X and B are experimentally measured values with >>>> uncertainties, what's the correct way to transfer that uncertainty to >>>> A? >>> >>> There exists to my knowledge no theoretical/closed form result. I would >>> rely on bootstrap: >>> http://en.wikipedia.org/wiki/Bootstrapping_%28statistics%29 >>> >>> G >>> >>> ------------------------------------------------------------------------------ >>> Everyone hates slow websites. So do we. >>> Make your web apps faster with AppDynamics >>> Download AppDynamics Lite for free today: >>> http://p.sf.net/sfu/appdyn_sfd2d_oct >>> _______________________________________________ >>> Scikit-learn-general mailing list >>> Scikit-learn-general@lists.sourceforge.net >>> https://lists.sourceforge.net/lists/listinfo/scikit-learn-general >> >> ------------------------------------------------------------------------------ >> Everyone hates slow websites. So do we. >> Make your web apps faster with AppDynamics >> Download AppDynamics Lite for free today: >> http://p.sf.net/sfu/appdyn_sfd2d_oct >> _______________________________________________ >> Scikit-learn-general mailing list >> Scikit-learn-general@lists.sourceforge.net >> https://lists.sourceforge.net/lists/listinfo/scikit-learn-general ------------------------------------------------------------------------------ Everyone hates slow websites. So do we. Make your web apps faster with AppDynamics Download AppDynamics Lite for free today: http://p.sf.net/sfu/appdyn_sfd2d_oct _______________________________________________ Scikit-learn-general mailing list Scikit-learn-general@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/scikit-learn-general
