Josef, could you explain that in slightly more detail? I'm afraid I'm not familiar with the literature you are referencing at all.
If you have some code I could take a look at, that would probably be the easiest thing for me. Thanks! Federico On Mon, Oct 22, 2012 at 4:40 PM, <josef.p...@gmail.com> wrote: > 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 ------------------------------------------------------------------------------ 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
