optimization problem in KF and MLE for state-space model
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From: Jenny Yin on 16 Jan 2010 13:00 Hi, everyone, I have some problem on the optimization during the maximun likelihood estimation for state-space model via Kalman filter. There are around 100 parameters to estimate. 1. fminsearch works, even it is very slow. 2. fminunc, cannot work. It always stops by the error of the covariance matrix of state vector is almost singular. Since the number of parameters is large, I am worrying about whether fminsearch can search the nice results. Is anyone who also have met the problem of the singularity problem of state vector covariance matrix? why fminsearch does not stop by the error of of the covariance matrix of state vector is almost singular? Thanks very much.
From: Jenny Yin on 17 Jan 2010 10:59 I mean the singularity of the covarince matrix of observation vector, not the state vector, sorry for the mistake. "Jenny Yin" <jennywwyin(a)gmail.com> wrote in message <hisurk$mpj$1(a)fred.mathworks.com>... > Hi, everyone, > > I have some problem on the optimization during the maximun likelihood estimation for state-space model via Kalman filter. > > There are around 100 parameters to estimate. > > 1. fminsearch works, even it is very slow. > > 2. fminunc, cannot work. It always stops by the error of the covariance matrix of state vector is almost singular. > > Since the number of parameters is large, I am worrying about whether fminsearch can search the nice results. Is anyone who also have met the problem of the singularity problem of state vector covariance matrix? > > why fminsearch does not stop by the error of of the covariance matrix of state vector is almost singular? > > Thanks very much.
From: Alan Weiss on 18 Jan 2010 07:47
The fminunc algorithm essentially approximates the objective function (likelihood in your case) locally by a quadratic model. In your case it seems the approximation has a singularity. fminsearch does not make any such model, it just walks downhill. For more information on the algorithms, see http://www.mathworks.com/access/helpdesk/help/toolbox/optim/ug/brnoxr7-1.html#brnpcye and http://www.mathworks.com/access/helpdesk/help/toolbox/optim/ug/brnoxr7-1.html#brnoxyk There are a couple of things to try. fminunc would probably do well if started at a different point, where the local quadratic model is better behaved. Also, you would probably find that patternsearch (from the Genetic Algorithm and Direct Search Toolbox) works reliably, and I believe it would work faster than fminsearch. Alan Weiss MATLAB mathematical toolbox documentation Jenny Yin wrote: > I mean the singularity of the covarince matrix of observation vector, > not the state vector, sorry for the mistake. > > > > "Jenny Yin" <jennywwyin(a)gmail.com> wrote in message > <hisurk$mpj$1(a)fred.mathworks.com>... >> Hi, everyone, >> >> I have some problem on the optimization during the maximun likelihood >> estimation for state-space model via Kalman filter. >> >> There are around 100 parameters to estimate. >> 1. fminsearch works, even it is very slow. >> 2. fminunc, cannot work. It always stops by the error of the >> covariance matrix of state vector is almost singular. >> >> Since the number of parameters is large, I am worrying about whether >> fminsearch can search the nice results. Is anyone who also have met >> the problem of the singularity problem of state vector covariance matrix? >> >> why fminsearch does not stop by the error of of the covariance matrix >> of state vector is almost singular? >> >> Thanks very much. |