Re: Constrained non linear regression using ML

[Corrado]

Dear Fredrik, dear Octave friends,

First of all thanks for coming back to me.

I have 40,000 vectors of observations: {y,p1,p2,p3,p4,p5 ..... pn}_j  
where j spans over the 40,000 vectors (that is from 1 to 40,000).

The k={k0,k1,k2,k3,k4,.....,kn} is the vector of parameters to be 
determined by fitting.

I believe you are right, in machine lerning language, the 
{1,p1,p2,....,pn} vector would be called the input.

y is the response variable.

PS: If you build a frequency histogram from the y_j, the distribution 
looks approximately beta, but fails tests because of the number of 
points ....

Best,

Fredrik Lingvall wrote:
> On 03/16/10 20:01, Corrado wrote:
>   
> > Dear Octave users,
> >
> > I have to fit the non linear regression:
> >
> > y~1-exp(-(k0+k1*p1+k2*p2+ .... +kn*pn))
> >
> > where ki>=0 for each i in [1 .... n] and pi are on R+.
> >
> > I am using, at the moment, nls, but I would rather use a Maximum
> > Likelhood based algorithm. The error is not necessarily normally
> > distributed.
> >
> > y is approximately beta distributed, and the volume of data is medium to
> > large (the y,pi may have ~ 40,000 elements).
> >
> > Any suggestion?
> >
> > Regards
> >   
> >     
> Corrado,
>
> Can you tell us a little more about your problem?
>
> As I understand it you have a model,
>
> y = 1 - exp(-k'*p) + e
>
> where k = [k_0 k_1 ... k_n]' and p = [1 p_1 p_2 ... p_n]' and where y is
> your data vector, p is your "input signal" and k is the parameter vector
> of your model. Have I understood you correctly?
>
> /Fredrik 
>   


--
Corrado Topi
PhD Researcher
Global Climate Change and Biodiversity
Area 18,Department of Biology
University of York, York, YO10 5YW, UK
Phone: + 44 (0) 1904 328645, E-mail: address@hidden