Re: bimodal data distribution

[Jaroslav Hajek]

On Mon, Aug 24, 2009 at 3:22 PM, Dupuis<address@hidden> wrote:
>
> Hello,
> I'm trying to extract parameters of a two levels signal described as
> x = N(m1, s1) with probability p
> x = N(m2, s2) with probability (1-p)
> |m1-m2| >> sqrt(s1^2+s2^2)
>
> The operation is similar to MatLab 'gmdistribution', identifying the
> parameters of a mixture of gaussian signals. I implemented the search like
> this:
> 1) use 'statistics' to get a number of indicators;
> 2) [p0, obj0, info0, iter0, nf0, lambda0] = sqp(p , 'bimodal_func', [], [],
> lb,ub); where the vector p contains 5 members: the ratio p defined above,
> m1, s1, m2, s2. Those values were initialised from the indicators: m1 and m3
> are the first and third quartiles, p is set to 0.5, s1 and s2 are sqrt(2) *
> the standard deviation. 'lb' and 'ub' provides constraints on the result: 0
> <= p <= 1; 0<= s1, s2 <= standard deviation, ...
> The bimodal_func is included, I have a few concerns. How could I correct
> them ?
> - data are passed through a global, I didn't see how to pass a supplemental
> parameter through sqp call

Use an anonymous function handle.

> - if I used gradient and hessian, it converges quadratically ... close to
> the minimum, and diverges otherwise. Is is possible with sqp to only use
> hessian close to the minimum, in the convergence region ? A practical
> criterion is that all eigenvalues should be > 0

I don't think so, but it shouldn't be hard to modify. Of course, you
can also augment your hessian yourself to ensure it's positive
semidefinite.

> - I'm also trying to the the Fisher information matrix at the solution. The
> definition on wikipedia is not clear; am I right in postulating that it is
> equal to hessian(p0)/length(x), where p0 is the optimal point ?
>
> Regards
>
> Pascal http://www.nabble.com/file/p25116016/bimodal_func.m bimodal_func.m
> --
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-- 
RNDr. Jaroslav Hajek
computing expert & GNU Octave developer
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz