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Re: 8 independent variable curve fitting.


From: Juan Pablo Carbajal
Subject: Re: 8 independent variable curve fitting.
Date: Tue, 2 Jun 2015 17:14:24 +0200

On Tue, Jun 2, 2015 at 5:06 PM, Doug Stewart <address@hidden> wrote:
>
> Hi Juan, thanks for your input.
> see below
>
> On Tue, Jun 2, 2015 at 3:21 AM, Juan Pablo Carbajal <address@hidden> wrote:
>>
>> On Mon, Jun 1, 2015 at 10:41 PM, Doug Stewart <address@hidden> wrote:
>> > I have a problem that has 8 independent variables and one output.
>> > We have taken 400 samples and now want to fit an equation to these data
>> > points.
>> > Some of the relation ships are nonlinear.
>> > Which octave function should I use to do the curve fitting?
>> >
>> >
>> > --
>> > DAS
>> >
>> >
>> > _______________________________________________
>> > Help-octave mailing list
>> > address@hidden
>> > https://lists.gnu.org/mailman/listinfo/help-octave
>> >
>>
>> Doug, depending on the complexity of those relationships 400 samples
>> could be too little.
>> Can you compress the input space? (PCA or other embedding)
>> You can try kernel regression on your data using either gp_regress.
>> There is also octgpr (http://octave.sourceforge.net/octgpr/) package
>
>
> I tried
> pkg install -forge octgpr
> gpr_predict.cc:26:30: error: ‘Octave_map’ does not name atype
>  octave_value getfield (const Octave_map& map, const char
>
> So octgpr does not install with octave 4.0.0
>
>
>
>>
>> or STK (http://kriging.sourceforge.net/htmldoc/). I haven't used any
>> of them so if you have comments or question it would be a nice
>> opportunity for me to take a look.
>>
>> Finally there is gpml, it should be easy to use (but probably hard to
>> master) http://www.gaussianprocess.org/gpml/code/matlab/doc/
>
>
> Again thanks for your's and others inputs.
>
> I played with leasqr  and came to a much better understanding of multi 
> variable regression.
> If you don't have enough data points then there are many equations  that will 
> fit the  8d data.
> Also if you don't have the right data ponits then there are many equ. that 
> fit.
> By many eq. I mean the same relationships but different coefficients.
> Think of only sampling the 8d space in one plain.
>
>  So we are looking at Taguchi methods of design of experiments, to decide on 
> a set of measurement points, that  minimally cover the region.
>
> Then use these point with leasqr  or other functions to do the curve fitting.
>
> Thanks again.
> Doug
>
>
>
> --
> DAS
>

Doug, Gaussian Processes (aka Kriging) are methods designed to fit
relations with sparse data. Do try them, either the simple gp_regress
or the other packages.

A 9d surface can be tricky to fit. Try embeddings (dimensionality
reduction, linear and nonlinear) to see if the actual structure lie in
a lower dimension.



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