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Re: 8 independent variable curve fitting.


From: Doug Stewart
Subject: Re: 8 independent variable curve fitting.
Date: Thu, 4 Jun 2015 10:37:37 -0400



On Tue, Jun 2, 2015 at 2:01 PM, Juan Pablo Carbajal <address@hidden> wrote:
On Tue, Jun 2, 2015 at 5:52 PM, Doug Stewart <address@hidden> wrote:
>
>
> On Tue, Jun 2, 2015 at 11:14 AM, Juan Pablo Carbajal <address@hidden>
> wrote:
>>
>> 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.
>
>
> kriging
> Would you please point me to an example  of Kriging, where I can see it
> working.
>
> --
> DAS
>
check

demo gp_regress

and

http://stats.stackexchange.com/questions/8907/how-do-i-use-the-gpml-package-for-multi-dimensional-input

for GPML

If you know the formula you want to fit to the data then any
optimization function will work. Use the packages in octave or try
cmas if you think dimension is an issue.


Thanks again for your Ideas and help

To help me understand how to use leasqr I have made up a demo.
See the attached file.
This file has more in it than just a demo of leasqr. It has comments about the general idea of multi-variable regression.

I think it should be adapted for a demo of ???? (leasqr  , multi-variable regression other functions). The leasqr could be replaced by other curve fitting functions.
Olaf and Jaun  what do you think.
Doug

--
DAS

Attachment: demoleasqr2.m
Description: Text Data


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