[SciPy-User] ODR multiresponse multidimensional

[Thomas Howells]

Thanks Matt,

I guess I can start by reformatting this into a single dimensional problem.
I admit that part of my motivation for trying to treat this in full comes
from this quote in the user reference. Here q is the number of responses:
"Note that when q > 1, the responses of a multiresponse orthogonal distance
regression problem cannot simply be treated as q separate observations as
can be done for ordinary least squares when the q responses are
uncorrelated. This is because ODRPACK would then treat the variables
associated with these q observations as unrelated, and thus not constrain
the errors δi in xi to be the same for each of the q occurrences of the ith
observation. The user must therefore indicate to ODRPACK when the
observations are multiresponse, so that ODRPACK can make the appropriate
adjustments to the estimation procedure. (See §2.B.ii, subroutine argument
NQ.)" (Page 7, ODR reference manual)

I can flatten the input variables though, and see if I can get it to work
as a multiresponse problem from that; then it would match the form of the
multiresponse test of the bindings while maintaining the association
between the two response observations.. I think. I should be able to try it
tonight or tomorrow.

P.S. [3,56] was a mistake, it should of course have been [2,56]. Sorry
about that, but it actually doesn't matter much for the posing of the
problem whether there are two or three control variables.

On Tue, Sep 29, 2015 at 3:51 PM Matt Newville <newville at cars.uchicago.edu>
wrote:

> On Tue, Sep 29, 2015 at 9:16 AM, Thomas Howells <t.howells42 at gmail.com>
> wrote:
>
>> On Tue, Sep 29, 2015 at 2:00 PM Robert Kern <robert.kern at gmail.com>
>> wrote:
>>
>>> On Tue, Sep 29, 2015 at 1:43 PM, Thomas Howells <t.howells42 at gmail.com>
>>> wrote:
>>> >
>>> > Dear Pythonistas,
>>> >
>>> > I'm new to the mailing list, my question here is related to scipy's
>>> Orthogonal Distance Regression (ODR) wrapper module. My apologies if you've
>>> received this before, I had some trouble with the mail delivery system.
>>> >
>>> > From perusal of the documentation for the wrapper and the underlying
>>> Fortran routines, it seems the Fortran code can handle a dataset that is
>>> both multiresponse and multidimensional. I have such a dataset that I would
>>> like to try and use the algorithm for; however as far as I can tell the ODR
>>> wrapper doesn't have the machinery to support this usage.
>>>
>>> What do you mean by "both multiresponse and multidimensional"? That the
>>> model is a function `f(x; beta) -> y` such that x and y are each vectors?
>>> Yes, it certainly supports this, and I think the docstrings are pretty
>>> clear about it. What did you read that makes you think otherwise?
>>>
>>> http://docs.scipy.org/doc/scipy/reference/generated/scipy.odr.Model.html
>>>
>>> --
>>> Robert Kern
>>>
>>>
>> I'll elucidate a little more: I have data with two control variables,
>> theta and E, for angle and energy. Each energy is measured at each angle;
>> this makes the data multidimensional (after checking the ODR reference
>> guide, http://docs.scipy.org/doc/external/odrpack_guide.pdf, this is
>> also referred to as multivariate; sorry if this caused confusion).
>>
>> For each combination of theta and E, I get two linked readings (or
>> responses), alpha and beta, that I want to fit simultaneously. This makes
>> it multi-response, as well as multivariate, a situation described on page 6
>> of the ODR reference guide.
>>
>> Ideally I need to find the best fit to all angles & both responses
>> simultaneously to reduce correlation between parameters. The odr.Model
>> object has instructions to handle multidimensional input x, and
>> corresponding multidimensional response y, but not what to do if you have
>> both a multidimensional input and multiresponse.
>>
>
> ORDPACK is a little strange in its support for multi-dimensional data.
> The simplest thing to do (and with the added benefit that it will allow you
> to also use other optimization methods) is to always change the problem to
> a single dimension.    Actually, this is not at all hard, just a slight
> change in perspective.
>
> To be clear, the term multivariate means "more than one variable
> parameter", not the number or shape of the observations.
>
> In fact, for (nearly?) all optimization problems, the algorithms seek  a
> set of values for parameters that make the model most closely match the
> data.  What makes ORDPACK special is its definition of "most closely
> match", not really that it is multi-dimensional.  That's sort of a
> distraction.
>
> The fact that you have two signals (alpha, beta) at each value of (angle,
> energy) is completely unimportant to the fitting algorithm.  It doesn't
> care what the independent variables are, or even that there *are*
> independent variables. It has (only) parameters and the result of the
> objective function.
>
> Within your objective function, you can do anything you want.  You can
> concatenate multiple arrays of data, and/or reduce your multi-dimensional
> arrays of data to one dimension with flatten() or whatever else you need to
> do.  Of course, if you are modelling data, your *model* might care about
> the independent variables, and you'll need to make sure the data and model
> are the same shape and align the observations, so you might have something
> like   [alpha_0, beta_0, alpha_1, beta_1, ....], but (of course) the
> algorithm doesn't care about that  order.
>
> Hope that helps,
>
> --Matt
>
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