Interpolation overhaul: multiple outputs in same structure

mnwhite commented 8 years ago

This is pretty closely linked with the other "interpolation overhaul" issue.

As is, a HARKinterpolator has a codomain of R, so that an instance must be created for each function output (e.g. a consumption function, a value function, a medical spending function, etc). These instances share an interpolation node structure, but this structure must be searched independently for each instance (e.g. a lookup for c(x_0), a lookup for v(x_0), and a lookup for m(x_0)). This is somewhat costly in the current 1D applications, and will be horribly inefficient for ND methods (which are the models most likely to want multiple values evaluated at the same points).

The interpolation framework needs a complete overhaul to allow a call to HARKinterpolator to return multiple outputs (e.g. getting c(x_0), v(x_0), and m(x_0) with a single lookup or search). By default, all outputs of an interpolator are returned, but the user can request less.

Open Q: format for specifying which outputs are returned? User must keep track of which output is in which "layer" (e.g. c is 0, v is 1, etc), or apply text labels ('c', 'v', etc).

mnwhite commented 8 years ago

This is a rather big item, and it's not actually clear that it can or should be done. We recommend that outside contributors stay away from this until the HARK team decides how to proceed.

mnwhite commented 6 years ago

Jeppe Druedahl has a methodological working paper (NEGM) that exploits something like this. In his case, he's explicitly working with multiple control variables. Now that HARK does have multiple control variable models, this item is probably worth coming back to.

sbenthall commented 4 years ago

I think Dolo handles this sort of functionality with a Grid construct.

albop commented 4 years ago

I"m not sure where I can reconstruct the whole discussion here. The interpolation logic is done in interpolation.py and works as follow:

you define a d-dimensional grid
you choose some values C on this grid:
- if V is d-dimensional then it represents the values of a scalar function on this grid
- if V is d+1-dimensional and last dimension is n_x, then it represents a vector valued function in R^{n_x}
in both cases, you can interpolate these values between the grid points, that is any vector of R^d or a vector of them In Dolo, in the code logic, all states or controls, are assumed to be vectors. A decision rule (function) object always represents a mapping R^{n_s}->R^{n_x}.

llorracc commented 4 years ago

Interesting.

So, one question.

Think about a standard model (say, a consumption model with uncertainty) where we know that in principle the solution is continuously differentiable everywhere.

Then to construct a good interpolation for points that are not on the grid, we might want to use facts like the fact from the theoretical model that the Envelope condition holds:

$v^{'}(m) = u^{'}(c(m))$

and so does its derivative wrt m:

$v^{''}(m) = u''(c(m))c'(m)$

and even the next derivative:

$v^{'''}(m) = u''(c(m))c''(m)+ u'''(c(m))(c'(m))^{2}$

in order to get a good representation of the value function at in-between points.

It is easy to construct all the different functions on the grid of values of $m$, and all of the relations above will hold at every gridpoint.

But is there a way to tell the interpolator to approximate the in-between points using the (unique) polynomial that matches all of these facts on the grid of points? For reasonably smooth problems, this allows the problem to be represented well with a fairly small number of gridpoints.

MridulS commented 4 years ago

Interface with interpolation.py, related issue https://github.com/econ-ark/HARK/issues/424

llorracc commented 4 years ago

@albop,

We have been wanting to move to interpolation.py as our central tool in HARK, but have held off because there are a few places where we need the deriviatives. We see that adding differentiation is on your "near-term to-do" list, and wonder whether that could be prioritized soon so we can go ahead and adopt interpolation.py?

@llorracc

albop commented 4 years ago

Yes

On Mon, Aug 24, 2020, 4:53 PM Christopher Llorracc Carroll < notifications@github.com> wrote:

@albop https://github.com/albop,

We have been wanting to move to interpolation.py as our central tool in HARK, but have held off because there are a few places where we need the deriviatives. We see that adding differentiation is on your "near-term to-do" list, and wonder whether that could be prioritized soon so we can go ahead and adopt interpolation.py?

@llorracc https://github.com/llorracc

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albop commented 4 years ago

@llorracc @mnwhite : I have just merged into the main branch of interpolation.py the ability to computer any combination of derivatives for splines. I also simplified the basic api to make it more complete and consistent. It is documented here : There are still performance issues due to numba development that I haven't fixed yet. Right now it require numba >=0.47 and <=0.50 but I'll remove the upper bound as soon as I understand what's going on. In the meantime you can test it and signal any special need I have probably overlooked.

albop commented 4 years ago

I forgot the link to the relevant page in the doc : here it is https://www.econforge.org/interpolation.py/splines/

albop commented 4 years ago

Re the title of this thread I should mention that interpolation.py supports vector valued functions.

llorracc commented 4 years ago

Awesome!

As far as I am concerned, we can now move "adoption of interpolation.py" from "sometime in the future" to "as soon as we can."

On Mon, Sep 14, 2020 at 9:14 AM Pablo Winant notifications@github.com wrote:

Re the title of this thread I should mention that interpolation.py supports vector valued functions.

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sbenthall commented 3 years ago

Is this related to #1011 ?

It would be nice if there was just a single multi-dimensional interpolator class. I bet that's possible with Python language tricks and Scipy support.

albop commented 3 years ago

I didn't follow the other thread closely, but my take is still that implementing hermite filtering in interpolation.py is a better way to go, at least, performance-wise than wrapping scipy.interpolate cubic-hermite. Only missing part in interpolation.py is a prefiltering routine taking derivatives as argument. It is not super complicated to implement though it requires to write down a few equations.

Le jeu. 27 mai 2021 à 17:41, Sebastian Benthall @.***> a écrit :

Is this related to #1011 https://github.com/econ-ark/HARK/pull/1011 ?

It would be nice if there was just a single multi-dimensional interpolator class. I bet that's possible with Python language tricks and Scipy support.

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mnwhite commented 4 months ago

Closing this issue because we have (some) integration with Pablo's interpolation.py.

econ-ark / HARK

Interpolation overhaul: multiple outputs in same structure #14