may help understand, why you think your method coefficients are well reconstructed

[Sandy4321]

may help understand, why you think your method coefficients from fig 4 are reconstructed well when they are still very different from original from fig 1

[vene]

4 is clearly better at identifying the support, although it gets the sign wrong for some of the coefficients. In any case this is a synthetic example, attempting to reproduce a figure from the cited paper: please refer to the paper itself (http://www.jmlr.org/proceedings/papers/v51/figueiredo16.pdf) for more information.

[Sandy4321]

yes they do have perfect coefficients reconstruction

but in your case also amplitude and also sings are the problem do you know another OWL implementations to try?

[vene]

I'm not aware of any others.

The difference may come from experimental conditions rather than implementation issues as you are suggesting :)

On Wed, Aug 7, 2019, 20:48 Sandy4321 [email protected] wrote:

yes they do have perfect coefficients reconstruction

but in your case also amplitude and also sings are the problem do you know another OWL implementations to try?

[image: image] https://user-images.githubusercontent.com/11426119/62653043-bbadb800-b92a-11e9-86d5-b05e65b64ffe.png

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[Sandy4321]

so what can be done to make your code run correctly?

[vene]

What is incorrect? Can you submit a failing test?

I believe the code runs correctly.

On Wed, Aug 7, 2019, 21:11 Sandy4321 [email protected] wrote:

so what can be done to make your code run correctly?

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[Sandy4321]

but original true coefficients around 25 samples have negative sign and amplitude of 0.2 (figure1) then your code gives positive and negative signs and amplitude is 0.050 (figure4) ?

[vene]

Hi,

All of these conversations are a bit exhausting.

Like I said above, I attribute this recovery error to be due to to experimental setup and hyperparameters, not to any algorithmic bugs. This is confirmed by the fact that the code passes the unit test included.

If you can construct an actual example where the provided implementation is wrong (i.e., when it incorrectly computes the proximal operator), that is indeed an issue that should be investigated, and I encourage you to submit such issues (for example, including a failing test case where the returned solution has suboptimal objective value, or similar.)

The example is an end-to-end demo of noisy recovery, which I would not expect to yield exact recovery (especially given the poor result of lasso). If I should expect otherwise, I must be missing something, and I welcome a (rigorous) explanation.

On Wed, Aug 7, 2019, 21:20 Sandy4321 [email protected] wrote:

but original true coefficients around 25 samples have negative sign and amplitude of 0.2 (figure1) then your code gives positive and negative signs and amplitude is 0.050 (figure4) ?

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[Sandy4321]

I see thanks I assumed that as in paper Figure 1: Toy example illustrating the qualitatively different behaviour of OWL and LASSO perfect reconstruction possible? as written in paper Of course, you are ware about this difference, therefore it would be very interesting how you explain this difference. Do they cheating by claiming , that they can achieve perfect reconstruction?
as they wrote:"while OWL successfully recovers its structure"

We conclude this section with a simple toy example (Fig. 1)
illustrating the qualitatively different behaviour of OWL
and LASSO regularization. In this example, p = 100,
n = 10, and x
? has 20 non-zero components in 2 groups of
size 10, with the corresponding columns of A being highly
correlated. Clearly, n = 10 is insufficient to allow LASSO
to recover x
?
, which is 20-sparse, while OWL successfully
recovers its structure.

[vene]

They may be generating the array A differently, or use a different noise level, or use different regularization strength. I am not claiming they are cheating. If you want to look into this further, you are welcome to play with the code and adjust things in the example.

I'm not discounting the possibility of a bug right now, but I am not working on this. If your investigations reveal bugs, please file an issue.

On Wed, Aug 7, 2019, 21:56 Sandy4321 [email protected] wrote:

I see thanks I assumed that as in paper Figure 1: Toy example illustrating the qualitatively different behaviour of OWL and LASSO perfect reconstruction possible? as written in paper Of course, you are ware about this difference, therefore it would be very interesting how you explain this difference. Do they cheating by claiming , that they can achieve perfect reconstruction? as they wrote:"while OWL successfully recovers its structure"

We conclude this section with a simple toy example (Fig. 1) illustrating the qualitatively different behaviour of OWL and LASSO regularization. In this example, p = 100, n = 10, and x ? has 20 non-zero components in 2 groups of size 10, with the corresponding columns of A being highly correlated. Clearly, n = 10 is insufficient to allow LASSO to recover x ? , which is 20-sparse, while OWL successfully recovers its structure.

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[Sandy4321]

as you wrote

I attribute this recovery error to be due to to
experimental setup and hyperparameters, not to any algorithmic bugs

it is axactly what I asked above

so what can be done to make your code run correctly?

Then answer is: "try tune hyperparameters", I am right?

[vene]

Well, it seems like your question was "how can I make pyowl return the correct coefficients on the toy problem in the example", not "making the code run correctly" (the latter implies that something is incorrect)

In this case yes, consider changing the hyperparameters. And keep in mind that what works on a simulated example might not work the same way on real data.

On Wed, Aug 7, 2019, 22:05 Sandy4321 [email protected] wrote:

as you wrote

I attribute this recovery error to be due to to experimental setup and hyperparameters, not to any algorithmic bugs

it is axactly what I asked above

so what can be done to make your code run correctly?

Then answer is: "try tune hyperparameters", I am right?

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[Sandy4321]

And keep in mind that what works on a simulated example might not work the same way on real data. But in paper they show simulation results? By the way, is it suitable for logistics regression?