Theorical reference

[xmttl]

Hello, Would you have a reference/definition of this iterative Tikhonov regularization ? I mean a mathematical definition, a plublication,...

Your iterative approach works great but I would like to understand it better.

Thank you

[kvasilaky]

Can you tell me who you are or what institutions you are affiliated with?

[xmttl]

Of course, I am Xavier, I am engineer and I work for a little company specialized in acoustics and vibration. An inverse method is sometimes used on vibration studies. I want to show that tikhonov regularisation can improve results in comparison of what is currently done in commercial softwares.

I have done some tests with your inverse method and results look good but I need to understand what I have used.

Do I answer your question? If you want to know more or to exchange about this study, tell me

Le 2016-10-19 17:44, "Katya Vasilaky" notifications@github.com a écrit :

Can you tell me who you are or what institutions you are affiliated with?

— You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub https://github.com/kathrynthegreat/InverseProblem/issues/1#issuecomment-254853519, or mute the thread https://github.com/notifications/unsubscribe-auth/AVwS8U5NqB0YvaByFtpM50mdR-hnTgGMks5q1jr0gaJpZM4KbHyp .

[xmttl]

So, are you OK to give theorical references of your method ?

[kvasilaky]

I'm happy to skype or google hangout some time. My skype id is katkalo07.

[kvasilaky]

Can you tell me who you are or where you work?

On Tue, Oct 25, 2016 at 10:29 AM, K Vasilaky knv4@columbia.edu wrote:

I did. Did you look at the link?

On Tue, Oct 25, 2016 at 10:29 AM, xmttl notifications@github.com wrote:

So, are you OK to give theorical references of your method ?

— You are receiving this because you commented. Reply to this email directly, view it on GitHub https://github.com/kathrynthegreat/InverseProblem/issues/1#issuecomment-256051005, or mute the thread https://github.com/notifications/unsubscribe-auth/ABpaV9WQXKY5EX60FZwJIjYKWbxvMjZ_ks5q3hIzgaJpZM4KbHyp .

Kat ​hryn​ N ​adine​ Vasilaky, PhD International Research Institute http://iri.columbia.edu/contact/staff-directory/kathryn-vasilaky/ Columbia University katyavasilaky.com

Kat ​hryn​ N ​adine​ Vasilaky, PhD International Research Institute http://iri.columbia.edu/contact/staff-directory/kathryn-vasilaky/ Columbia University katyavasilaky.com

[kvasilaky]

I did. Did you look at the link?

On Tue, Oct 25, 2016 at 10:29 AM, xmttl notifications@github.com wrote:

So, are you OK to give theorical references of your method ?

— You are receiving this because you commented. Reply to this email directly, view it on GitHub https://github.com/kathrynthegreat/InverseProblem/issues/1#issuecomment-256051005, or mute the thread https://github.com/notifications/unsubscribe-auth/ABpaV9WQXKY5EX60FZwJIjYKWbxvMjZ_ks5q3hIzgaJpZM4KbHyp .

Kat ​hryn​ N ​adine​ Vasilaky, PhD International Research Institute http://iri.columbia.edu/contact/staff-directory/kathryn-vasilaky/ Columbia University katyavasilaky.com

[kvasilaky]

Hi Xavier: The derivations are here https://academiccommons.columbia.edu/catalog/ac%3A194857

There's an error in one equation number. The updates version should be up soon.

One thing that would be helpful to me is if you can share any data that this was helpful for. I would only use it as a demonstration in seminars and cute you. Would you be able to post the work you speak of on github? Katya

On Oct 19, 2016 5:04 PM, "xmttl" notifications@github.com wrote:

Of course, I am Xavier, I am engineer and I work for a little company specialized in acoustics and vibration. An inverse method is sometimes used on vibration studies. I want to show that tikhonov regularisation can improve results in comparison of what is currently done in commercial softwares.

I have done some tests with your inverse method and results look good but I need to understand what I have used.

Do I answer your question? If you want to know more or to exchange about this study, tell me

Le 2016-10-19 17:44, "Katya Vasilaky" notifications@github.com a écrit :

Can you tell me who you are or what institutions you are affiliated with?

— You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub https://github.com/kathrynthegreat/InverseProblem/issues/1# issuecomment-254853519, or mute the thread https://github.com/notifications/unsubscribe-auth/ AVwS8U5NqB0YvaByFtpM50mdR-hnTgGMks5q1jr0gaJpZM4KbHyp .

— You are receiving this because you commented. Reply to this email directly, view it on GitHub https://github.com/kathrynthegreat/InverseProblem/issues/1#issuecomment-254940348, or mute the thread https://github.com/notifications/unsubscribe-auth/ABpaV78nuBhOIvypAZ9MMLaC5cJaVfSyks5q1oXagaJpZM4KbHyp .

[xmttl]

My manager agrees to share data. I will select and prepare data but I have to work on some other projects. So, I will send data friday or next week.

Next time I will email you using my profesionnal account.

Best regards, Xavier

2016-10-25 23:57 GMT+02:00 Katya Vasilaky notifications@github.com:

Hi Xavier: The derivations are here https://academiccommons.columbia.edu/catalog/ac%3A194857

There's an error in one equation number. The updates version should be up soon.

One thing that would be helpful to me is if you can share any data that this was helpful for. I would only use it as a demonstration in seminars and cute you. Would you be able to post the work you speak of on github? Katya

On Oct 19, 2016 5:04 PM, "xmttl" notifications@github.com wrote:

Of course, I am Xavier, I am engineer and I work for a little company specialized in acoustics and vibration. An inverse method is sometimes used on vibration studies. I want to show that tikhonov regularisation can improve results in comparison of what is currently done in commercial softwares.

I have done some tests with your inverse method and results look good but I need to understand what I have used.

Do I answer your question? If you want to know more or to exchange about this study, tell me

Le 2016-10-19 17:44, "Katya Vasilaky" notifications@github.com a écrit :

Can you tell me who you are or what institutions you are affiliated with?

— You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub https://github.com/kathrynthegreat/InverseProblem/issues/1# issuecomment-254853519, or mute the thread https://github.com/notifications/unsubscribe-auth/ AVwS8U5NqB0YvaByFtpM50mdR-hnTgGMks5q1jr0gaJpZM4KbHyp .

— You are receiving this because you commented. Reply to this email directly, view it on GitHub https://github.com/kathrynthegreat/InverseProblem/issues/1# issuecomment-254940348, or mute the thread https://github.com/notifications/unsubscribe-auth/ ABpaV78nuBhOIvypAZ9MMLaC5cJaVfSyks5q1oXagaJpZM4KbHyp .

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[vincecr0ft]

Hi Kat, This problem is seen extensively in high energy physics (but we call it unfolding). I'm trying to do some comparisons between our existing software and your package. At a quick glance it seems like this is the method discussed in chapter 6 here but could you confirm? (this might be a nice way of updating both of our standard references on the topic ) Cheers

[kvasilaky]

Hi Vince,

My software will not work for you “as is”. My software is for the standard Tikhonov regularization and in your case it is the general form.

Standard: invert (X’X + hI)x = X’y

General: invert (X’X +hH)x = X’y

In general Tikhonov the identity matrix I is replaced by some smoothing matrix H (your case).

It’s interesting that you guys are estimating the density function by histograms, which is about the least desirable way to estimate a function.

But perhaps there is a reason for it. You could try cubic splines and use Generalized Cross Validation to pick a smoothing parameter. I hear wavelets do even better but I don’t know much about wavelets.

I am working on extending my method to generalized Tikhonov and cubic splines to estimate a smooth f(x), but it’s not nearly ready yet.

All the best,

Katya

On Tue, Oct 10, 2017 at 12:48 PM, Vince Croft notifications@github.com wrote:

Hi Kat, This problem is seen extensively in high energy physics (but we call it unfolding). I'm trying to do some comparisons between our existing software http://hepunx.rl.ac.uk/%7Eadye/software/unfold/RooUnfold.html#phystat2011-RooUnfold and your package. At a quick glance it seems like this is the method discussed in chapter 6 here http://www.ippp.dur.ac.uk/Workshops/02/statistics/proceedings/cowan.ps but could you confirm? (this might be a nice way of updating both of our standard references on the topic ) Cheers

— You are receiving this because you commented. Reply to this email directly, view it on GitHub https://github.com/kathrynthegreat/InverseProblem/issues/1#issuecomment-335587051, or mute the thread https://github.com/notifications/unsubscribe-auth/ABpaV-uLcUN6bzix1iI4tD4OmEIb99_Zks5sq8oSgaJpZM4KbHyp .

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Kat ​hryn​ N ​adine​ Vasilaky, PhD International Research Institute http://iri.columbia.edu/contact/staff-directory/kathryn-vasilaky/ Columbia University katyavasilaky.com

[vincecr0ft]

Hi Katya, indeed almost the entire field of particle physics is built on using histograms.

It's by no means ideal but, nominally, for every single measurement there are usually upwards of 50 seperate parameters that can influence the value, these are either measured elsewhere (and propagated) or simulated (and validated in a separate measurement), so only their effect on the density function is estimated. In addition we often find ourselves trying to estimate parameters from only a handful of events. In both cases (statistically and computationally) it's much easier to deal with a set of weights rather than a continuous ill defined function. Perhaps most notable is the fact that historically, the notion of histograms matches well with the limited resolution of our detectors, and thus all of our statistical tools have adapted thus and this is a difficult idea to change.

Maybe you could enlighten me (or point me to a reference) as to a mathematical reason why a smooth function is more desirable then the discreetness of a histogram in this case?

Currently I'm in the process of re-writing the standard tools such that it's easier to cross-validate different methods (and I'm picking up what I can about the theory slowly as I go...) please let me know if you make progress with the generalised case and hopefully by then I might be in a position to compare to a wide range of examples in HEP and we can discuss further.

[kvasilaky]

Some undesirable histogram properties:

1. The resulting estimate is not smooth.
2. An observation may be closer to an observation in the neighboring bin than it is to points in its own bin.
3. The smoothing parameter in histograms is the bin-width. Bias is proportional to bin-width^2 (low bin-width is good for bias), while variance is proportional to bin-width^(-1) (low bin-width is bad for variance). You need to get the best bin-width.

The attached lectures may shed some light on histograms and splines:

• “Smoothing concepts” http://web.as.uky.edu/statistics/users/pbreheny/621/f10/notes/10-26.pdf has a section on histograms.
• “Kernel density” http://web.as.uky.edu/statistics/users/pbreheny/621/f10/notes/10-28.pdf tells why histograms are not the best way to go.
• “Splines” http://web.as.uky.edu/statistics/users/pbreheny/621/f10/notes/11-23.pdf discusses fitting cubic splines.

On Wed, Oct 18, 2017 at 8:32 AM, Vince Croft notifications@github.com wrote:

Hi Katya, indeed almost the entire field of particle physics is built on using histograms.

It's by no means ideal but, nominally, for every single measurement there are usually upwards of 50 seperate parameters that can influence the value, these are either measured elsewhere (and propagated) or simulated (and validated in a separate measurement), so only their effect on the density function is estimated. In addition we often find ourselves trying to estimate parameters from only a handful of events. In both cases (statistically and computationally) it's much easier to deal with a set of weights rather than a continuous ill defined function. Perhaps most notable is the fact that historically, the notion of histograms matches well with the limited resolution of our detectors, and thus all of our statistical tools have adapted thus and this is a difficult idea to change.

Maybe you could enlighten me (or point me to a reference) as to a mathematical reason why a smooth function is more desirable then the discreetness of a histogram in this case?

Currently I'm in the process of re-writing the standard tools such that it's easier to cross-validate different methods (and I'm picking up what I can about the theory slowly as I go...) please let me know if you make progress with the generalised case and hopefully by then I might be in a position to compare to a wide range of examples in HEP and we can discuss further.

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