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by JohnLeM
October 15th, 2019, 2:01 pm
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12689

Re: Universal Approximation theorem

Cuch, you complain that there's not enough maths in ML. Is this paper sufficiently mathy for you?  https://arxiv.org/pdf/1908.10828.pdf I tried again to read this paper. Here is the Main Theorem , but I am afraid that an entire life would not be enough to understand it...I wonder if they are using ...
by JohnLeM
October 15th, 2019, 1:46 pm
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12689

Re: Universal Approximation theorem

Cuch, you complain that there's not enough maths in ML. Is this paper sufficiently mathy for you?  https://arxiv.org/pdf/1908.10828.pdf I tried again to read this paper. Here is the Main Theorem , but I am afraid that an entire life would not be enough to understand it...I wonder if they are using ...
by JohnLeM
October 15th, 2019, 12:25 pm
Forum: Technical Forum
Topic: Why is Bellman Equation solved by backwards?
Replies: 32
Views: 2318

Re: Why is Bellman Equation solved by backwards?

Thank you all, but I what I cannot understand is the real reason that Bellman equation is ususally solved by backwards. Can any one give an exmaple in which both intitial and terminal conditions are well defined, but the Bellman equation can only be solved by backwards? I think there are tons of ex...
by JohnLeM
October 15th, 2019, 11:51 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12689

Re: Universal Approximation theorem

Cuch, you complain that there's not enough maths in ML. Is this paper sufficiently mathy for you?  https://arxiv.org/pdf/1908.10828.pdf I tried again to read this paper. Here is the Main Theorem , but I am afraid that an entire life would not be enough to understand it...I wonder if they are using ...
by JohnLeM
October 15th, 2019, 11:03 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12689

Re: Universal Approximation theorem

Yes. dduffy AT datasim DOT nl
ok thanks
Sent !
by JohnLeM
October 15th, 2019, 10:22 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12689

Re: Universal Approximation theorem

Yes. dduffy AT datasim DOT nl
ok thanks
by JohnLeM
October 15th, 2019, 10:19 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12689

Re: Universal Approximation theorem

oh wait, a function you don't even know? We all know that it doesn't make sense. That's one possible weltanschauung , that does not produce interesting cases.  In mathematics, you scope the class of problems you want to model, e.g. Sobolev spaces, Fourier etc. and then investigate which activation ...
by JohnLeM
October 15th, 2019, 10:01 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12689

Re: Universal Approximation theorem

The mathematical precision in Cybenko 1988 has been superceded/improved on here http://www2.math.technion.ac.il/~pinkus/papers/acta.pdf In particular, Theorems 3.1, 4.1, 5.1, 6.2, 6.7,  Proposition 3.3.  Seems like ML' maths is stuck in the 80s. The mathematical subtleties surrounding activation fu...
by JohnLeM
October 15th, 2019, 9:57 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12689

Re: Universal Approximation theorem

Cuch, you complain that there's not enough maths in ML. Is this paper sufficiently mathy for you? https://arxiv.org/pdf/1908.10828.pdf
I don't buy this paper !! Try to read it, you will understand what I mean :)
by JohnLeM
October 9th, 2019, 6:33 am
Forum: Book And Research Paper Forum
Topic: MSc Theses on Machine Learning and Computational Finance
Replies: 9
Views: 698

Re: MSc Theses on Machine Learning and Computational Finance

JohnlL.eM, Adding to your list of questions, I wrote this a while back @Cuchullain, for me, Gradient Descent is a swiss-knife methods. Always produce results, but can be stuck in local minima. Local minima, if it is lucky, That's the least of your worries. GD has a whole lot of issues: Off the top ...
by JohnLeM
October 9th, 2019, 6:24 am
Forum: Book And Research Paper Forum
Topic: MSc Theses on Machine Learning and Computational Finance
Replies: 9
Views: 698

Re: MSc Theses on Machine Learning and Computational Finance

6.  but nobody can tell if the resulting algorithm is performant or not. Not sure if I completely agree --> cross-validation and 5-folds were used. I don't contest the numerical figures, you did a great job to guarantee them with this K-fold method, as well as teaching me the existence of this meth...
by JohnLeM
October 8th, 2019, 12:32 pm
Forum: Book And Research Paper Forum
Topic: MSc Theses on Machine Learning and Computational Finance
Replies: 9
Views: 698

Re: MSc Theses on Machine Learning and Computational Finance

6.  but nobody can tell if the resulting algorithm is performant or not. Not sure if I completely agree --> cross-validation and 5-folds were used. I don't contest the numerical figures, you did a great job to guarantee them with this K-fold method, as well as teaching me the existence of this meth...
by JohnLeM
October 8th, 2019, 7:57 am
Forum: Book And Research Paper Forum
Topic: MSc Theses on Machine Learning and Computational Finance
Replies: 9
Views: 698

Re: MSc Theses on Machine Learning and Computational Finance

Cuchullain, Hello. I have read the first one,  Dalvir Mandara Artificial Neural Networks for Black-Scholes Option Pricing and Prediction of Implied Volatility for the SABR Stochastic Volatility Model First congratulations to the student and their supervisor, this is a nice work for a MsC. It is very...
by JohnLeM
October 7th, 2019, 11:23 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 178
Views: 12689

Re: Universal Approximation theorem

Yes, I will post this thesis in a few days. And a number of your questions will hopefully be resolved, including some good tips from Itkin's paper. Regarding your remarks on error estimation, cross-validation is the way. The 1st student did BS/SABR and the other did BS/Heston (not public). You can ...
by JohnLeM
October 7th, 2019, 10:38 am
Forum: Numerical Methods Forum
Topic: How to determine basket of stocks in pair trading.
Replies: 2
Views: 381

Re: How to determine basket of stocks in pair trading.

Hello,  I am not sure that this helps for pair-trading, but I did some related works in a more complex situation : find the best basket for Autocalls, based over some criteria as coupon values. You can have a look here for some resuts, where we tested any combinations of Autocalls written on any bas...
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