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by JohnLeM
Today, 10:32 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 148
Views: 11768

Re: Universal Approximation theorem

Speak of the devil Sobolev training , train the function and its derivatives. That sound relevant. http://mcneela.github.io/machine_learning/2018/02/19/A-Synopsis-Of-DeepMinds-Sobolev-Training-Of-Neural-Networks.html Sounds like a logical step. Sobolev spaces are the bread and butter of advanced nu...
by JohnLeM
Today, 9:00 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 148
Views: 11768

Re: Universal Approximation theorem

My one-penny guess : take any square-integrable function [$]\phi[$], and call the convolution [$]\varphi = \phi \ast \phi[$] an activation function. Then you can use it in Cybenko Theorem. That's already a lot of examples. But there exists much more examples. In fact, give me any probability measure...
by JohnLeM
Yesterday, 2:12 pm
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 148
Views: 11768

Re: Universal Approximation theorem

Homework for Cuch: this recent paper (jun 2017) is getting many people excited, it proposes SELU (instead of RELU, sigmoid). It works really well, I'm seeing very stable learning with deep networks. You can go straight to the appendix with the proofs (page 9 ..100) that motivate why it should work ...
by JohnLeM
Yesterday, 2:01 pm
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 148
Views: 11768

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
Yesterday, 1:46 pm
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 148
Views: 11768

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
Yesterday, 12:25 pm
Forum: Technical Forum
Topic: Why is Bellman Equation solved by backwards?
Replies: 26
Views: 2090

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
Yesterday, 11:51 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 148
Views: 11768

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
Yesterday, 11:03 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 148
Views: 11768

Re: Universal Approximation theorem

Yes. dduffy AT datasim DOT nl
ok thanks
Sent !
by JohnLeM
Yesterday, 10:22 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 148
Views: 11768

Re: Universal Approximation theorem

Yes. dduffy AT datasim DOT nl
ok thanks
by JohnLeM
Yesterday, 10:19 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 148
Views: 11768

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
Yesterday, 10:01 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 148
Views: 11768

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
Yesterday, 9:57 am
Forum: Numerical Methods Forum
Topic: Universal Approximation theorem
Replies: 148
Views: 11768

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: 657

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: 657

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: 657

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...
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