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Amin
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Re: If you are bored with Deep Networks

November 24th, 2018, 5:01 pm

Here is an interesting paper for friends relevant to this thread. An Artificial Neural Network Representation of the SABR Stochastic Volatility Model by William Mcghee.
 
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Cuchulainn
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Re: If you are bored with Deep Networks

November 26th, 2018, 8:55 am

Here is an interesting paper for friends relevant to this thread. An Artificial Neural Network Representation of the SABR Stochastic Volatility Model by William Mcghee.
Unfortunately, the run-time performance of both ANN (3 hours) and FDM(20 days!) are disappointing. Must be chalking up a yuge electricity bill?
With 'traditional' FDM popular consensus says it can be done in 15 minutes.

IMO, I am becoming more and more convinced that NN and PDE don't mix, really. Maybe that 'Eureka moment' will come...

For this kind of problem, I would expect Lewis/Papadoupolis FDM to be a good baseline.

https://arxiv.org/abs/1801.06141
 
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FaridMoussaoui
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Re: If you are bored with Deep Networks

November 26th, 2018, 11:38 am

I just read the paper per diagonals :)

Isn't the 475 hours for solving 300k FDM as the goal was to generate 3 millions volatilities (10 at a time)?
 
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Cuchulainn
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Re: If you are bored with Deep Networks

November 29th, 2018, 10:36 pm

Update 
Section 4.3 

1. 1st and 2nd derivatives are not calculated using NN directly (by AD, whatever)... no reason given why. I suspect difficult to implement etc.
2. Instead author uses cubic splines and its derivatives. Something I have done some work on while back for FEM.

OK then, mathematically, each time you differentiate a spline it gets worser and worser (overshoot) as I discuss in mathematical detail and in numbers in the recent 2nd edition of my C++ book. 

Two screen shoots coming up.
Last edited by Cuchulainn on December 1st, 2018, 11:05 pm, edited 8 times in total.
 
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Cuchulainn
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Re: If you are bored with Deep Networks

November 29th, 2018, 10:39 pm

Image
 
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Cuchulainn
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Re: If you are bored with Deep Networks

November 29th, 2018, 10:42 pm

Thanks to @billy7 who asked me to clarify the small discrepancies (and my precise answer).

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ISayMoo
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Re: If you are bored with Deep Networks

December 3rd, 2018, 11:00 am

Deep networks fold better!

It's actually a great success for medicine and biology.
 
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FaridMoussaoui
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Re: If you are bored with Deep Networks

December 3rd, 2018, 11:21 am

You can have a look to their NN library, derived from TensorFlow on github.

https://github.com/deepmind/sonnet

Or visit their shared libraries at https://github.com/deepmind
 
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ISayMoo
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Re: If you are bored with Deep Networks

December 3rd, 2018, 11:23 am

I know their libraries pretty well ;-)
 
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Cuchulainn
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Re: If you are bored with Deep Networks

December 3rd, 2018, 6:50 pm

I know their libraries pretty well ;-)
Are they Bayesian or non-Bayesian? Probably black boxes..
Of course, gemome data is not finance data.
 
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katastrofa
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Re: If you are bored with Deep Networks

December 3rd, 2018, 8:50 pm

That's nothing impressive. They used the full power of Google data centres and solved it brute force. That's why emails worked so slowly. (That was, obviously - ?, a joke. I don't know what resources they used compared to their competition, but that's something that should be taken into account into.)
Last edited by katastrofa on December 4th, 2018, 6:55 am, edited 1 time in total.
 
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FaridMoussaoui
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Re: If you are bored with Deep Networks

December 4th, 2018, 12:25 am

Are they Bayesian or non-Bayesian? Probably black boxes..
Of course, gemome data is not finance data.
They are open source, written in python. They moved from Torch7 (another NN open source project) to TensorFlow (by Google).
 
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Cuchulainn
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Re: If you are bored with Deep Networks

December 4th, 2018, 8:30 am

Are they Bayesian or non-Bayesian? Probably black boxes..
Of course, gemome data is not finance data.
They are open source, written in python. They moved from Torch7 (another NN open source project) to TensorFlow (by Google).
So, NNs can describe but cannot explain. If so, where's the AI part?
 
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katastrofa
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Re: If you are bored with Deep Networks

December 4th, 2018, 1:11 pm

The "Why?" a.k.a. deductive nomological model of reasoning from classical physics doesn't apply to statistics. It's full of hindsight bias.
 
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Cuchulainn
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Re: If you are bored with Deep Networks

December 5th, 2018, 1:11 pm

Let's take a step backwards.

Gradient descent methods as we know and love them are nothing more than Euler's (ugh) method applied to ODEs (aka gradient system):

[$]dx/dt = - grad f(x) = -\nabla f(x)[$] where [$]f[$] is the function to be minimised.

The local minima of [$]f[$] are the critical points of this ODE system. (Poincaré-Lyapunov-Bendixson theory).

I have tried it on a number of benchmark unconstrained optimisation problem and solved using C++ boost::odeint without any of the infamous learning rate fudges.


We use more robust ODE solvers than Euler which means that we don't get the well-documented issues with GD methods.

For SGD, you might ask how is the discrete equivalent of an SDE.
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