Forums  > Pricing & Modelling  > stupidity and parametric forms  
     
Page 1 of 1
Display using:  

Strange


Total Posts: 1557
Joined: Jun 2004
 
Posted: 2019-03-23 17:18
Please don't laugh. I am trying to convert an "if - then" statement into a parametric form that would allow for a smoothed transition between states. It's probably something fairly simple, but I am completely blanking (seems to happen more and more lately). Here is the gist of the problem in it's current state:

A, B are continuous variables
Z is threshold
X is scale value

so I have the following statement in the code:

Q = (X if A > 0 and B > Z else 1) x (X if A less than 0 and B less than Z else 1)

Obviously, the above not a very optimal way of doing it, since Q changes from 1 to X discretely and I want to avoid that type of behavior. Ideally, it would be some sort of a continuous 2-d function that can be tweaked from a completely discrete state above to a more continuous form via several variables. A simple version is to make a X a linear function of B and keep the conditions above, but that does not get rid of discontinuity wrt to A.

Eher Ende mit Schrecken als Schrecken ohne Ende

gaj


Total Posts: 44
Joined: Apr 2018
 
Posted: 2019-03-23 17:47
The last part of the formula for Q is cut off. Anyway the first part can be written as

(A > 0) * (B > Z) * (X-1) + 1

Then you can replace the binary variables with sigmoid:

sigmoid(A) * sigmoid(B - Z) * (X - 1) + 1


Strange


Total Posts: 1557
Joined: Jun 2004
 
Posted: 2019-03-23 17:57
Thanks!

corrected it - it's essentially the same statement in reverse (if both A and B are less than zero and Z respectively).

The sigmoid version is interesting (indeed it removes the discontinuity with respect to both B and A) and I I am guessing I can extend it to have continuous decay from 1 instead of X

sigmoid(A) * sigmoid(B - Z) * ( decay(B) - 1) + 1

Eher Ende mit Schrecken als Schrecken ohne Ende

nikol


Total Posts: 729
Joined: Jun 2005
 
Posted: 2019-03-23 21:57
This algebra is developed in Fuzzy logic

TonyC
Nuclear Energy Trader

Total Posts: 1295
Joined: May 2004
 
Posted: 2019-03-24 04:51
the "sigmoid' function that is used in the backpropagation algorithm of neural networks is a very smooth transition between 0 and 1 ... and good explanations are in every introductory neural network machine learning text.


and if you think it's weird that I'm replying at a quarter of midnight on a Saturday in New York, it's even weirder that I'm actually replying at a quarter of 5 a.m. on a Sunday in Vernazza

flaneur/boulevardier/remittance man/energy trader

TonyC
Nuclear Energy Trader

Total Posts: 1295
Joined: May 2004
 
Posted: 2019-03-24 04:52
oh wait, you already mentioned sigmoid functions, which means my prior reply is superfluous and that I am an idiot ...

... or at least I'm an idiot 5 a.m. in the morning

flaneur/boulevardier/remittance man/energy trader

nikol


Total Posts: 729
Joined: Jun 2005
 
Posted: 2019-03-24 10:51
TonyC:
that's a wide-spread phenomenon - stupidity with positive feedback. ))
Previous Thread :: Next Thread 
Page 1 of 1