Re: Eureqa - Can the following function be simplified somehow

[Michael Schmidt]

I can't think of a good way to do this currently. We might add support for group-wise coefficients at some point that could do this. 

I'm not sure if this is useful here, but there is a correlation coefficient error metric you can choose. This would ignore differences in offset (and scale) and just focus on shape.

Another trick you might use to turn a single coefficient into many is to use a periodic function, for example you might try:

y = f0()*sin( f1()*par + f2() ) + f3()*x

I'm not certain how well this would work though, especially with 60 different offsets, but might be worth a shot.

Michael

On Wed, May 29, 2013 at 8:59 AM, <bene...@gbg.bg> wrote:

Lets say I have the following function:

f(x) = C + a*x

Real function has many more parameters, but that's irrelevant for this topic.
The data I have looks like:
par      x        f(x)
1        2         204
1        3         206
1        4         208
2        2         104
2        3         106
2        4         108
3        2         504
3        3         506
3        4         508

In this case the solution would be f(x) = C + 2*x, where C[3] = [200, 100, 500]

The way I simulate this currently is with the following syntax

f(x) = if ( par=1, f0() , if ( par=2, f1(), f2() ) ) + f3()*x

The problem is that par ranges between 1-60. Writing that with nested if - then - else modules would be unreadable. Is there a way to do the same without 60 nested 'if's?

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[benedict gbg]

Well, no, the trick didn't work unfortunately. What I'm experiencing though is Eureqa slowing down to a crawl and getting quite inefficient. Here's one of the functions I'm trying to solve:

wi = if(tr = 1, f11(), if(tr = 2, f12(), if(tr = 3, f13(), if(tr = 4, f14(), if(tr = 5, f15(), if(tr = 6, f16(), if(tr = 7, f17(), if(tr = 8, f18(), if(tr = 9, f19(), if(tr = 10, f20(), if(tr = 11, f21(), if(tr = 12, f22(), if(tr = 13, f23(), if(tr = 14, f24(), if(tr = 15, f25(), if(tr = 16, f26(), if(tr = 17, f27(), if(tr = 18, f28(), if(tr = 19, f29(), f30()))))))))))))))))))) + if(tr = 1, f111(), if(tr = 2, f112(), if(tr = 3, f113(), if(tr = 4, f114(), if(tr = 5, f115(), if(tr = 6, f116(), if(tr = 7, f117(), if(tr = 8, f118(), if(tr = 9, f119(), if(tr = 10, f120(), if(tr = 11, f121(), if(tr = 12, f122(), if(tr = 13, f123(), if(tr = 14, f124(), if(tr = 15, f125(), if(tr = 16, f126(), if(tr = 17, f127(), if(tr = 18, f128(), if(tr = 19, f129(), f130())))))))))))))))))))*ta + f2()*l1 + f3()*l3 + f4()*l4 + f5()*l5 + f6()*s1 + f7()*s3 + f8()*s4 + f9()*s5

which in normal terms would look like
wi = A[tr] + B[tr]*ta + f2()*l1 + f3()*l3 + f4()*l4 + f5()*l5 + f6()*s1 + f7()*s3 + f8()*s4 + f9()*s5, where tr goes from 1 to 20.

On a dual core cpu this ends up with 2-3 generations per second, understandably getting a result takes forever. What's more, the system doesn't realize which values it needs to adjust and seemingly just randomly changes all of them till it achieves a result with lower error. For example if I've got a result with a minimal margin of error and I add more data for tr 20, Eureqa should only change the value of f30() and f130(), but instead it changes everything, losing accuracy on other data sets.

I don't know, maybe I'm using the wrong tool for solving my problem, but I haven't found one yet. Ignoring this issue Eureqa is an amazing piece of software and it has helped me greatly so far.