Finding approximation function which depend on 8-parameters

Question

I have a lot entries of data, each entry consists of 8 (eight) numbers.

For each entry I know "fitness score" (i.e. how "good" this entry).

And, I want to build/find approximation function ("fitness score" dependent on those 8 parameters). Not only mathematical representation of this function is ok for me, but any implementation (like NN) wich will give me plausible "fitness score" for arbitrary (new) entry.

I tried Neural Networks(Encog library) and Genetic approach (Watchmaker library). Second approach gave me much better results than NN. However, I represent approximation function as sum of eight "a * pow(x, b)" components, where "a" and "b" are mutated by GA and "x" is parameter of data entry. Despite on fact that I have some positive results with help of GA, obviously, this is not the best approach.

So, the questions are : what are the ways to improve searching approximation function in my case? Are there any other methods than NN and GA ?

Thanks.

Answer 1

There are dozens of such methods, as your problem is simply regression. Just google for such methods, this is really to broad to even list it here. Among other, you have:

• k-nn regression
• regression trees
• support vector regression
• ridge regression
• ...

Apart from other methods - remember, that even neural networks alone are very complex objects, with many parameters and formulas, so in order to get good results you need to spend much time on tuning them.