0
$\begingroup$

Suppose the value at any point in the space is defined by Y = f(x1, x2 .. xk). For simplicity, we can assume that x takes only binary values. Which means that we have a total of 2^k possible values. I want to find the point in this k-dimensional space such that Y at this point is the highest.

The constraint lies in the cost of calculating Y. Because it is very 'expensive' to calculate Y, I want to do it as infrequently as possible. That being said, I have the ability to measure Y for any point in this k-dimensional space. I'm looking for a way to use only a small subset of values n, where n << 2^k and use it build a prediction model that extrapolates to the entire space

I've been able to do this by starting off with a set of randomly selected n points and using them to construct a regression tree. The prediction error is acceptable. But the size of n is still quite high.

Is there a more intelligent way to choose my n samples? What are some alternative approaches to extrapolate n measurements into the entire feature space?

If I'm willing to settle for the local maxima, how can I find it? Seems like a straight forward problem in linear algebra. But it's been ages and I could really use some help. TIA!

$\endgroup$
1
$\begingroup$

I think you probably should use some randomized optimization algorithm such as randomized hill climbing or genetic algorithm. These are probably more suited for such a problem

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.