## Posts

Showing posts from May, 2007

### Minimize!

A matlab code for minimizing a multivariate function whose partial derivatives are available by Carl Rasmussen is downloadable from here. The routine looks pretty efficient, at least on the classical Rosenbrock function.

### A notion of function compression

The following compressibility concept is introduced by Harnik and Naor in their recent paper: Given a function $f$ over some domain, a compression algorithm for $f$ should efficiently compress an input $x$ in a way that will preserve the information needed to compute $f(x)$. Note that if $f$ is available (and efficiently computable) then compression is trivial as then $y=f(x)$ will serve the purpose of the compact representation of $x$. Actually, the concept was originally studied in the framework of NP decision problems where unless $P=NP$ $f$ is not efficiently computable, hence the trivial solution is not available.

I am wondering if this compressibility notion could be used in learning theory or function approximation? Consider e.g. classification problems so that the output of $f$ is $\{0,1\}$. In order to prevent the trivial solution we may require that $x$ be compressed to some $y$ such that for some fixed (efficiently computable) function $g$, $f(g(y))=f(x)$. We do not require…