## On the exact learnability of graph parameters: The case of partition functions

13 Jun 2016  ·  , ·

We study the exact learnability of real valued graph parameters $f$ which are known to be representable as partition functions which count the number of weighted homomorphisms into a graph $H$ with vertex weights $\alpha$ and edge weights $\beta$. M. Freedman, L. Lov\'asz and A. Schrijver have given a characterization of these graph parameters in terms of the $k$-connection matrices $C(f,k)$ of $f$... Our model of learnability is based on D. Angluin's model of exact learning using membership and equivalence queries. Given such a graph parameter $f$, the learner can ask for the values of $f$ for graphs of their choice, and they can formulate hypotheses in terms of the connection matrices $C(f,k)$ of $f$. The teacher can accept the hypothesis as correct, or provide a counterexample consisting of a graph. Our main result shows that in this scenario, a very large class of partition functions, the rigid partition functions, can be learned in time polynomial in the size of $H$ and the size of the largest counterexample in the Blum-Shub-Smale model of computation over the reals with unit cost. read more

PDF Abstract

# Code Add Remove Mark official

No code implementations yet. Submit your code now

# Datasets

Add Datasets introduced or used in this paper

# Results from the Paper Add Remove

Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.