  We present a novel approach to semi-supervised learning which is based on
statistical physics. Most of the former work in the field of semi-supervised
learning classifies the points by minimizing a certain energy function, which
corresponds to a minimal k-way cut solution. In contrast to these methods, we
estimate the distribution of classifications, instead of the sole minimal k-way
cut, which yields more accurate and robust results. Our approach may be applied
to all energy functions used for semi-supervised learning. The method is based
on sampling using a Multicanonical Markov chain Monte-Carlo algorithm, and has
a straightforward probabilistic interpretation, which allows for soft
assignments of points to classes, and also to cope with yet unseen class types.
The suggested approach is demonstrated on a toy data set and on two real-life
data sets of gene expression.
