  Probabilistic graphical models are a key tool in machine learning
applications. Computing the partition function, i.e., normalizing constant, is
a fundamental task of statistical inference but it is generally computationally
intractable, leading to extensive study of approximation methods. Iterative
variational methods are a popular and successful family of approaches. However,
even state of the art variational methods can return poor results or fail to
converge on difficult instances. In this paper, we instead consider computing
the partition function via sequential summation over variables. We develop
robust approximate algorithms by combining ideas from mini-bucket elimination
with tensor network and renormalization group methods from statistical physics.
The resulting "convergence-free" methods show good empirical performance on
both synthetic and real-world benchmark models, even for difficult instances.
