Ahmed Abbas (PhD Student)

Structured prediction problems are one of the fundamental tools in machine
learning. In order to facilitate algorithm development for their numerical
solution, we collect in one place a large number of datasets in easy to read
formats for a diverse set of problem classes. We provide archival links to
datasets, description of the considered problems and problem formats, and a
short summary of problem characteristics including size, number of instances
etc. For reference we also give a non-exhaustive selection of algorithms
proposed in the literature for their solution. We hope that this central
repository will make benchmarking and comparison to established works easier.
We welcome submission of interesting new datasets and algorithms for inclusion
in our archive.

We present a massively parallel Lagrange decomposition method for solving 0-1
integer linear programs occurring in structured prediction. We propose a new
iterative update scheme for solving the Lagrangean dual and a perturbation
technique for decoding primal solutions. For representing subproblems we follow
Lange et al. (2021) and use binary decision diagrams (BDDs). Our primal and
dual algorithms require little synchronization between subproblems and
optimization over BDDs needs only elementary operations without complicated
control flow. This allows us to exploit the parallelism offered by GPUs for all
components of our method. We present experimental results on combinatorial
problems from MAP inference for Markov Random Fields, quadratic assignment and
cell tracking for developmental biology. Our highly parallel GPU implementation
improves upon the running times of the algorithms from Lange et al. (2021) by
up to an order of magnitude. In particular, we come close to or outperform some
state-of-the-art specialized heuristics while being problem agnostic.

We consider general discrete Markov Random Fields(MRFs) with additional
bottleneck potentials which penalize the maximum (instead of the sum) over
local potential value taken by the MRF-assignment. Bottleneck potentials or
analogous constructions have been considered in (i) combinatorial optimization
(e.g. bottleneck shortest path problem, the minimum bottleneck spanning tree
problem, bottleneck function minimization in greedoids), (ii) inverse problems
with $L_{\infty}$-norm regularization, and (iii) valued constraint satisfaction
on the $(\min,\max)$-pre-semirings. Bottleneck potentials for general discrete
MRFs are a natural generalization of the above direction of modeling work to
Maximum-A-Posteriori (MAP) inference in MRFs. To this end, we propose MRFs
whose objective consists of two parts: terms that factorize according to (i)
$(\min,+)$, i.e. potentials as in plain MRFs, and (ii) $(\min,\max)$, i.e.
bottleneck potentials. To solve the ensuing inference problem, we propose
high-quality relaxations and efficient algorithms for solving them. We
empirically show efficacy of our approach on large scale seismic horizon
tracking problems.