4 research outputs found
From Sets to Multisets: Provable Variational Inference for Probabilistic Integer Submodular Models
Submodular functions have been studied extensively in machine learning and
data mining. In particular, the optimization of submodular functions over the
integer lattice (integer submodular functions) has recently attracted much
interest, because this domain relates naturally to many practical problem
settings, such as multilabel graph cut, budget allocation and revenue
maximization with discrete assignments. In contrast, the use of these functions
for probabilistic modeling has received surprisingly little attention so far.
In this work, we firstly propose the Generalized Multilinear Extension, a
continuous DR-submodular extension for integer submodular functions. We study
central properties of this extension and formulate a new probabilistic model
which is defined through integer submodular functions. Then, we introduce a
block-coordinate ascent algorithm to perform approximate inference for those
class of models. Finally, we demonstrate its effectiveness and viability on
several real-world social connection graph datasets with integer submodular
objectives