In this manuscript, we offer a gentle review of submodularity and supermodularity and their
properties. We offer a plethora of submodular definitions; a full description of a number of …

Submodular set-functions have many applications in combinatorial optimization, as they can
be minimized and approximately maximized in polynomial time. A key element in many of …

Can we incorporate discrete optimization algorithms within modern machine learning
models? For example, is it possible to use in deep architectures a layer whose output is the …

Optimal Transport has recently gained interest in machine learning for applications ranging
from domain adaptation to sentence similarities or deep learning. Yet, its ability to capture …

We analyze the problem of maximum likelihood estimation for Gaussian distributions that
are multivariate totally positive of order two (MTP_2). By exploiting connections to …

We discuss properties of distributions that are multivariate totally positive of order two
(MTP2) related to conditional independence. In particular, we show that any independence …

We introduce a new convex optimization problem, termed quadratic decomposable
submodular function minimization (QDSFM), which allows to model a number of learning …

Modeling diversity of sets of items is important in many applications such as product
recommendation and data summarization. Probabilistic submodular models, a family of …

We introduce a new approach to decomposable submodular function minimization (DSFM)
that exploits incidence relations. Incidence relations describe which variables effectively …

Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions
over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) …