Discrete Structures in Machine Learning

Traditionally, machine learning has been focused on methods where objects reside in continuous domains. The goal of this workshop is to advance state-of-the-art methods in machine learning that involve discrete structures.

Models with ultimately discrete solutions play an important role in machine learning. At its core, statistical machine learning is concerned with making inferences from data, and when the underlying variables of the data are discrete, both the tasks of model inference as well as predictions using the inferred model are inherently discrete algorithmic problems. Many of these problems are notoriously hard, and even those that are theoretically tractable become intractable in practice with abundant and steadily increasing amounts of data. As a result, standard theoretical models and off-the-shelf algorithms become either impractical or intractable (and in some cases both).

While many problems are hard in the worst case, the problems of practical interest are often much more well-behaved, and have the potential to be modeled in ways that make them tractable. Indeed, many discrete problems in machine learning can possess beneficial structure; such structure has been an important ingredient in many successful (approximate) solution strategies. Examples include submodularity, marginal polytopes, symmetries and exchangeability.

Machine learning, algorithms, discrete mathematics and combinatorics as well as applications in computer vision, speech, NLP, biology and network analysis are all active areas of research, each with an increasingly large body of foundational knowledge. The workshop aims to ask questions that enable communication across these fields. In particular, this year we aim to address the investigation of combinatorial structures allows to capture complex, high-order dependencies in discrete learning problems prevalent in deep learning, social networks, etc. An emphasis will be given on uncertainty and structure that results from problem instances being estimated from data.