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In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a properly colored spanning tree, i.e., a spanning tree in which any two adjacent edges have distinct colors. The problem…
The offset optimization problem seeks to coordinate and synchronize the timing of traffic signals throughout a network in order to enhance traffic flow and reduce stops and delays. Recently, offset optimization was formulated into a…
We prove that finding all globally optimal two-layer ReLU neural networks can be performed by solving a convex optimization program with cone constraints. Our analysis is novel, characterizes all optimal solutions, and does not leverage…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
Bayesian networks are basic graphical models, used widely both in statistics and artificial intelligence. These statistical models of conditional independence structure are described by acyclic directed graphs whose nodes correspond to…
Recent numerical experiments have demonstrated that the choice of optimization geometry used during training can impact generalization performance when learning expressive nonlinear model classes such as deep neural networks. These…
We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by…
Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A…
Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the…
Recently, several works have shown that natural modifications of the classical conditional gradient method (aka Frank-Wolfe algorithm) for constrained convex optimization, provably converge with a linear rate when: i) the feasible set is a…
The general intractability of the constraint satisfaction problem has motivated the study of restrictions on this problem that permit polynomial-time solvability. One major line of work has focused on structural restrictions, which arise…
Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views,…
Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised…
We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the tree-reweighted variational objective lends itself to a…
Tree-width and path-width are widely successful concepts. Many NP-hard problems have efficient solutions when restricted to graphs of bounded tree-width. Many efficient algorithms are based on a tree decomposition. Sometimes the more…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
We give a novel formal theoretical framework for unsupervised learning with two distinctive characteristics. First, it does not assume any generative model and based on a worst-case performance metric. Second, it is comparative, namely…
We consider the problem of supervised learning with convex loss functions and propose a new form of iterative regularization based on the subgradient method. Unlike other regularization approaches, in iterative regularization no constraint…
In this paper we study the Spanning Tree Congestion problem, where we are given a graph $G=(V,E)$ and are asked to find a spanning tree $T$ of minimum maximum congestion. Here, the congestion of an edge $e\in T$ is the number of edges…
In this paper we present a new width measure for a tree decomposition, minor-matching hypertree width, $\mu\text{-}tw$, for graphs and hypergraphs, such that bounding the width guarantees that set of maximal independent sets has a…