Related papers: Half-integrality, LP-branching and FPT Algorithms
The SetCover problem has been extensively studied in many different models of computation, including parallel and distributed settings. From an approximation point of view, there are two standard guarantees: an $O(\log…
There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these…
We give the first fully polynomial-time algorithm for learning halfspaces with respect to the uniform distribution on the hypercube in the presence of contamination, where an adversary may corrupt some fraction of examples and labels…
Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…
We consider weakly supervised segmentation where only a fraction of pixels have ground truth labels (scribbles) and focus on a self-labeling approach optimizing relaxations of the standard unsupervised CRF/Potts loss on unlabeled pixels.…
Given a graph $G$, let $vc(G)$ and $vc^+(G)$ be the sizes of a minimum and a maximum minimal vertex covers of $G$, respectively. We say that $G$ is well covered if $vc(G)=vc^+(G)$ (that is, all minimal vertex covers have the same size).…
We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm…
Partial-label learning (PLL) generally focuses on inducing a noise-tolerant multi-class classifier by training on overly-annotated samples, each of which is annotated with a set of labels, but only one is the valid label. A basic promise of…
The phase-transition behavior of the NP-hard vertex-cover (VC) combinatorial optimization problem is studied numerically by linear programming (LP) on ensembles of random graphs. As the basic Simplex (SX) algorithm suitable for such LPs may…
For verifying the safety of neural networks (NNs), Fazlyab et al. (2019) introduced a semidefinite programming (SDP) approach called DeepSDP. This formulation can be viewed as the dual of the SDP relaxation for a problem formulated as a…
Weighted geometric set-cover problems arise naturally in several geometric and non-geometric settings (e.g. the breakthrough of Bansal-Pruhs (FOCS 2010) reduces a wide class of machine scheduling problems to weighted geometric set-cover).…
Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…
Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There…
Neural models for the various flavours of morphological inflection tasks have proven to be extremely accurate given ample labeled data -- data that may be slow and costly to obtain. In this work we aim to overcome this annotation bottleneck…
The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…
Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular…
Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…
Vertex integrity is a graph parameter that measures the connectivity of a graph. Informally, its meaning is that a graph has small vertex integrity if it has a small separator whose removal disconnects the graph into connected components…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
The paper contributes to an ongoing effort to extend the conformal bootstrap beyond its traditional focus on systems of four-point correlation functions. Recently, it was demonstrated that semidefinite programming can be used to formulate a…