Local Reconstruction

Seshadhri, C.

doi:10.1007/978-1-4939-2864-4_698

Cited by 2 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, Nakano et al [30] discuss an algorithm to construct weighted graphs such that the total weight of the edges incident to a node is at least the given weight of the node. Finally, other property combinations that have been addressed in the context of network generation algorithms include the (a) degree distribution and degree-dependent clustering [18,26,39,40], (b) joint degree-degree distribution [14,47], (c) joint degree-degree distribution and modularity [50], (d) degree-degree correlations and degree-dependent clustering [37], and (e) eigenvector centrality [34].…”

Section: Introductionmentioning

confidence: 99%

Designing networks: A mixed‐integer linear optimization approach

et al. 2016

View full text Add to dashboard Cite

Designing networks with specified collective properties is useful in a variety of application areas, enabling the study of how given properties affect the behavior of network models, the downscaling of empirical networks to workable sizes, and the analysis of network evolution. Despite the importance of the task, there currently exists a gap in our ability to systematically generate networks that adhere to theoretical guarantees for the given property specifications. In this paper, we propose the use of Mixed-Integer Linear Optimization modeling and solution methodologies to address this Network Generation Problem. We present a number of useful modeling techniques and apply them to mathematically express and constrain network properties in the context of an optimization formulation. We then develop complete formulations for the generation of networks that attain specified levels of connectivity, spread, assortativity and robustness, and we illustrate these via a number of computational case studies.

show abstract

Section: Introductionmentioning

confidence: 99%

Designing networks: A mixed‐integer linear optimization approach

et al. 2016

View full text Add to dashboard Cite

show abstract

Properly learning monotone functions via local correction

Lange

Rubinfeld

Vasilyan

2022

2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)

View full text Add to dashboard Cite

We give the first agnostic, efficient, proper learning algorithm for monotone Boolean functions. Given 2 Õ( √ n/ε) uniformly random examples of an unknown function f : {±1} n → {±1}, our algorithm outputs a hypothesis g : {±1} n → {±1} that is monotone and (opt + ε)-close to f , where opt is the distance from f to the closest monotone function. The running time of the algorithm (and consequently the size and evaluation time of the hypothesis) is also 2 Õ( √ n/ε) , nearly matching the lower bound of [BCO + 15]. We also give an algorithm for estimating up to additive error ε the distance of an unknown function f to monotone using a run-time of 2 Õ( √ n/ε) . Previously, for both of these problems, sample-efficient algorithms were known, but these algorithms were not run-time efficient. Our work thus closes this gap in our knowledge between the run-time and sample complexity.This work builds upon the improper learning algorithm of [BT96] and the proper semiagnostic learning algorithm of [LRV22], which obtains a non-monotone Boolean-valued hypothesis, then "corrects" it to monotone using query-efficient local computation algorithms on graphs. This black-box correction approach can achieve no error better than 2opt + ε information-theoretically; we bypass this barrier by a) augmenting the improper learner with a convex optimization step, and b) learning and correcting a real-valued function before rounding its values to Boolean.Our real-valued correction algorithm solves the "poset sorting" problem of [LRV22] for functions over general posets with non-Boolean labels.

show abstract

Local Reconstruction

Cited by 2 publications

References 11 publications

Designing networks: A mixed‐integer linear optimization approach

Designing networks: A mixed‐integer linear optimization approach

Properly learning monotone functions via local correction

Contact Info

Product

Resources

About