A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Filters
Optimal Bounds on Approximation of Submodular and XOS Functions by Juntas
[article]
2015
arXiv
pre-print
Preserved Fulltext
Other Versions
We investigate the approximability of several classes of real-valued functions by functions of a small number of variables ( juntas). ...
Our main results are tight bounds on the number of variables required to approximate a function f:{0,1}^n → [0,1] within ℓ_2-error ϵ over the uniform distribution: 1. ...
Acknowledgements We would like to thank Seshadhri Comandur and Pravesh Kothari for useful discussion. We also thank the anonymous FOCS and SICOMP referees for their comments and useful suggestions. ...
arXiv:1307.3301v3
fatcat:tfwzel6yajhk7jznjs2gbacvim
Optimal bounds on approximation of submodular and XOS functions by juntas
2014
2014 Information Theory and Applications Workshop (ITA)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
It relies crucially on our approximation by junta result. As follows from the lower bounds in [1] both of these algorithms are close to optimal. ...
We investigate the approximability of several classes of real-valued functions by functions of a small number of variables (juntas). ...
ACKNOWLEDGEMENTS We would like to thank Seshadhri Comandur, Pravesh Kothari and the anonymous FOCS referees for their comments and useful suggestions. ...
doi:10.1109/ita.2014.6804263
dblp:conf/ita/FeldmanV14
fatcat:gxjyiofvrfdyxdgf6dfyrkdsaa
Optimal Bounds on Approximation of Submodular and XOS Functions by Juntas
2013
2013 IEEE 54th Annual Symposium on Foundations of Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
It relies crucially on our approximation by junta result. As follows from the lower bounds in [1] both of these algorithms are close to optimal. ...
We investigate the approximability of several classes of real-valued functions by functions of a small number of variables (juntas). ...
ACKNOWLEDGEMENTS We would like to thank Seshadhri Comandur, Pravesh Kothari and the anonymous FOCS referees for their comments and useful suggestions. ...
doi:10.1109/focs.2013.32
dblp:conf/focs/FeldmanV13
fatcat:wpq2nientjb2he6em6psgfwwz4
Optimal Bounds on Approximation of Submodular and XOS Functions by Juntas
2016
SIAM journal on computing (Print)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
It relies crucially on our approximation by junta result. As follows from the lower bounds in [1] both of these algorithms are close to optimal. ...
We investigate the approximability of several classes of real-valued functions by functions of a small number of variables (juntas). ...
ACKNOWLEDGEMENTS We would like to thank Seshadhri Comandur, Pravesh Kothari and the anonymous FOCS referees for their comments and useful suggestions. ...
doi:10.1137/140958207
fatcat:id7g5y2pfbcwjij6u2yhtishp4
Structure and learning of valuation functions
2014
ACM SIGecom Exchanges
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2016; you can also visit the original URL.
The file type is application/pdf.
We discuss structural results and learning algorithms for submodular and fractionally subadditive valuation functions. ...
While learning these valuation functions over general distributions turns out to be hard, we present compact approximate representations and efficient learning algorithms for such functions over the uniform ...
XOS functions are 1-selfbounding and submodular functions are 2-self-bounding. However, subadditive and a-self-bounding functions are incomparable. ...
doi:10.1145/2692359.2692371
fatcat:4njjqvdmsrcqlmmt7ydo5s4fee
Tight Bounds on Low-Degree Spectral Concentration of Submodular and XOS Functions
2015
2015 IEEE 56th Annual Symposium on Foundations of Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
This improves on previous approaches that all showed an upper bound of O(1/ 2 ) for submodular [CKKL12, FKV13, FV13] and XOS [FV13] functions. ...
Our techniques reveal new structural properties of submodular and XOS functions and the upper bounds lead to nearly optimal PAC learning algorithms for these classes of functions. 1 Here and below we normalize ...
Acknowledgements We would like to thank Pravesh Kothari for useful discussions and his help with the proof of Lemma 6.1. ...
doi:10.1109/focs.2015.61
dblp:conf/focs/FeldmanV15
fatcat:er54355hsfhkvdb34nf2vddr7a
Tight Bounds on ℓ_1 Approximation and Learning of Self-Bounding Functions
[article]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2017 pre-print arXiv:1404.4702v2 fatcat:rbosmqpayvhz3lzosdk6rfvgj4Other Versions
Self-bounding functions include such well-known classes of functions as submodular and fractionally-subadditive (XOS) functions. ...
Our main result is a nearly tight ℓ_1-approximation of self-bounding functions by low-degree juntas. ...
Feldman and Vondrák [FV16]
studied approximation of submodular, XOS and self-bounding functions by juntas. ...
arXiv:1404.4702v3
fatcat:wnmchrdiubeujertmzg3zz6u5m
Tight Bounds on Low-degree Spectral Concentration of Submodular and XOS functions
[article]
2015
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
This improves on previous approaches that all showed an upper bound of O(1/ϵ^2) for submodular and XOS functions. The best previous lower bound was Ω(1/ϵ^2/3) for monotone submodular functions. ...
Our techniques reveal new structural properties of submodular and XOS functions and the upper bounds lead to nearly optimal PAC learning algorithms for these classes of functions. ...
Acknowledgements We would like to thank Pravesh Kothari for useful discussions and his help with the proof of Lemma 6.1. ...
arXiv:1504.03391v2
fatcat:y5rwgeraafh67lzpdmgag4esci
Tight Bounds on ℓ 1 Approximation and Learning of Self-Bounding Functions
2017
International Conference on Algorithmic Learning Theory
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Self-bounding functions include such wellknown classes of functions as submodular and fractionally-subadditive (XOS) functions. ...
Our bounds rely on the analysis of noise stability of self-bounding functions together with a stronger connection between noise stability and 1 approximation by low-degree polynomials. ...
The main tool used in this work is the notion of noise stability. Feldman and Vondrák (2016) studied approximation of submodular, XOS and self-bounding functions by juntas. ...
dblp:conf/alt/FeldmanKV17
fatcat:veyihsja3vcxnmyxvhju5o7tdy
Testing Submodularity and Other Properties of Valuation Functions
2017
Innovations in Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
coverage functions, and self-bounding functions. ...
This result, combined with a recent junta theorem of Feldman and Vondrák ( 2016 ), yields the constant-query testability of submodularity. ...
The authors wish to thank the anonymous referees for valuable feedback, Amit Levi for insightful discussions and Karl Wimmer for pointing out [31] to us. ...
doi:10.4230/lipics.itcs.2017.33
dblp:conf/innovations/BlaisB17
fatcat:o7vrglavaff2rkad2uoo2l3bz4
Testing submodularity and other properties of valuation functions
[article]
2016
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
coverage functions, and self-bounding functions. ...
This result, combined with a recent junta theorem of Feldman and Vondrak (2016), yields the constant-query testability of submodularity. ...
through the lenses of learning theory [2, 3, 15] , optimization [13, 14] , approximation [16, 17] , and sketching [1] . ...
arXiv:1611.07879v1
fatcat:3p3yvqz3jfcwxife35jdxvysqu
Constrained signaling for welfare and revenue maximization
2013
ACM SIGecom Exchanges
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Each candidate signaling scheme induces an incompleteinformation game among the buyers, and the goal of the mechanism designer is to choose the signaling scheme that optimizes either welfare or revenue ...
For example, the auctioneer may be able to communicate only a bounded length message for each good (equivalently, he may be constrained to using only a fixed number of signals in total). ...
4.1.3 we show how to express optimization over these mappings as submodular function maximization subject to a matroid 9 constraint, which admits an e/(e − 1) approximation algorithm by the result of ...
doi:10.1145/2509013.2509022
fatcat:auj2ved2bvf6pgfwli6llrhyxi
Approximate F_2-Sketching of Valuation Functions
2019
International Workshop on Approximation Algorithms for Combinatorial Optimization
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
α-Lipschitz submodular and matroid rank functions. ...
Using known connections with dynamic streaming algorithms, both upper and lower bounds on dimension obtained in our work extend to the space complexity of algorithms evaluating f (x) under long sequences ...
of classes for which we already have an Ω(n) lower bound (e.g. submodular, subadditive, etc.) or because such a lower bound follows trivially (e.g. for OXS/XOS since for XS-functions a lower bound of ...
doi:10.4230/lipics.approx-random.2019.69
dblp:conf/approx/YaroslavtsevZ19
fatcat:dqv5xlu2krfrhoolutor6q7vi4
Representation, Approximation and Learning of Submodular Functions Using Low-rank Decision Trees
[article]
2013
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Our result is proved by constructing an approximation of a submodular function by a DT of rank 4/ϵ^2 and a proof that any rank-r DT can be ϵ-approximated by a DT of depth 5/2(r+(1/ϵ)). ...
We study the complexity of approximate representation and learning of submodular functions over the uniform distribution on the Boolean hypercube {0,1}^n. ...
There exists an algorithm AEFT, that given an integer d, θ > 0 and δ ∈ (0, 1], access to value queries of any f : {0, 1} n → [−1, 1], with probability at least 1 − δ, returns a function h represented by ...
arXiv:1304.0730v1
fatcat:utrdrx5nrrffzpidqpho5vjzme
Learning Coverage Functions and Private Release of Marginals
[article]
2014
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We study the problem of approximating and learning coverage functions. ...
They are a natural subclass of submodular functions and arise in a number of applications. ...
Acknowledgements We are grateful to Jan Vondrak for helpful advice and numerous discussions about this work. ...
arXiv:1304.2079v3
fatcat:lor5pjhisfd4vo534nxcwml2im
« Previous
Showing results 1 — 15 out of 17 results