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On Boosting with Optimal Poly-Bounded Distributions [chapter]

Nader H. Bshouty, Dmitry Gavinsky
2001 Lecture Notes in Computer Science  
We construct a framework which allows an algorithm to turn the distributions produced by some boosting algorithms into polynomially smooth distributions (w.r.t. the PAC oracle's distribution), with minimal  ...  Our scheme allows the execution of AdaBoost in the on-line boosting mode (i.e., to perform boosting "by filtering").  ...  equivalence between poly-distribution-dependent strong PAC learning and poly-distribution-dependent weak PAC learning.  ... 
doi:10.1007/3-540-44581-1_32 fatcat:hcmhfchnyjc7rhtuu5krgiwfcu

Distribution-Specific Agnostic Boosting [article]

Vitaly Feldman
2009 arXiv   pre-print
Conversely, our boosting algorithm gives a simple hard-core set construction with an (almost) optimal hard-core set size.  ...  This allows boosting a distribution-specific weak agnostic learner to a strong agnostic learner with respect to the same distribution.  ...  In order to bound the number of boosting stages we need to lower bound γ ·N h .  ... 
arXiv:0909.2927v1 fatcat:4ckz5ryasngmzmu4bxsbgietam

Optimally-Smooth Adaptive Boosting and Application to Agnostic Learning [chapter]

Dmitry Gavinsky
2002 Lecture Notes in Computer Science  
This allows adaptively solving problems whose solution is based on smooth boosting (like noise tolerant boosting and DNF membership learning), while preserving the original (non-adaptive) solution's complexity  ...  We derive a lower bound for the final error achievable by boosting in the agnostic model and show that our algorithm actually achieves that accuracy (within a constant factor).  ...  On the one hand, non-smoothness obliges to use boosting by sampling.  ... 
doi:10.1007/3-540-36169-3_10 fatcat:nu6xunw5jfhfxam3d32k36auka

Efficient Algorithms for Privately Releasing Marginals via Convex Relaxations [article]

Cynthia Dwork, Aleksandar Nikolov, Kunal Talwar
2013 arXiv   pre-print
Using private boosting we are also able to give nearly matching worst-case error bounds. Our algorithms are based on the geometric techniques of Nikolov, Talwar, and Zhang.  ...  In this work we present a polynomial time algorithm that, for any distribution on marginal queries, achieves average error at most Õ(√(n) d^ k/2 /4).  ...  The above approach gives us average error bounds for any distribution on queries. To get a worst case error bound, we use the Boosting for Queries framework of [15] .  ... 
arXiv:1308.1385v1 fatcat:mkyd5sl3hzgylethpru7kad3dy

Page 8146 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
Servedio, Smooth boosting and learning with mali- cious noise (473—489); Nader H. Bshouty and Dmitry Gavinsky, On boosting with optimal poly-bounded distributions (490-506); Shai Ben-David, Philip M.  ...  additive models online with fast evaluating kernels (444-460); Shie Mannor and Ron Meir, Geometric bounds for generalization in boosting (461—472).  ... 

Efficient Algorithms for Privately Releasing Marginals via Convex Relaxations

Cynthia Dwork, Aleksandar Nikolov, Kunal Talwar
2015 Discrete & Computational Geometry  
Using private boosting we are also able to give nearly matching worst-case error bounds. Our algorithms are based on the geometric techniques of Nikolov, Talwar, and Zhang.  ...  In this work we present a polynomial time algorithm that, for any distribution on marginal queries, achieves average error at mostÕ( √ nd ⌈k/2⌉ 4 ).  ...  The above approach gives us average error bounds for any distribution on queries. To get a worst case error bound, we use the Boosting for Queries framework of [15] .  ... 
doi:10.1007/s00454-015-9678-x fatcat:ztwwmcdminat7nmp2ubmrpixsa

Improved Distributed Approximations for Maximum Independent Set

Ken-ichi Kawarabayashi, Seri Khoury, Aaron Schild, Gregory Schwartzman, Hagit Attiya
2020 International Symposium on Distributed Computing  
One may wonder whether it is possible to approximate MaxIS with high probability in fewer than poly(log log n) rounds.  ...  However, it is unclear how to convert this algorithm to one that succeeds with high probability without sacrificing a large number of rounds.  ...  To lower bound the size of the obtained independent set I, one therefore just needs to get a lower bound on the sum of the increment probabilities Pr[v t ∈ I|I t−1 ]. 35:8 Improved Distributed Approximations  ... 
doi:10.4230/lipics.disc.2020.35 dblp:conf/wdag/KawarabayashiKS20 fatcat:yhe43goz2nds7a7vedkvnwx524

Boosting Variational Inference: an Optimization Perspective [article]

Francesco Locatello, Rajiv Khanna, Joydeep Ghosh, Gunnar Rätsch
2018 arXiv   pre-print
Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one.  ...  Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a mixture of densities by greedily adding components to the mixture.  ...  If the set A contains truncated Gaussian distributions with non-degenerate covariance matrix but with small enough determinant to perfectly approximate any density defined on a bounded support it also  ... 
arXiv:1708.01733v2 fatcat:35kinigowza6pbzuzvgrhwxwxu

Learning Halfspaces with Malicious Noise [chapter]

Adam R. Klivans, Philip M. Long, Rocco A. Servedio
2009 Lecture Notes in Computer Science  
We give poly(n, 1/ε)-time algorithms for solving the following problems to accuracy ε: • Learning origin-centered halfspaces in R n with respect to the uniform distribution on the unit ball with malicious  ...  (The best previous result was Ω(ε/(n log(n/ε)) 1/4 ).) • Learning origin-centered halfspaces with respect to any isotropic logconcave distribution on R n with malicious noise rate η = Ω(ε 3 / log 2 (n/  ...  (The extra factor of ε in the bound of Theorem 2 compared with Theorem 1 comes from the fact that the boosting algorithm constructs "1/ε-skewed" distributions.)  ... 
doi:10.1007/978-3-642-02927-1_51 fatcat:hk66wrjug5ebtjfsxpczwqaqmy

Martingale Boosting [chapter]

Philip M. Long, Rocco A. Servedio
2005 Lecture Notes in Computer Science  
Martingale boosting is a simple and easily understood technique with a simple and easily understood analysis.  ...  A slight variant of the approach provably achieves optimal accuracy in the presence of misclassification noise.  ...  Conclusion We are working on implementing the algorithm and evaluating its performance and noise tolerance on real world data.  ... 
doi:10.1007/11503415_6 fatcat:aakbf45cxzfz5ign74eyjkan5y

Optimal Bounds on Approximation of Submodular and XOS Functions by Juntas

Vitaly Feldman, Jan Vondrák
2016 SIAM journal on computing (Print)  
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.  ...  Our uniform distribution algorithm runs in time 2 1/poly(γ ) poly(n).  ...  One of the key pieces of the proof is the use a "boosting lemma 1 " on down-monotone events of Goemans and Vondrak [26] .  ... 
doi:10.1137/140958207 fatcat:id7g5y2pfbcwjij6u2yhtishp4

Optimal Bounds on Approximation of Submodular and XOS Functions by Juntas

Vitaly Feldman, Jan Vondrak
2013 2013 IEEE 54th Annual Symposium on Foundations of Computer Science  
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.  ...  Our uniform distribution algorithm runs in time 2 1/poly(γ ) poly(n).  ...  One of the key pieces of the proof is the use a "boosting lemma 1 " on down-monotone events of Goemans and Vondrak [26] .  ... 
doi:10.1109/focs.2013.32 dblp:conf/focs/FeldmanV13 fatcat:wpq2nientjb2he6em6psgfwwz4

Optimal bounds on approximation of submodular and XOS functions by juntas

Vitaly Feldman, Jan Vondrak
2014 2014 Information Theory and Applications Workshop (ITA)  
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.  ...  Our uniform distribution algorithm runs in time 2 1/poly(γ ) poly(n).  ...  One of the key pieces of the proof is the use a "boosting lemma 1 " on down-monotone events of Goemans and Vondrak [26] .  ... 
doi:10.1109/ita.2014.6804263 dblp:conf/ita/FeldmanV14 fatcat:gxjyiofvrfdyxdgf6dfyrkdsaa

Boosting and Differential Privacy

Cynthia Dwork, Guy N. Rothblum, Salil Vadhan
2010 2010 IEEE 51st Annual Symposium on Foundations of Computer Science  
Combining this with evolution of confidence arguments from the literature, we get stronger bounds on the expected cumulative privacy loss due to multiple mechanisms, each of which provides ε-differential  ...  Given a base synopsis generator that takes a distribution on Q and produces a "weak" synopsis that yields "good" answers for a majority of the weight in Q, our Boosting for Queries algorithm obtains a  ...  We say that M is a (k, λ, η, β)base synopsis generator if for any distribution D on Q, when M is activated on a database x ∈ X n and on k queries sampled independently from D, with all but β probability  ... 
doi:10.1109/focs.2010.12 dblp:conf/focs/DworkRV10 fatcat:figgtroohrfjvjplnf46oiygoa

Logarithmic Time One-Against-Some [article]

Hal Daume III, Nikos Karampatziakis, John Langford, Paul Mineiro
2016 arXiv   pre-print
We show that several simple techniques give rise to an algorithm that can compete with one-against-all in both space and predictive power while offering exponential improvements in speed when the number  ...  Compared to previous approaches, we obtain substantially better statistical performance for two reasons: First, we prove a tighter and more complete boosting theorem, and second we translate the results  ...  With this criterion we are in a position to directly optimize information boosting. Definition 1.  ... 
arXiv:1606.04988v2 fatcat:7laxfux7djarfhwuo2orv4xbxe
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