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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).  ...  Our upper bound on the final error is 1 1/2 − β err D (F ) + ζ, where ζ is any real so that the time complexity of the solution is polynomial in 1/ζ.  ... 
doi:10.1007/3-540-36169-3_10 fatcat:nu6xunw5jfhfxam3d32k36auka

Page 4863 of Mathematical Reviews Vol. , Issue 2004f [page]

2004 Mathematical Reviews  
(IL-TECH-C; Haifa) ; Gavinsky, Dmitry (IL-TECH-C; Haifa) On boosting with polynomially bounded distributions. (English summary) J. Mach. Learn. Res. 3 (2002), Spec. Issue Comput. Learn.  ...  A smooth boosting algorithm constructs only distributions D; for the weak learner which are polynomially near to the original distribution D, i.e.  ... 

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  ...  Further, we explore the case of Freund and Schapire's AdaBoost algorithm, bounding its distributions to polynomially smooth.  ...  Definitions and Notation We call a boosting algorithm producing only polynomially near-D distributions polynomially near-D (the word "polynomially" will be omitted sometimes).  ... 
doi:10.1007/3-540-44581-1_32 fatcat:hcmhfchnyjc7rhtuu5krgiwfcu

An Efficient Membership-Query Algorithm for Learning DNF with Respect to the Uniform Distribution

Jeffrey C Jackson
1997 Journal of computer and system sciences (Print)  
We present a membership-query algorithm for eficiently learning DNF with respect to the uniform distribution.  ...  The algorithm utilizes one of Freund's boosting techniques and relies on the fact that boosting does not require a completely dist ri but ion-in depend ent weak learner.  ...  Yoav Freund graciously provided unpublished details about his boosting algorithm. Avrim Blum and Merrick Furst provided many useful comments on an early draft of this paper.  ... 
doi:10.1006/jcss.1997.1533 fatcat:pys4awlasbd7zhijra7f2u7ffa

Agnostic Boosting [chapter]

Shai Ben-David, Philip M. Long, Yishay Mansour
2001 Lecture Notes in Computer Science  
error of an hypothesis from F under the distribution P (note that for some distributions the bound may exceed a half).  ...  While this generalization guarantee is significantly weaker than the one resulting from the known PAC boosting algorithms, one should note that the assumption required for -weak agnostic learner is much  ...  We therefore work out an upper bound on the rate at which the boosting distributions may change.  ... 
doi:10.1007/3-540-44581-1_33 fatcat:wc7x7pes6fcjlaldhpwajdtsae

General Bounds on Statistical Query Learning and PAC Learning with Noise via Hypothesis Boosting

Javed A. Aslam, Scott E. Decatur
1998 Information and Computation  
We derive general bounds on the complexity of learning in the Statistical Query model and in the PAC model with classification noise.  ...  The boosting is efficient and is used to show our main result of the first general upper bounds on the complexity of strong SQ learning.  ...  We may then use the boosting technique to arrive at a strong SQ learning algorithm with nearly optimal dependence on E. bounded the number of queries and lower bounded the minimum tolerance in terms of  ... 
doi:10.1006/inco.1998.2664 fatcat:ekl7hiex3rhpnbghyqzlw7662q

Boosting in the presence of noise

Adam Kalai, Rocco A. Servedio
2003 Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03  
We also give a matching lower bound by showing that no efficient black-box boosting algorithm can boost accuracy beyond the noise rate (assuming that one-way functions exist).  ...  Boosting algorithms are procedures that "boost" low-accuracy weak learning algorithms to achieve arbitrarily high accuracy.  ...  Theorem 13 gives a lower bound of on the accuracy level which any polynomial time black box boosting algorithm can achieve.  ... 
doi:10.1145/780542.780573 dblp:conf/stoc/KalaiS03 fatcat:ebwkgtcxqzgsrj4o3drr4cnoli

Boosting in the presence of noise

Adam Kalai, Rocco A. Servedio
2003 Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03  
We also give a matching lower bound by showing that no efficient black-box boosting algorithm can boost accuracy beyond the noise rate (assuming that one-way functions exist).  ...  Boosting algorithms are procedures that "boost" low-accuracy weak learning algorithms to achieve arbitrarily high accuracy.  ...  Theorem 13 gives a lower bound of on the accuracy level which any polynomial time black box boosting algorithm can achieve.  ... 
doi:10.1145/780572.780573 fatcat:n47hwiaovbg2rp6stysmsslsnq

Boosting in the presence of noise

Adam Tauman Kalai, Rocco A. Servedio
2005 Journal of computer and system sciences (Print)  
We also give a matching lower bound by showing that no efficient black-box boosting algorithm can boost accuracy beyond the noise rate (assuming that one-way functions exist).  ...  Boosting algorithms are procedures that "boost" low-accuracy weak learning algorithms to achieve arbitrarily high accuracy.  ...  Theorem 13 gives a lower bound of on the accuracy level which any polynomial time black box boosting algorithm can achieve.  ... 
doi:10.1016/j.jcss.2004.10.015 fatcat:yrv5mk3cnvdo5ojrar4zi7vxbe

Distribution-Specific Agnostic Boosting [article]

Vitaly Feldman
2009 arXiv   pre-print
This allows boosting a distribution-specific weak agnostic learner to a strong agnostic learner with respect to the same distribution.  ...  ., 2008) follow the same strategy as boosting algorithms in the PAC model: the weak learner is executed on the same target function but over different distributions on the domain.  ...  Theorem 1.2 If C is efficiently agnostically learnable with respect to distribution D then TH(W, C) is efficiently PAC learnable over D for any W upper-bounded by a polynomial in the learning parameters  ... 
arXiv:0909.2927v1 fatcat:4ckz5ryasngmzmu4bxsbgietam

Cryptographic hardness of distribution-specific learning

Michael Kharitonov
1993 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing - STOC '93  
Fortunately, there exist known boosting algorithms with the property that if the initial distribution is uniform, then all distributions constructed by the boosting algorithm will remain close to uniform  ...  We show that the size bound for this parity -and hence the running time of our algorithmdepends directly on the extent of D's deviation from the uniform distribution.  ...  Fortunately, there exist known boosting algorithms with the property that if the initial distribution is uniform, then all distributions constructed by the boosting algorithm will remain close to uniform  ... 
doi:10.1145/167088.167197 dblp:conf/stoc/Kharitonov93 fatcat:xkpthlaatzhthgqvnd63fbr6lq

Page 4956 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
From the proposed boosting method for the SQ model, general bounds on the complexity of SQ learning are derived.  ...  PAC learning with noise via hypothesis boosting.  ... 

Algorithms and hardness results for parallel large margin learning

Rocco A. Servedio, Philip M. Long
2011 Neural Information Processing Systems  
Our main negative result deals with boosting, which is a standard approach to learning large-margin halfspaces.  ...  In contrast, naive parallel algorithms that learn a γ-margin halfspace in time that depends polylogarithmically on n have Ω(1/γ 2 ) runtime dependence on γ.  ...  Composing polynomials constantly many times yields a polynomial, which gives the claimed bit-length bound for u + . 2 The first inequality is (9.50) from [3] .  ... 
dblp:conf/nips/ServedioL11 fatcat:zpw3jhgzfne7xnel3r35qexcli

Learning DNF Expressions from Fourier Spectrum [article]

Vitaly Feldman
2013 arXiv   pre-print
We introduce a new approach to learning (or approximating) a polynomial threshold functions which is based on creating a function with range [-1,1] that approximately agrees with the unknown function on  ...  This improves on ((s ·(ns/))^(s/)·(1/), n) bound of Servedio (2001).  ...  Such an algorithm is necessary since, in the boosting-based approach of Jackson (1997) , the weak learner needs to learn with respect to distributions which depend on previous weak hypotheses.  ... 
arXiv:1203.0594v3 fatcat:b6n62mueyjaf3fxgb3rflbogza

Open Problem: The Statistical Query Complexity of Learning Sparse Halfspaces

Vitaly Feldman
2014 Annual Conference Computational Learning Theory  
This definition was originally stated in the context of online mistake-bound model (Littlestone, 1987) .  ...  In this problem the learner is given random examples labeled by an unknown halfspace function f on R n . Further f is r-sparse, that is it depends on at most r out of n variables.  ...  A lower bound on the query complexity of the SQ algorithm gives a lower bound on its running time.  ... 
dblp:conf/colt/Feldman14 fatcat:vkvvrabtujf2rdlktijiibvjcu
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