Filters








339 Hits in 3.8 sec

Exact learning of subclasses of CDNF formulas with membership queries [chapter]

Carlos Domingo
1996 Lecture Notes in Computer Science  
In particular we show the exact learnability of read-k monotone CDNF formulas, Satk O(log n)-CDNF, and O( p log n)-size CDNF from membership queries only.  ...  We show how to combine known learning algorithms that use membership and equivalence queries to obtain new learning results only with memberships.  ...  Furthermore, nearly monotone k-term DNF formulas CGL97] (monotone k-term DNF formulas with a constant number of non monotone literals per term) and monotone k-term decision list GLR97] are also known  ... 
doi:10.1007/3-540-61332-3_151 fatcat:u6a2fcl3vvc5zg72crdgw2lqjq

Optimal Cryptographic Hardness of Learning Monotone Functions [chapter]

Dana Dachman-Soled, Homin K. Lee, Tal Malkin, Rocco A. Servedio, Andrew Wan, Hoeteck Wee
2008 Lecture Notes in Computer Science  
To date, the only negative result for learning monotone functions in this model is an information-theoretic lower bound showing that certain superpolynomial-size monotone circuits cannot be learned to  ...  optimal in terms of the circuit size parameter by known positive results as well (Servedio, Information and Computation '04).  ...  Thus the class of 2 O( √ log n) -term monotone DNF can be learned to any constant accuracy in poly(n) time, but no such result is known for 2 O( √ log n) -term general DNF. 3.  ... 
doi:10.1007/978-3-540-70575-8_4 fatcat:v6zgngwvpzb27jhxalzfytr6d4

P-sufficient statistics for PAC learning k-term-DNF formulas through enumeration

B. Apolloni, C. Gentile
2000 Theoretical Computer Science  
Working in the framework of PAC-learning theory, we present special statistics for accomplishing in polynomial time proper learning of DNF boolean formulas having a ÿxed number of monomials.  ...  We develop a theory of most powerful learning for analyzing the performance of learning algorithms, with particular reference to trade-o s between power and computational costs.  ...  P using k-term-DNF representation; and the class of monotone k-term-DNF formulas is polynomially poly-relaxedly SQ-learnable w.r.t. P using monotone k-term-DNF representation.  ... 
doi:10.1016/s0304-3975(98)00215-1 fatcat:y3efuhnh4jhf5caohkhwhwe7rm

Extraction of Coverings as Monotone DNF Formulas [chapter]

Kouichi Hirata, Ryosuke Nagazumi, Masateru Harao
2003 Lecture Notes in Computer Science  
In this paper, we extend monotone monomials as large itemsets in association rule mining to monotone DNF formulas.  ...  Next, we design the algorithm dnf cover to extract coverings as monotone DNF formulas satisfying both the minimum support and the maximum overlap.  ...  [5] , we can design the algorithm to extract coverings as monotone k-term DNF formulas, where k is the upperbound of the number of monomials.  ... 
doi:10.1007/978-3-540-39644-4_15 fatcat:tae2vdufbrhtrgsq5fqtslmguq

DNF are teachable in the average case

Homin K. Lee, Rocco A. Servedio, Andrew Wan
2007 Machine Learning  
As our main result, we extend Balbach's teaching result for 2-term DNF by showing that for any 1 ≤ s ≤ 2 Θ(n) , the well-studied concept classes of at-most-s-term DNF and at-most-s-term monotone DNF each  ...  The proofs use detailed analyses of the combinatorial structure of "most" DNF formulas and monotone DNF formulas.  ...  The idea is to show that almost every at-most-s-term monotone DNF in fact has exactly s terms; as we will see, these exactly-s-term monotone DNFs can be taught very efficiently with O(ns) examples.  ... 
doi:10.1007/s10994-007-5007-9 fatcat:krwctnwy7rfephfyyfo4cpeivi

DNF Are Teachable in the Average Case [chapter]

Homin K. Lee, Rocco A. Servedio, Andrew Wan
2006 Lecture Notes in Computer Science  
As our main result, we extend Balbach's teaching result for 2-term DNF by showing that for any 1 ≤ s ≤ 2 Θ(n) , the well-studied concept classes of at-most-s-term DNF and at-most-s-term monotone DNF each  ...  The proofs use detailed analyses of the combinatorial structure of "most" DNF formulas and monotone DNF formulas.  ...  The idea is to show that almost every at-most-s-term monotone DNF in fact has exactly s terms; as we will see, these exactly-s-term monotone DNFs can be taught very efficiently with O(ns) examples.  ... 
doi:10.1007/11776420_18 fatcat:xvjgunz2irhvvhmkjlscfbtdem

Tight Bounds on Proper Equivalence Query Learning of DNF [article]

Lisa Hellerstein, Devorah Kletenik, Linda Sellie, Rocco Servedio
2011 arXiv   pre-print
We also give a new result on certificates for DNF-size, a simple algorithm for properly PAC-learning DNF, and new results on EQ-learning n-term DNF and decision trees.  ...  Using the lemma, we give the first subexponential algorithm for proper learning of DNF in Angluin's Equivalence Query (EQ) model.  ...  The above bound on seed size is nearly tight for a monotone DNF formula on n variables having √ n disjoint terms, each of size √ n.  ... 
arXiv:1111.1124v1 fatcat:3nwcachm5bervhoxgpy4bg2uqm

Preference Elicitation and Query Learning [chapter]

Avrim Blum, Jeffrey C. Jackson, Tuomas Sandholm, Martin Zinkevich
2003 Lecture Notes in Computer Science  
learning theory.  ...  In this paper we explore the relationship between "preference elicitation", a learning-style problem that arises in combinatorial auctions, and the problem of learning via queries studied in computational  ...  classes of monotone functions in machine learning is that of monotone DNF formulas.  ... 
doi:10.1007/978-3-540-45167-9_3 fatcat:ekdfwj2475gc7ixyma52mbwm24

Learning with Unreliable Boundary Queries

Avrim Blum, Prasad Chalasani, Sally A Goldman, Donna K Slonim
1998 Journal of computer and system sciences (Print)  
We also describe algorithms for learning several subclasses of monotone DNF formulas.  ...  We show how to learn the intersection of two halfspaces when membership queries near the boundary may be answered incorrectly.  ...  Finally return T U D( 1, T). u Learning (r+ 1)-Separable k-Term Monotone DNF Formulas We now show that a subclass of monotone k-term DNF formulas are properly learnable in the false-positive-only UBQ  ... 
doi:10.1006/jcss.1997.1559 fatcat:krwyws5rbrbjdncygbaklf26si

Learning with unreliable boundary queries

Avrim Blum, Prasad Chalasani, Sally A. Goldman, Donna K. Slonim
1995 Proceedings of the eighth annual conference on Computational learning theory - COLT '95  
We also describe algorithms for learning several subclasses of monotone DNF formulas.  ...  We show how to learn the intersection of two halfspaces when membership queries near the boundary may be answered incorrectly.  ...  Finally return T U D( 1, T). u Learning (r+ 1)-Separable k-Term Monotone DNF Formulas We now show that a subclass of monotone k-term DNF formulas are properly learnable in the false-positive-only UBQ  ... 
doi:10.1145/225298.225310 dblp:conf/colt/BlumCGS95 fatcat:7vhgbr3vdbfv7mvmg22ir5igvm

Efficiently Approximating Weighted Sums with Exponentially Many Terms [chapter]

Deepak Chawla, Lin Li, Stephen Scott
2001 Lecture Notes in Computer Science  
The applications we examine are pruning classifier ensembles using WM and learning general DNF formulas using Winnow.  ...  So using the 2 n possible terms as Winnow's inputs, it can learn k-term monotone DNF with only 2 + 2kn prediction mistakes.  ...  Our algorithm implicitly enumerates all possible DNF terms and uses Winnow to learn a monotone disjunction over these terms, which it can do while making O(k log N ) prediction mistakes, where k is the  ... 
doi:10.1007/3-540-44581-1_6 fatcat:azrll3l4yrca3ownzuohcnwlvu

Exact Learning of Formulas in Parallel

Nader H. Bshouty
1997 Machine Learning  
We investigate the parallel complexity of learning formulas from membership and equivalence queries.  ...  We show that many restricted classes of boolean functions cannot be efficiently learned in parallel with a polynomial number of processors.  ...  The classes are k-term DNF formulas for k = O(log n) (DNF with at most k terms), monotone DNF formulas (DNF with no negated variables) and DNF formulas. Result 3.  ... 
doi:10.1023/a:1007320031970 dblp:journals/ml/Bshouty97 fatcat:wkec6qdpkncmfkwaucxeuu22z4

Tight Bounds on ℓ_1 Approximation and Learning of Self-Bounding Functions [article]

Vitaly Feldman, Pravesh Kothari, Jan Vondrák
2019 arXiv   pre-print
We show that both the degree and junta-size are optimal up to logarithmic terms.  ...  Our main result is a nearly tight ℓ_1-approximation of self-bounding functions by low-degree juntas.  ...  In fact, even PAC learning of non-monotone a-self-bounding functions requires time nΩ(a/ǫ) assuming hardness of learning k-term DNF to accuracy 1/4 in time nΩ(k) .  ... 
arXiv:1404.4702v3 fatcat:wnmchrdiubeujertmzg3zz6u5m

A Model of Interactive Teaching

H.David Mathias
1997 Journal of computer and system sciences (Print)  
An important concept class that is not known to be learnable is DNF formulas. We demonstrate the power of our approach by providing a deterministic teacher and learner for the class of DNF formulas.  ...  In this paper we present an interactive model in which the learner has the ability to ask queries as in the query learning model of Angluin.  ...  K We note that in some sense this result subsumes the T I L pair using the monotone theory since any function can be taught in time polynomial in its DNF size without regard for its monotone dimension.  ... 
doi:10.1006/jcss.1997.1491 fatcat:7dp7hsez3zhaxgcujby3dqj5pa

Page 4583 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews  
Peter Auer (Graz) 982:68139 68T05S 03B05 68Q99 Castro, Jorge (E-UPB-LI; Barcelona); Guijarro, David (E-UPB-LI; Barcelona); Lavin, Victor (E-UPB-LI; Barcelona) Learning nearly monotone k-term DNF.  ...  Vitanyi’s result for monotone k-term DNF.” {For the entire collection see MR 98f:68007. } 982:68140 68TO5 68Q55 68Q68 68Q75 Edalat, A. (4-LNDIC-C; London Domain theory in learning processes.  ... 
« Previous Showing results 1 — 15 out of 339 results