Communications of the ACM
A general lower bound on the number of examples needed for learning
Information and Computation
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
The Strength of Weak Learnability
Machine Learning
Boosting a weak learning algorithm by majority
COLT '90 Proceedings of the third annual workshop on Computational learning theory
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Toward efficient agnostic learning
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Learning in the presence of malicious errors
SIAM Journal on Computing
Efficient noise-tolerant learning from statistical queries
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Learning with restricted focus of attention
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
Data filtering and distribution modeling algorithms for machine learning
Data filtering and distribution modeling algorithms for machine learning
Weakly learning DNF and characterizing statistical query learning using Fourier analysis
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On learning from noisy and incomplete examples
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
The harmonic sieve: a novel application of Fourier analysis to machine learning theory and practice
The harmonic sieve: a novel application of Fourier analysis to machine learning theory and practice
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Machine Learning
Learning decision lists and trees with equivalence-queries
EuroCOLT '95 Proceedings of the Second European Conference on Computational Learning Theory
Learnability with Restricted Focus of Attention guarantees Noise-Tolerance
AII '94 Proceedings of the 4th International Workshop on Analogical and Inductive Inference: Algorithmic Learning Theory
Learning fixed-dimension linear thresholds from fragmented data
COLT '99 Proceedings of the twelfth annual conference on Computational learning theory
Learning fixed-dimension linear thresholds from fragmented data
Information and Computation
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
Learning from examples with unspecified attribute values
Information and Computation
Multiple-Instance Learning of Real-Valued Geometric Patterns
Annals of Mathematics and Artificial Intelligence
Every Linear Threshold Function has a Low-Weight Approximator
Computational Complexity
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
SIAM Journal on Computing
Testing (subclasses of) halfspaces
Property testing
Testing (subclasses of) halfspaces
Property testing
SIAM Journal on Computing
Nearly optimal solutions for the chow parameters problem and low-weight approximation of halfspaces
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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In the k-Restricted-Focus-of-Attention (k-RFA) model, only k of the nattributes of each example are revealed to the learner, although the set ofvisible attributes in each example is determined by the learner. While thek-RFA model is a natural extension of the PAC model, there arealso significant differences. For example, it was previously known thatlearnability in this model is not characterized by the VC-dimension and thatmany PAC learning algorithms are not applicable in the k-RFAsetting.In this paper we further explore the relationship between the PAC andk-RFA models, with several interesting results. First, wedevelop an information-theoretic characterization of k-RFAlearnability upon which we build a general tool for proving hardnessresults. We then apply this and other new techniques for studying RFAlearning to two particularly expressive function classes,k-decision-lists (k-DL) and k-TOP,the class of thresholds of parity functions in which each parity functiontakes at most k inputs. Among other results, we prove a hardness result for k-RFA learnability of k-DL,k ≤ n-2. In sharp contrast, an (n-1)-RFAalgorithm for learning (n-1)-DL is presented. Similarly, weprove that 1-DL is learnable if and only if at least half of the inputs arevisible in each instance. In addition, we show that there is auniform-distribution k-RFA learning algorithm for the class ofk-DL. For k-TOP we show weak learnability by ak-RFA algorithm (with efficient time and sample complexity forconstant k) and strong uniform-distribution k-RFAlearnability of k-TOP with efficient sample complexity for constant k. Finally, by combining some of our k-DLand k-TOP results, we show that, unlike the PAC model, weaklearning does not imply strong learning in thek-RFA model.