Communications of the ACM
Statistical analysis with missing data
Statistical analysis with missing data
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
On learning a union of half spaces
Journal of Complexity
Types of noise in data for concept learning
COLT '88 Proceedings of the first annual workshop on Computational learning theory
Computational learning theory: an introduction
Computational learning theory: an introduction
Decision theoretic generalizations of the PAC model for neural net and other learning applications
Information and Computation
Efficient noise-tolerant learning from statistical queries
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Almost optimal set covers in finite VC-dimension: (preliminary version)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Efficient distribution-free learning of probabilistic concepts
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
On the learnability of discrete distributions
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
An introduction to computational learning theory
An introduction to computational learning theory
Information and Computation
Learning from examples with unspecified attribute values (extended abstract)
COLT '97 Proceedings of the tenth annual conference on Computational learning theory
On Restricted-Focus-of-Attention Learnability of Boolean Functions
Machine Learning - Special issue on the ninth annual conference on computational theory (COLT '96)
Noise-tolerant distribution-free learning of general geometric concepts
Journal of the ACM (JACM)
Learning with unreliable boundary queries
Journal of Computer and System Sciences - Special issue on the eighth annual workshop on computational learning theory, July 5–8, 1995
Learning with restricted focus of attention
Journal of Computer and System Sciences
Exact Learning of Discretized Geometric Concepts
SIAM Journal on Computing
Machine Learning
Linear Programming - Randomization and Abstract Frameworks
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
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
A polynomial-time algorithm for learning noisy linear threshold functions
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Covering numbers for real-valued function classes
IEEE Transactions on Information Theory
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We investigate PAC-learning in a situation in which examples (consisting of an input vector and 0/1 label) have some of the components of the input vector concealed from the learner. This is a special case of restricted focus of attention (RFA) learning. Our interest here is in 1-RFA learning, where only a single component of an input vector is given, for each example. We argue that 1-RFA learning merits special consideration within the wider field of RFA learning. It is the most restrictive form of RFA learning (so that positive results apply in general), and it models a type of "data fusion" scenario, where we have sets of observations from a number of separate sensors, but these sensors are uncorrelated sources. Within this setting we study the well-known class of linear threshold functions, the characteristic functions of Euclidean half-spaces. The sample complexity (i.e., sample-size requirement as a function of the parameters) of this learning problem is affected by the input distribution. We show that the sample complexity is always finite, for any given input distribution, but we also exhibit methods for defining "bad" input distributions for which the sample complexity can grow arbitrarily fast. We identify fairly general sufficient conditions for an input distribution to give rise to sample complexity that is polynomial in the PAC parameters -1 and -1. We give an algorithm whose sample complexity is polynomial in these parameters and the dimension (number of input components), for input distributions that satisfy our conditions. The run-time is polynomial in -1 and -1 provided that the dimension is any constant. We show how to adapt the algorithm to handle uniform misclassification noise. 2001 Elsevier Science.