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This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors.
ε \varepsilon -entropy and ε \varepsilon -capacity of sets in function spaces
A. N. Kolmogorov and V. M. Tikhomirov · 1959
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ε \varepsilon -entropy and ε \varepsilon -capacity of sets in function spaces
A. N. Kolmogorov and V. M. Tikhomirov · 1961
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Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition
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Theory of Pattern Recognition
V. Vapnik and A. Chervonenkis · 1974
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Relating data compression and learnability
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On learning Boolean functions
B. K. Natarajan · 1987
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Learnability and the Vapnik-Chervonenkis dimension
A. Blumer, A. Ehrenfeucht, D. Haussler, and M. Warmuth · 1989
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A general lower bound on the number of examples needed for learning
A. Ehrenfeucht, D. Haussler, M. Kearns, and L. Valiant · 1989
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Learning nested differences of intersection-closed concept classes
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Improving generalization with active learning
D. Cohn, L. Atlas, and R. Ladner · 1994
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Predicting { 0 , 1 } \{0,1\} -functions on randomly drawn points
D. Haussler, N. Littlestone, and M. Warmuth · 1994
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Sample compression, learnability, and the Vapnik-Chervonenkis dimension
S. Floyd and M. Warmuth · 1995
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Sphere packing numbers for subsets of the Boolean n-cube with bounded Vapnik-Chervonenkis dimension
D. Haussler · 1995
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Weak Convergence and Empirical Processes
A. W. van der Vaart and J. A. Wellner · 1996
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Neural Network Learning: Theoretical Foundations
M. Anthony and P. L. Bartlett · 1999
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On teaching and learning intersection-closed concept classes
C. Kuhlmann · 1999
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Smooth discrimination analysis
E. Mammen and A.B. Tsybakov · 1999
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Information-theoretic determination of minimax rates of convergence
Y. Yang and A. Barron · 1999
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The one-inclusion graph algorithm is near-optimal for the prediction model of learning
Y. Li, P. M. Long, and A. Srinivasan · 2001
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Learning Kernel Classifiers
R. Herbrich · 2002
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Bounded geometries, fractals, and low-distortion embeddings
A. Gupta, R. Krauthgamer, and J. R. Lee · 2003
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An upper bound on the sample complexity of PAC learning halfspaces with respect to the uniform distribution
P. M. Long · 2003
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Learning and Generalization with Applications to Neural Networks
M. Vidyasagar · 2003
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A new PAC bound for intersection-closed concept classes
P. Auer and R. Ortner · 2004
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Theoretical Foundations of Active Learning
S. Hanneke · 2009
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Introduction to Nonparametric Estimation
A. B. Tsybakov · 2009
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On the foundations of noise-free selective classification
R. El-Yaniv and Y. Wiener · 2010
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Rademacher complexities and bounding the excess risk in active learning
V. Koltchinskii · 2010
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Agnostic selective classification
R. El-Yaniv and Y. Wiener · 2011
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Rates of convergence in active learning
S. Hanneke · 2011
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Lower bounds for passive and active learning
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Optimal aggregation of classifiers in statistical learning
A. B. Tsybakov · 2004
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The optimal PAC algorithm
M. Warmuth · 2004
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Analysis of perceptron-based active learning
S. Dasgupta, A. T. Kalai, and C. Monteleoni · 2005
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Agnostic active learning
M.-F. Balcan, A. Beygelzimer, and J. Langford · 2006
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Convexity, classification, and risk bounds
P. Bartlett, M. I. Jordan, and J. McAuliffe · 2006
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Discussion: Local Rademacher complexities and oracle inequalities in risk minimization
P. L. Bartlett and S. Mendelson · 2006
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M. Raginsky and A. Rakhlin · 2011
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A local maximal inequality under uniform entropy
A. van der Vaart and J. A. Wellner · 2011
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Active learning via perfect selective classification
R. El-Yaniv and Y. Wiener · 2012
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Activized learning: Transforming passive to active with improved label complexity
S. Hanneke · 2012
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Surrogate losses in passive and active learning
S. Hanneke and L. Yang · 2012
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Active and passive learning of linear separators under log-concave distributions
M.-F. Balcan and P. M. Long · 2013
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Active learning using smooth relative regret approximations with applications
N. Ailon, R. Begleiter, and E. Ezra · 2014
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An Introductory Course in Functional Analysis
A. Bowers and N. J. Kalton · 2014
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Theory of disagreement-based active learning
S. Hanneke · 2014
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Beyond disagreement-based agnostic active learning
C. Zhang and K. Chaudhuri · 2014
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The optimal PAC bound for intersection-closed concept classes
M. Darnstädt · 2015
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Minimax analysis of active learning
S. Hanneke and L. Yang · 2015
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A compression technique for analyzing disagreement-based active learning
Y. Wiener, S. Hanneke, and R. El-Yaniv · 2015
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The optimal sample complexity of PAC learning
S. Hanneke · 2016
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