Learning in Neural Networks: Theoretical Foundations

By Martin H. Anthony, Peter L. Bartlett. 1999

Subfields: Model Architectures, Scaling & Learning Theory

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Citations in the corpus

On the Number of Linear Regions of Deep Neural Networks (2014, background): “There is a wealth of literature discussing approximation, estimation, and complexity of artiﬁcial neural networks (see, e.g., Anthony and Bartlett 1999).”
Rademacher and Gaussian Complexities: Risk Bounds and Structural Results (2003, methodology): “Neural network methods (see, for example, Anthony and Bartlett, 1999) use repeated compositions of linear functions with scalar nonlinearities, σ : R → [−1, 1], where σ is typically monotonic and smooth.”
Robustness and Regularization of Support Vector Machines (2008, background): “Moreover, there has not been an explicit connection to the regularized classi-ﬁer, although at a high-level it is known that regularization and robust optimization are related (e.g., El Ghaoui and Lebret, 1997; Anthony and Bartlett, 1999).”
On the Foundations of Noise-free Selective Classification (2010, background): “Theorem 20 (Vapnik and Chervonenkis, 1971; Anthony and Bartlett, 1999, p.53)Let F be a hypothesis space with VC-dimension h.”
Transfer bounds for linear feature learning (2009, methodology): “Lemma 15.5 in Anthony and Bartlett 1999 ) our bound can be modified to permit the choice of d after seeing the data (x 1 , y 1 ), ...,( x n , y n ) at only a logarithmic penalty in d. 2. The input distribution must be high-dimensional so that d C ∞ m −1 .T o make this ex-”
Linear Programming Boosting via Column Generation (2002, methodology): “We bound |A| = |U | using the following theorem due to Zhang (1999), though a slightly weaker version can also be found in Anthony and Bartlett (1999).”
Many-Layered Learning (2002, background): “The number of examples required for an unthresholded linear combination is described by a sim- ilar formula m 128ε2 (log2( 16 δ )+2Pdim(u) log2( 34 ε )) where Pdim(u) is the pseudo-dimension of u and the confidence δ = 0:01 and accuracy ε = 0:1 (Anthony & Bartlett, 1999).”