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1,025 results on '"Rubinstein J"'

205. Shifting : one-inclusion mistake bounds and sample compression

Author

Rubinstein, Benjamin I.P., Bartlett, Peter L., and Rubinstein, J. Hyam

Subjects
OAVJ, 080600 INFORMATION SYSTEMS
Abstract

We present new expected risk bounds for binary and multiclass prediction, and resolve several recent conjectures on sample compressibility due to Kuzmin and Warmuth. By exploiting the combinatorial structure of concept class F, Haussler et al. achieved a VC(F)/n bound for the natural one-inclusion prediction strategy. The key step in their proof is a d=VC(F) bound on the graph density of a subgraph of the hypercube—one-inclusion graph. The first main result of this report is a density bound of n∙choose(n-1,≤d-1)/choose(n,≤d) < d, which positively resolves a conjecture of Kuzmin and Warmuth relating to their unlabeled Peeling compression scheme and also leads to an improved one-inclusion mistake bound. The proof uses a new form of VC-invariant shifting and a group-theoretic symmetrization. Our second main result is an algebraic topological property of maximum classes of VC-dimension d as being d-contractible simplicial complexes, extending the well-known characterization that d=1 maximum classes are trees. We negatively resolve a minimum degree conjecture of Kuzmin and Warmuth—the second part to a conjectured proof of correctness for Peeling—that every class has one-inclusion minimum degree at most its VC-dimension. Our final main result is a k-class analogue of the d/n mistake bound, replacing the VC-dimension by the Pollard pseudo-dimension and the one-inclusion strategy by its natural hypergraph generalization. This result improves on known PAC-based expected risk bounds by a factor of O(log n) and is shown to be optimal up to a O(log k) factor. The combinatorial technique of shifting takes a central role in understanding the one-inclusion (hyper)graph and is a running theme throughout

Published
2007

208. One-sided Heegaard splittings of $\mathbb{R}\mathrm{P}^3$

Author

Bartolini, Loretta and Rubinstein, J Hyam

Subjects
one-sided Heegaard splitting, 57N10, 57M27, geometrically compressible
Abstract

Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of [math] are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of [math] are standard.

Published
2006

218. Corrigendum to 'Shifting: One-inclusion mistake bounds and sample compression' [J. Comput. System Sci. 75 (1) (2009) 37-59]

Author

Rubinstein, Benjamin, Bartlett, Peter, Rubinstein, J. Hyam, Rubinstein, Benjamin, Bartlett, Peter, and Rubinstein, J. Hyam

Abstract

H. Simon and B. Szörényi have found an error in the proof of Theorem 52 of “Shifting: One-inclusion mistake bounds and sample compression”, Rubinstein et al. (2009). In this note we provide a corrected proof of a slightly weakened version of this theorem. Our new bound on the density of one-inclusion hypergraphs is again in terms of the capacity of the multilabel concept class. Simon and Szörényi have recently proved an alternate result in Simon and Szörényi (2009).

Published
2010

219. Shifting: One-inclusion mistake bounds and sample compression

Author

Rubinstein, Benjamin, Bartlett, Peter, Rubinstein, J. Hyam, Rubinstein, Benjamin, Bartlett, Peter, and Rubinstein, J. Hyam

Abstract

We present new expected risk bounds for binary and multiclass prediction, and resolve several recent conjectures on sample compressibility due to Kuzmin and Warmuth. By exploiting the combinatorial structure of concept class F, Haussler et al. achieved a VC(F)/n bound for the natural one-inclusion prediction strategy. The key step in their proof is a d = VC(F) bound on the graph density of a subgraph of the hypercube—oneinclusion graph. The first main result of this paper is a density bound of n [n−1 <=d-1]/[n <=d] < d, which positively resolves a conjecture of Kuzmin and Warmuth relating to their unlabeled Peeling compression scheme and also leads to an improved one-inclusion mistake bound. The proof uses a new form of VC-invariant shifting and a group-theoretic symmetrization. Our second main result is an algebraic topological property of maximum classes of VC-dimension d as being d contractible simplicial complexes, extending the well-known characterization that d = 1 maximum classes are trees. We negatively resolve a minimum degree conjecture of Kuzmin and Warmuth—the second part to a conjectured proof of correctness for Peeling—that every class has one-inclusion minimum degree at most its VCdimension. Our final main result is a k-class analogue of the d/n mistake bound, replacing the VC-dimension by the Pollard pseudo-dimension and the one-inclusion strategy by its natural hypergraph generalization. This result improves on known PAC-based expected risk bounds by a factor of O(logn) and is shown to be optimal up to an O(logk) factor. The combinatorial technique of shifting takes a central role in understanding the one-inclusion (hyper)graph and is a running theme throughout.

Published
2009

229. Knots and k-width

Author

Hass, Joel, Hass, Joel, Rubinstein, J. Hyam, Thompson, Abigail, Hass, Joel, Hass, Joel, Rubinstein, J. Hyam, and Thompson, Abigail

Abstract

We investigate several integer invariants of curves in 3-space. We demonstrate relationships of these invariants to crossing number and to total curvature.

Published
2006

237. Four Powers To Bury the British System: From Franklin Roosevelt To Lyndon LaRouche.

Author

Rubinstein, J. Philip

Subjects
INTERNATIONAL relations
Abstract

The article discusses the importance of the U.S. collaborating with major world powers like Russia, India and China to challenge the British System of world finance and discusses how politicians like Franklin Delano Roosevelt and Lyndon LaRouche worked to challenge the British system.

Published
2017

246. Period three actions on the three-sphere

Author

Maher, Joseph, Rubinstein, J. Hyam, Maher, Joseph, and Rubinstein, J. Hyam

Abstract

We show that a free period three action on the three-sphere is standard, ie, the quotient is homeomorphic to a lens space. We use a minimax argument involving sweepouts.

Published
2003

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