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Creation date: 2016-02-10
Creation time: 01-36-11
--- Number of references
7
article
6038
Falsificationism and Statistical Learning Theory: Comparing the Popper and Vapnik-Chervonenkis Dimensions
Journal for General Philosophy of Science
2009
7
40
1
51-58
We compare Karl Poppers ideas concerning the falsifiability of a theory with similar notions from the part of statistical learning theory known as VC-theory. Poppers notion of the dimension of a theory is contrasted with the apparently very similar VC-dimension. Having located some divergences, we discuss how best to view Poppers work from the perspective of statistical learning theory, either as a precursor or as aiming to capture a different learning activity.
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Schölkopf
http://www.springerlink.com/content/n2420j2072h67722/fulltext.pdf
Biologische Kybernetik
Max-Planck-Gesellschaft
en
10.1007/s10838-009-9091-3
dcorfieldDCorfield
bsBSchölkopf
vapnikVVapnik
article
2158
Bounds on Error Expectation for Support Vector Machines
Neural Computation
2000
12
9
2013-2036
We introduce the concept of span of support vectors (SV) and show
that the generalization ability of support vector machines (SVM) depends on this
new
geometrical concept. We prove that the value of the span is always smaller
(and can be much smaller) than the diameter of the smallest sphere containing th
e support
vectors, used in previous bounds. We also demonstate
experimentally that the prediction of the test error given by the span is very
accurate and has direct application in model selection (choice of the optimal
parameters of the SVM)
http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/ps2158.gz
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Biologische Kybernetik
Max-Planck-Gesellschaft
vapnikVVapnik
chapelleOChapelle
inproceedings
3916
Inference with the Universum
Proceedings of the 23rd International Conference on Machine Learning (ICML 2006)
2006
6
1009-1016
In this paper we study a new framework introduced by Vapnik (1998) and Vapnik (2006) that is an alternative capacity concept to the large margin approach. In the particular case of binary classification, we are given a set of labeled examples, and a collection of "non-examples" that do not belong to either class of interest. This collection, called the Universum, allows one to encode prior knowledge by representing meaningful concepts in the same domain as the problem at hand. We describe an algorithm to leverage the Universum by maximizing the number of observed contradictions, and show experimentally that this approach delivers accuracy improvements over using labeled data alone.
http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/icml_3916[0].pdf
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Schölkopf
http://portal.acm.org/citation.cfm?id=1143971&jmp=abstract&coll=GUIDE&dl=GUIDE&CFID=1380099&CFTOKEN=72073021#abstract
Cohen, W. W., A. Moore
ACM Press
New York, NY, USA
Biologische Kybernetik
Max-Planck-Gesellschaft
Pittsburgh, PA, USA
23rd International Conference on Machine Learning (ICML 2006)
en
1-59593-383-2
10.1145/1143844.1143971
westonJWeston
RCollobert
fabeeFSinz
LBottou
vapnikVVapnik
inproceedings
2053
Kernel Dependency Estimation
2003
10
873-880
http://www.kyb.tuebingen.mpg.defileadmin/user_upload/files/publications/NIPS-2002-Weston.pdf
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Schölkopf
http://books.nips.cc/nips15.html
Becker, S. , S. Thrun, K. Obermayer
MIT Press
Cambridge, MA, USA
Advances in Neural Information Processing Systems 15
Biologische Kybernetik
Max-Planck-Gesellschaft
Vancouver, BC, Canada
Sixteenth Annual Conference on Neural Information Processing Systems (NIPS 2002)
0-262-02550-7
westonJWeston
chapelleOChapelle
andreAElisseeff
bsBSchölkopf
vapnikVVapnik
inproceedings
1823
Support Vector methods in learning and feature extraction
1998
2
72-78
The last years have witnessed an increasing interest in Support Vector (SV) machines, which use Mercer kernels for efficiently performing computations in high-dimensional spaces. In pattern recognition, the SV algorithm constructs nonlinear decision functions by training a classifier to perform a linear separation in some high-dimensional space which is nonlinearly related to input space. Recently, we have developed a technique for Nonlinear Principal Component Analysis (Kernel PCA) based on the same types of kernels. This way, we can for instance efficiently extract polynomial features of arbitrary order by computing projections onto principal components in the space of all products of n pixels of images. We explain the idea of Mercer kernels and associated feature spaces, and describe connections to the theory of reproducing kernels and to regularization theory, followed by an overview of the above algorithms employing these kernels. 1. Introduction For the case of two-class pattern.
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.1638
Downs, T. , M. Frean, M. Gallagher
University of Queensland
Brisbane, Australia
Biologische Kybernetik
Max-Planck-Gesellschaft
Brisbane, Australia
Ninth Australian Conference on Neural Networks (ACNN'98)
1-86499-026-0
bsBSchölkopf
smolaAJSmola
klausK-RMüller
CBurges
vapnikVVapnik
inproceedings
796
Incorporating invariances in support vector learning machines
Artificial Neural Networks --- ICANN‘96
1996
7
47-52
Developed only recently, support vector learning machines achieve high generalization ability by minimizing a bound on the expected test error; however, so far there existed no way of adding knowledge about invariances of a classification problem at hand. We present a method of incorporating prior knowledge about transformation invariances by applying transformations to support vectors, the training examples most critical for determining the classification boundary.
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Bülthoff
http://www.springerlink.com/content/p27724q228212166/fulltext.pdf
von der Malsburg, C. , W. von Seelen, J. C. Vorbrüggen, B. Sendhoff
Springer
Berlin, Germany
Lecture Notes in Computer Science ; 1112
Artificial Neural Networks - ICANN 96
Biologische Kybernetik
Max-Planck-Gesellschaft
Bochum, Germany
6th International Conference on Artificial Neural Networks
3-540-61510-5
10.1007/3-540-61510-5_12
bsBSchölkopf
CBurges
vapnikVVapnik
techreport
3724
Popper, Falsification and the VC-dimension
2005
11
30
145
http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/TR_145_[0].pdf
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Schölkopf
Biologische Kybernetik
Max-Planck-Gesellschaft
Max Planck Institute for Biological Cybernetics
en
dcorfieldDCorfield
bsBSchölkopf
vapnikVVapnik