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A Note on Support Vector Machine Degeneracy [chapter]

Ryan Rifkin, Massimiliano Pontil, Alessandro Verri
1999 Lecture Notes in Computer Science  
When training Support Vector Machines (SVMs) over non-separable data sets, one sets the threshold b using any dual cost coefficient that is strictly between the bounds of 0 and C.  ...  We also derive necessary and sufficient conditions on the input data for this to occur.  ...  Support Vector Machine Degeneracy In this section, we explore SVM training problems with a dual optimal solution satisfying λ i ∈ {0, C} for all i.  ... 
doi:10.1007/3-540-46769-6_21 fatcat:hoiwjshwzbhyji554ba3u4w2di

Integrating Genomic Data to Predict Transcription Factor Binding

Dustin T. Holloway, Mark Kon, Charles De Lisi
2005 Genome Informatics Series  
On average, a support vector machine can classify binding sites with high sensitivity and an accuracy of almost 80%.  ...  Then, binding sites were predicted with a support vector machine (SVM) using all methods alone and in combination.  ...  A support vector machine (SVM) is essentially a classification scheme for generating a linear classifier in some feature space defined by the data.  ... 
doi:10.11234/gi1990.16.83 fatcat:djra4nrvfbaavchuyodf6i4jm4

Integrating genomic data to predict transcription factor binding

Dustin T Holloway, Mark Kon, Charles DeLisi
2005 Genome Informatics Series  
On average, a support vector machine can classify binding sites with high sensitivity and an accuracy of almost 80%.  ...  Then, binding sites were predicted with a support vector machine (SVM) using all methods alone and in combination.  ...  Support Vector Machine as a Method of Data Integration A support vector machine (SVM) is essentially a classification scheme for generating a linear classifier in some feature space defined by the data  ... 
pmid:16362910 fatcat:nopywrbj3nbxfpyuo7gprqh77m

A Note on Posterior Probability Estimation for Classifiers [article]

Georgi Nalbantov, Svetoslav Ivanov
2019 arXiv   pre-print
One of the central themes in the classification task is the estimation of class posterior probability at a new point x.  ...  Here, we provide a way to estimate the posterior probability without resorting to using classification scores.  ...  For instance, for support vector machines it is common to use the proposed method by Platt (Platt, 1999) which is based on negative log-likelihood estimation.  ... 
arXiv:1909.05894v1 fatcat:2574gu56nfhkhe7goid7b2vuzu

Symmetry and degeneracy in microstructured optical fibers

M. J. Steel, T. P. White, C. Martijn de Sterke, R. C. McPhedran, L. C. Botten
2001 Optics Letters  
A fiber with rotational symmetry of order higher than 2 has modes that either are nondegenerate and support the complete fiber symmetry or are twofold degenerate pairs of lower symmetry.  ...  The symmetry of an optical waveguide determines its modal degeneracies.  ...  We find degeneracy in the HE states to the order of 10-8 , corresponding to differences near machine precision for n~ff' Note that for 2 10 < Npw < 2 16 the HE curves flatten out, from which one might  ... 
doi:10.1364/ol.26.000488 pmid:18040361 fatcat:nnli5je4ufb6tadwx2o57i73y4

Proposing a Localized Relevance Vector Machine for Pattern Classification [article]

Farhood Rismanchian, Karim Rahimian
2019 arXiv   pre-print
Relevance vector machine (RVM) can be seen as a probabilistic version of support vector machines which is able to produce sparse solutions by linearly weighting a small number of basis functions instead  ...  This can be seen as a piece-wise learner which locally classifies test instances. The model is hence called localized relevance vector machine (LRVM).  ...  To do so, we are inspired by a paper in the literature which improves support vector machine (SVM) and is called localized SVM (LSVM) [16] .  ... 
arXiv:1904.03688v1 fatcat:x5i3ggvkhnbx7hgi6v34xso7yi

Remote Computing Cluster for the Optimization of Preventive Maintenance Strategies: Models and Algorithms [chapter]

Aleksandr Kirillov, Sergey Kirillov, Vitaliy Iakimkin, Michael Pecht
2018 Maintenance Management [Working Title]  
Based on the model, systems of recognizing automata are constructed, which are a set of interacting modified Turing machines.  ...  The chapter describes a mathematical model of the early prognosis of the state of high-complexity mechanisms.  ...  It has already been noted above that when using analogies of this kind, it is only necessary to redefine the notion of a degeneracy space.  ... 
doi:10.5772/intechopen.81996 fatcat:a52s3hzxdrckbhbgfuvkxg5dpq

Properties and Bayesian fitting of restricted Boltzmann machines [article]

Andee Kaplan, Daniel Nordman, Stephen Vardeman
2018 arXiv   pre-print
A restricted Boltzmann machine (RBM) is an undirected graphical model constructed for discrete or continuous random variables, with two layers, one hidden and one visible, and no conditional dependency  ...  By treating a hidden layer of one RBM as the visible layer in a second RBM, a deep architecture can be created.  ...  FIGURE 2 2 An example restricted Boltzmann machine (RBM), consisting of two layers, one hidden () and one visible (), with no connections within a layer.  ... 
arXiv:1612.01158v3 fatcat:tcidrnfy55hanpy3zzlgh4v5qa

Properties and Bayesian fitting of restricted Boltzmann machines

Andee Kaplan, Daniel Nordman, Stephen Vardeman
2018 Statistical analysis and data mining  
A restricted Boltzmann machine (RBM) is an undirected graphical model constructed for discrete or continuous random variables, with two layers, one hidden and one visible, and no conditional dependency  ...  Abstract A restricted Boltzmann machine (RBM) is an undirected graphical model constructed for discrete or continuous random variables, with two layers, one hidden and one visible, and no conditional dependency  ...  Figure 2 : 2 An example restricted Boltzmann machine (RBM), consisting of two layers, one hidden (H) and one visible (V), with no connections within a layer.  ... 
doi:10.1002/sam.11396 fatcat:yrgfa7dg2renrmgsmg4mhzuf5y

Constraint qualification failure in action

Hassan Hijazi, Leo Liberti
2016 Operations Research Letters  
We introduce a lifted second-order cone formulation of such on/off constraints and discuss related constraint qualification issues. A solution is proposed to avoid solvers' failure.  ...  This note presents a theoretical analysis of disjunctive constraints featuring unbounded variables. In this framework, classical modeling techniques, including big-M approaches, are not applicable.  ...  Acknowledgement Financial support by grants: Digiteo Emergence "PASO", Digiteo Chair 2009-14D "RM-NCCO", Digiteo Emergence 2009-55D "ARM" is gratefully acknowledged.  ... 
doi:10.1016/j.orl.2016.05.006 fatcat:fpdnlf4ocfezddaumt57t4nsim

Inferring Hidden Symmetries of Exotic Magnets from Learning Explicit Order Parameters [article]

Nihal Rao, Ke Liu, Lode Pollet
2020 arXiv   pre-print
The method is applied to the Heisenberg-Kitaev model on a honeycomb lattice, where our machine learns the transformations that manifest its hidden O(3) symmetry, without using data of these high-symmetry  ...  In addition, our machine also learns the local constraints at the phase boundaries, which manifest a subdimensional symmetry.  ...  corresponds to a support vector.  ... 
arXiv:2007.07000v3 fatcat:iz4ir2z7qzc7zfgkpuushvq6k4

Neural networks for parameter estimation in microstructural MRI: application to a diffusion-relaxation model of white matter

João P. de Almeida Martins, Markus Nilsson, Björn Lampinen, Marco Palombo, Peter T. While, Carl-Fredrik Westin, Filip Szczepankiewicz
2021 NeuroImage  
Moreover, the degree to which machine learning can alleviate the degeneracy problem is poorly understood.  ...  The developed learning-based fitting pipelines were tested on relaxation-diffusion data acquired with optimal and sub-optimal acquisition protocols.  ...  While were supported by a grant from the Research Council of Norway (FRIPRO Researcher Project 302624) and M. Palombo by the UKRI Future Leaders Fellowship (MR/T020296/1).  ... 
doi:10.1016/j.neuroimage.2021.118601 pmid:34562578 fatcat:gszzasf44rezfpmhglfbt23aim

Deconstructing Kernel Machines [chapter]

Mohsen Ali, Muhammad Rushdi, Jeffrey Ho
2014 Lecture Notes in Computer Science  
Specifically, we assume the feature space R d is known and the kernel machine has m support vectors such that d > m (or d >> m), and in addition, the classifier C is laconic in the sense that for a feature  ...  We speculate briefly on the future application potential of deconstructing kernel machines and we present experimental results validating the proposed method.  ...  The trained kernel machine has 275 support vectors.  ... 
doi:10.1007/978-3-662-44848-9_3 fatcat:xkwquzzff5amdaerndfjycecsq

Multi-parametric solution-path algorithm for instance-weighted support vector machines

Masayuki Karasuyama, Naoyuki Harada, Masashi Sugiyama, Ichiro Takeuchi
2011 2011 IEEE International Workshop on Machine Learning for Signal Processing  
We consider a suboptimal solution path algorithm for the Support Vector Machine.  ...  The solution path algorithm is an effective tool for solving a sequence of a parametrized optimization problems in machine learning.  ...  Solution Path for Support Vector Machine In this section, we describe the solution path algorithm for regularization parameters of Support Vector Machine (SVM).  ... 
doi:10.1109/mlsp.2011.6064551 dblp:conf/mlsp/KarasuyamaHST11 fatcat:jvu2rh5u2napbnugqzbruwmm4i

Efficient Revised Simplex Method for SVM Training

C. Sentelle, G. C. Anagnostopoulos, M. Georgiopoulos
2011 IEEE Transactions on Neural Networks  
Index Terms-Active set method, null space method, quadratic programming, revised simplex method, support vector machine.  ...  Existing active set methods reported in the literature for support vector machine (SVM) training must contend with singularities when solving for the search direction.  ...  In addition, we perform comparisons with a library for support vector machine (LIBSVM) and SVMLight, which are two popular working set decomposition methods.  ... 
doi:10.1109/tnn.2011.2165081 pmid:21900073 fatcat:7h7chsck6berlglcnrxizvoc4a
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