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Dimension Reduction: A Guided Tour

Christopher J. C. Burges
2009 Foundations and Trends® in Machine Learning  
A sequence Xn of random variables is said to converge in probability to a random variable X if limn→∞P (|Xn − X| > ) = 0 for all > 0 [45]. 4 The Cauchy distribution in one dimension has density c/(c 2  ...  The Nyström method, which links several of the manifold algorithms, is also reviewed. We use a publicly available data set to illustrate some of the methods.  ...  Thanks also to the management team at Microsoft Research for their support of this effort.  ... 
doi:10.1561/2200000002 fatcat:tve4cy6rljcwnkrg23jhphxapm

A Random Forest Guided Tour [article]

Gérard Biau
2015 arXiv   pre-print
The random forest algorithm, proposed by L. Breiman in 2001, has been extremely successful as a general-purpose classification and regression method.  ...  Emphasis is placed on the mathematical forces driving the algorithm, with special attention given to the selection of parameters, the resampling mechanism, and variable importance measures.  ...  Conclusion and perspectives The authors trust that this review paper has provided an overview of some of the recent literature on random forests and offered insights into how new and emerging fields are  ... 
arXiv:1511.05741v1 fatcat:h3frz7blzfdtjouoh4vdas655q

A random forest guided tour

Gérard Biau, Erwan Scornet
2016 Test (Madrid)  
The random forest algorithm, proposed by L. Breiman in 2001, has been extremely successful as a general-purpose classification and regression method.  ...  Emphasis is placed on the mathematical forces driving the algorithm, with special attention given to the selection of parameters, the resampling mechanism, and variable importance measures.  ...  We thank the Editors and three anonymous referees for valuable comments and insightful suggestions.  ... 
doi:10.1007/s11749-016-0481-7 fatcat:t5gukabxtbhcjfculifjlzlaxi

Dilation theory: a guided tour [article]

Orr Shalit
2020 arXiv   pre-print
U',V' are unitaries that satisfy the commutation relation V'U' = e^iθ' U'V'.  ...  In the last part, I will present relatively new dilation problems in the noncommutative setting which are related to the study of matrix convex sets and operator systems, and are motivated by applications  ...  along the way, that CP-semigroups are strongly continuous [14, 28, 102] .  ... 
arXiv:2002.05596v2 fatcat:6mzbzccqdbdzpfs3qurj4yvhxu

Tensor categories: A selective guided tour [article]

Michael Mueger
2010 arXiv   pre-print
These are the lecture notes for a short course on tensor categories. The coverage in these notes is relatively non-technical, focussing on the essential ideas.  ...  Once the basic definitions are given, the focus is mainly on k-linear categories with finite dimensional hom-spaces.  ...  The choice of references was guided by the principal thrust of these lectures, namely linear categories.  ... 
arXiv:0804.3587v3 fatcat:si3pliliofdkzmenkrt36keski

Climate Variability Indices—A Guided Tour

Mateusz Norel, Michał Kałczyński, Iwona Pińskwar, Krzysztof Krawiec, Zbigniew W. Kundzewicz
2021 Geosciences  
The objective of this study is to provide a comprehensive review and characterization of selected climate variability indices.  ...  All these oscillation modes are of broad interest and considerable relevance, also in climate impact studies related to teleconnections, i.e., relationships between climate variations at distant locations  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/geosciences11030128 fatcat:b4ycbseecvglpmwionmirkjv3u

A Beautiful Tour in Need of a Guide

Charles K. Prokop
1989 Contemporary Psychology  
In view of the lack of integrative chapters, the difficulty in using the index as a guide to related material is a signif- icant liability.  ...  Group dynamics: The psychology of small group behavior (3rd ed.). New York: McGraw-Hill. A Beautiful Tour in Need of a Guide Thomas H. Schmidt, Theodore M. Dembroski, and Gerhard Bliimchen (Eds.)  ... 
doi:10.1037/027776 fatcat:h3cuvcqyvzeeje4y4lh6zj7mqe

A Guided Tour to Normalized Volume [article]

Chi Li, Yuchen Liu, Chenyang Xu
2019 arXiv   pre-print
This is a survey on the recent theory on minimizing the normalized volume function attached to any klt singularities.  ...  We note thatΞ t is linear with respect to t, and each region ∆Ξ t is cut out by a hyperplane H t on the convex coneσ. Moreover, all H t passes through a fixed point.  ...  In [MSY08] , the relation between the existence of Sasaki-Einstein metric along (X, ξ) and the K-stability of (X, ξ), a mimic of the absolute case, was explored.  ... 
arXiv:1806.07112v2 fatcat:ra4a2s6fhbbxvjtxq7hcxr6kma

A guide tour of video watermarking

Gwenaël Doërr, Jean-Luc Dugelay
2003 Signal processing. Image communication  
On the other hand, the situation is rather different in the context of video watermarking, where unrelated articles are scattered throughout the literature.  ...  The purpose of this paper is consequently to give an in-depth overview of video watermarking and to point out that it is not only a simple extension of still images watermarking.  ...  In spite of all those challenges, many algorithms have already been proposed in the literature.  ... 
doi:10.1016/s0923-5965(02)00144-3 fatcat:2tmq7qovffh4fbersvy2a43c5y

Pointed Hopf algebras: a guided tour to the liftings [article]

Iván Angiono, Agustín García Iglesias
2018 arXiv   pre-print
On the other, we present a step-by-step guide to carry out the strategy developed to construct the liftings.  ...  On the one hand, it is a survey about the classification of finite-dimensional pointed Hopf algebras with abelian coradical, whose final step is the computation of the liftings or deformations of graded  ...  Both authors wish to thank him for his constant support and generosity along these years; most of the results in this note have been achieved in collaboration with him or motivated by him.  ... 
arXiv:1807.07154v2 fatcat:gt5o7emedrhellmhfvpuyom2mi

Sign-Based Construction Grammar: A guided tour

FRANK VAN EYNDE
2015 Journal of Linguistics  
This review gives a guided tour of the framework, explaining its central notions and assumptions, as well as the notation in which they are cast.  ...  Sign-Based Construction Grammar (sbcg) is, on the one hand, a formalized version of Berkeley Construction Grammar (bcg), and, on the other hand, a further development of constructionist Head-driven Phrase  ...  For this reason we start the guided tour with a look at the central notions of the framework, paying special attention to the way in which they are captured in formal notation.  ... 
doi:10.1017/s0022226715000341 fatcat:4jruwa5ujfcs5as5ocpyqexhhm

Noncommutative spectral geometry: A guided tour for theoretical physicists [article]

Mairi Sakellariadou
2012 arXiv   pre-print
We argue that the doubling of the algebra is intimately related to dissipation and the gauge field structure.  ...  The space-time geometry is described by the tensor product of a four-dimensional Riemanian manifold by a discrete noncommutative space consisting of only two points.  ...  |Ψ(τ) = exp iϕ − ī h τ 0 Ψ(t)|H|Ψ(t) dt |Ψ(0) = exp (−i2πn) |Ψ(0) , (3. (3.30) The index n signals the n dependence of the state and the corresponding energy.  ... 
arXiv:1204.5772v1 fatcat:cfvpjoeiuze4fnu4yayhutqbqi

Pointed Hopf algebras: a guided tour to the liftings

Iván Angiono, Agustín García Iglesias
2019 Revista Colombiana de Matemáticas  
On the other, we present a step-by-step guide to carry out the strategy developed to construct the liftings.  ...  This article serves a two-fold purpose.  ...  We thank the referee for a careful reading of this article and many useful remarks.  ... 
doi:10.15446/recolma.v53nsupl.83958 fatcat:zntjfgctkncdzfhwmai6pahywu

Two applications of the analytic conformal bootstrap: A quick tour guide [article]

Agnese Bissi, Parijat Dey, Giulia Fardelli
2021 arXiv   pre-print
We focus on two applications of the analytic conformal bootstrap: the study of the ϵ expansion of the Wilson Fisher model via the introduction of a dispersion relation and the large N expansion of maximally  ...  We review the recent developments in the study of conformal field theories in generic space time dimensions using the methods of the conformal bootstrap, in its analytic aspect.  ...  Norma Sanchez for inviting us to contribute with this review article to the Open Access Special Issue "Women Physicists  ... 
arXiv:2107.10097v2 fatcat:xa6g62oubjdnxdl24g5a3yaxya

How to tell a good tour guide under different strategic orientations

Leo Huang
2011 African Journal of Business Management  
A two-stage survey is employed to explore the performance measurement systems of tour guides and to build up a meaningful evaluating model.  ...  The second stage, rating and identifying the dimension attributes and building a model that also presents those cause-and-effect relationships among the four dimensions of tour guides' performance measurement  ...  ACKNOWLEDGEMENTS The author would like to thank the National Science Council of the Republic of China in Taiwan for financially supporting this research under Contract NSC98-2410-H-328-006-MY2.  ... 
doi:10.5897/ajbm11.1291 fatcat:wn7smjavmvcsvm5ezhekjc33vy
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