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Sparse PCA
Sparse principal component analysis (sparse PCA) is a specialised technique used in statistical analysis and, in particular, in the analysis of multivariate data sets. It extends the classic method of principal component analysis (PCA) for the reduction of dimensionality of data by introducing sparsity structures to the input variables. A particular disadvantage of ordinary PCA is that the principal components are usually linear combinations of all input variables. Sparse PCA overcomes this disadvantage by finding linear combinations that contain just a few input variables. Contemporary datasets often have the number of input variables (p) comparable with or even much larger than the number of samples (n). It has been shown that if p/n does not converge to zero, the classical PCA is not consistent. But sparse PCA can retain consistency even if p\gg n. Mathematical formulation Consider a data matrix, X, where each of the p columns represent an input variable, and each of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multivariate Analysis
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied. In addition, multivariate statistics is concerned with multivariate probability distributions, in terms of both :*how these can be used to represent the distributions of observed data; :*how they can be used as part of statistical inference, particularly where several different quantities are of interest to the same analysis. Certain types of problems involving multivariate data, for example simple linear regression an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-hard
In computational complexity theory, NP-hardness ( non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard problem is the subset sum problem. A more precise specification is: a problem ''H'' is NP-hard when every problem ''L'' in NP can be reduced in polynomial time to ''H''; that is, assuming a solution for ''H'' takes 1 unit time, ''H''s solution can be used to solve ''L'' in polynomial time. As a consequence, finding a polynomial time algorithm to solve any NP-hard problem would give polynomial time algorithms for all the problems in NP. As it is suspected that P≠NP, it is unlikely that such an algorithm exists. It is suspected that there are no polynomial-time algorithms for NP-hard problems, but that has not been proven. Moreover, the class P, in which all problems can be solved in polynomial time, is contained in the NP class. Def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planted Clique
In computational complexity theory, a planted clique or hidden clique in an undirected graph is a clique formed from another graph by selecting a subset of vertices and adding edges between each pair of vertices in the subset. The planted clique problem is the algorithmic problem of distinguishing random graphs from graphs that have a planted clique. This is a variation of the clique problem; it may be solved in quasi-polynomial time but is conjectured not to be solvable in polynomial time for intermediate values of the clique size. The conjecture that no polynomial time solution exists is called the planted clique conjecture; it has been used as a computational hardness assumption. Definition A clique in a graph is a subset of vertices, all of which are adjacent to each other. A planted clique is a clique created from another graph by adding edges between all pairs of a selected subset of vertices. The planted clique problem can be formalized as a decision problem over a random di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Statistics
The ''Annals of Statistics'' is a peer-reviewed statistics journal published by the Institute of Mathematical Statistics. It was started in 1973 as a continuation in part of the '' Annals of Mathematical Statistics (1930)'', which was split into the ''Annals of Statistics'' and the '' Annals of Probability''. The journal CiteScore is 5.8, and its SCImago Journal Rank is 5.877, both from 2020. Articles older than 3 years are available on JSTOR, and all articles since 2004 are freely available on the arXiv. Editorial board The following persons have been editors of the journal: * Ingram Olkin (1972–1973) * I. Richard Savage (1974–1976) * Rupert Miller (1977–1979) * David V. Hinkley (1980–1982) * Michael D. Perlman (1983–1985) * Willem van Zwet (1986–1988) * Arthur Cohen (1988–1991) * Michael Woodroofe (1992–1994) * Larry Brown and John Rice (1995–1997) * Hans-Rudolf Künsch and James O. Berger (1998–2000) * John Marden and Jon A. Wellner (2001–2003 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operations Research Letters
''Operations Research Letters'' is a bimonthly peer-reviewed academic journal covering operations research. It was established in 1981 and is published by Elsevier. The editor-in-chief is Wolfram Wiesemann. Abstracting and indexing The journal is indexed and abstracted An abstracting service is a service that provides abstracts of publications, often on a subject or group of related subjects, usually on a subscription basis. An indexing service is a service that assigns descriptors and other kinds of access poi ... in: References External links *{{Official website, https://www.journals.elsevier.com/operations-research-letters Industrial engineering journals Elsevier academic journals English-language journals Bimonthly journals Academic journals established in 1981 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Set
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex region is a subset that intersects every line into a single line segment (possibly empty). For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex. The boundary of a convex set is always a convex curve. The intersection of all the convex sets that contain a given subset of Euclidean space is called the convex hull of . It is the smallest convex set containing . A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semidefinite Programming
Semidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron. Semidefinite programming is a relatively new field of optimization which is of growing interest for several reasons. Many practical problems in operations research and combinatorial optimization can be modeled or approximated as semidefinite programming problems. In automatic control theory, SDPs are used in the context of linear matrix inequalities. SDPs are in fact a special case of cone programming and can be efficiently solved by interior point methods. All linear programs and (convex) quadratic programs can be expressed as SDPs, and via hierarchies of SDPs the solutions of polynomial optimization problems can be approximated. Semidefinite programming has been ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The IEEE
The ''Proceedings of the IEEE'' is a monthly peer review, peer-reviewed scientific journal published by the Institute of Electrical and Electronics Engineers (IEEE). The journal focuses on electrical engineering and computer science. According to the ''Journal Citation Reports'', the journal has a 2017 impact factor of 9.107, ranking it sixth in the category "Engineering, Electrical & Electronic." In 2018, it became fifth with an enhanced impact factor of 10.694. History of the Proceedings The journal was established in 1909, known as the ''Proceedings of the Wireless Institute''. Six issues were published under this banner by Greenleaf Pickard and Alfred Goldsmith. Then in 1911, a merger between the Wireless Institute (New York) and the Society of Wireless Telegraph Engineers (Boston) resulted in a society named the Institute of Radio Engineers (IRE). In January 1913 newly formed IRE published the first issue of the ''Proceedings of the IRE''. Later, a 1000-page special issue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Machine Learning Research Workshop And Conference Proceedings
A journal, from the Old French ''journal'' (meaning "daily"), may refer to: *Bullet journal, a method of personal organization *Diary, a record of what happened over the course of a day or other period *Daybook, also known as a general journal, a daily record of financial transactions * Logbook, a record of events important to the operation of a vehicle, facility, or otherwise * Record (other) *Transaction log, a chronological record of data processing *Travel journal In publishing, ''journal'' can refer to various periodicals or serials: *Academic journal, an academic or scholarly periodical ** Scientific journal, an academic journal focusing on science ** Medical journal, an academic journal focusing on medicine **Law review, a professional journal focusing on legal interpretation * Magazine, non-academic or scholarly periodicals in general **Trade magazine, a magazine of interest to those of a particular profession or trade ** Literary magazine, a magazine devoted to l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Programming Computation
The Mathematical Optimization Society (MOS), known as the Mathematical Programming Society until 2010, . is an international association of researchers active in . The MOS encourages the research, development, and use of optimization—including , [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization And Engineering
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Machine Learning Research
The ''Journal of Machine Learning Research'' is a peer-reviewed open access scientific journal covering machine learning. It was established in 2000 and the first editor-in-chief was Leslie Kaelbling Leslie Pack Kaelbling is an American roboticist and the Panasonic Professor of Computer Science and Engineering at the Massachusetts Institute of Technology. She is widely recognized for adapting partially observable Markov decision process from .... The current editors-in-chief are Francis Bach ( Inria) and David Blei ( Columbia University). History The journal was established as an open-access alternative to the journal ''Machine Learning''. In 2001, forty editorial board members of ''Machine Learning'' resigned, saying that in the era of the Internet, it was detrimental for researchers to continue publishing their papers in expensive journals with pay-access archives. The open access model employed by the ''Journal of Machine Learning Research'' allows authors to publish ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
