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- ...'' is a paradigm for analyzing data that combines the ideas of [[dimension reduction]] with the concept of [[sufficient statistic|sufficiency]]. ...yalsocietypublishing.org/content/367/1906/4385.full ''Sufficient Dimension Reduction and Prediction in Regression''] In: ''Philosophical Transactions of the Roy ...12 KB (1,824 words) - 00:36, 15 May 2024
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- ...'' is a paradigm for analyzing data that combines the ideas of [[dimension reduction]] with the concept of [[sufficient statistic|sufficiency]]. ...yalsocietypublishing.org/content/367/1906/4385.full ''Sufficient Dimension Reduction and Prediction in Regression''] In: ''Philosophical Transactions of the Roy ...12 KB (1,824 words) - 00:36, 15 May 2024
- ...ield|local]] or [[global field]] ''F'' is a measure of how "bad" the [[bad reduction]] at some prime is. It is connected to the [[Ramification (mathematics)|ra ...</sub>'' be the dimension of the unipotent group and ''t<sub>P</sub>'' the dimension of the torus. The order of the conductor at ''P'' is ...4 KB (640 words) - 18:56, 7 July 2020
- {{Short description|Method for dimension reduction in statistics}} ...|first=Ker-Chau |date=1991 |title=Sliced Inverse Regression for Dimension Reduction |url=https://www.jstor.org/stable/2290563 |journal=Journal of the American ...8 KB (1,285 words) - 18:11, 25 March 2024
- The reduction theory goes back to the influential 1954 paper by Northcott and Rees, the p Given ideals ''J'' ⊂ ''I'' in a ring ''R'', the ideal ''J'' is said to be a ''reduction'' of ''I'' if there is some integer ''m'' > 0 such that <math>JI^m = I^{m+1 ...3 KB (421 words) - 23:49, 12 August 2023
- ===Petrov-Galerkin dimension reduction=== ...>V_n \subset V</math> of dimension ''n'' and <math>W_m \subset W</math> of dimension ''m'' and solve the projected problem: ...4 KB (775 words) - 15:53, 31 August 2024
- If <math>V</math> is of finite [[dimension (vector space)|dimension]] <math>r</math> and <math>W</math> is a reducing subspace of the map <math ...book|author=R. Dennis Cook|title=An Introduction to Envelopes : Dimension Reduction for Efficient Estimation in Multivariate Statistics|publisher=Wiley|year=20 ...2 KB (393 words) - 02:13, 22 October 2023
- ...n]]s interacting via [[four fermion interaction]]s in 3 spatial and 1 time dimension. It was introduced in 1938 by [[Dmitri Ivanenko]] In one dimension, ...5 KB (745 words) - 11:43, 7 March 2023
- ...ther fixed simplicial complex. The problem is undecidable for complexes of dimension 5 or more.<ref>{{citation |last=Stillwell |first=John |title=Classical Topo * If the complexes are of dimension at most 3, then the problem is decidable. This follows from the proof of th ...4 KB (568 words) - 17:59, 29 January 2024
- ...case when the [[implicit function theorem]] does not work. It permits the reduction of infinite-dimensional equations in Banach spaces to finite-dimensional eq ...ator <math> f_x(x,\lambda) </math> is non-invertible, the Lyapunov–Schmidt reduction can be applied in the following ...6 KB (822 words) - 01:19, 22 May 2021
- ...im(R/P)=\dim R</math>; otherwise <math>\dim R[It]=\dim R</math>. The Krull dimension of the extended Rees algebra is <math>\dim R[It, t^{-1}]=\dim R+1</math>.<r ...R[It]</math> is [[Integral extension|integral]] if and only if ''J'' is a reduction of ''I''.<ref name=":0" /> ...3 KB (553 words) - 13:49, 23 January 2025
- '''Maximally informative dimensions''' is a [[dimensionality reduction]] technique used in the statistical analyses of [[neural coding|neural resp ...<math>\mathbf{v}</math>. Under this formulation, the relevant subspace of dimension <math>K = 1</math> would be defined by the direction <math>\mathbf{v}</math ...5 KB (799 words) - 18:39, 18 June 2024
- ...a theory of gravity with [[dilaton]] coupling in one spatial and one time dimension. It should not be confused<ref>{{cite journal | last1 = Grumiller | first1 ...2=Xiangdong|last3=Mann|first3=Robert|last4=Fee|first4=G.J.|title=Canonical reduction for dilatonic gravity in 3 + 1 dimensions|journal=[[Physical Review D]]|vol ...3 KB (397 words) - 14:17, 19 February 2025
- ...e plane is monostatic. This was shown by [[Vladimir Arnold|V. Arnold]] via reduction to the [[four-vertex theorem]]. ...are no monostatic [[simplex|simplices]] in dimension up to eight. In three-dimension, this is due to Conway. In dimensions up to six, this is due to R. J.& ...4 KB (587 words) - 07:01, 23 February 2025
- ...tatistics, '''random projection''' is a technique used to [[dimensionality reduction|reduce the dimensionality]] of a set of points which lie in [[Euclidean spa | title = Random projection in dimensionality reduction: Applications to image and text data ...14 KB (1,913 words) - 06:45, 22 January 2025
- ...nce to hold. Roughly, if the event-family is sufficiently simple (its [[VC dimension]] is sufficiently small) then uniform convergence holds. Here "simple" means that the [[Vapnik–Chervonenkis dimension]] of the class <math>H</math> is small relative to the size of the sample. ...13 KB (2,287 words) - 18:32, 13 May 2024
- ...re]]. The Consani–Scholton quintic provides a non-rigid example, where the dimension is four. Consani and Scholten constructed a [[Hilbert modular form]] and co ...4 KB (495 words) - 02:48, 23 June 2024
- ...tem, and therefore motivates the use of SSMs in [[nonlinear dimensionality reduction]]. SSMs are chiefly employed for the exact model reduction of dynamical systems. For the automated computation of SSMs and the analysi ...8 KB (1,095 words) - 19:09, 12 November 2024
- ...\min(n_1, n_2, n_3)</math>, which can be effective when the difference in dimension sizes is large. [[Category:Dimension reduction]] ...5 KB (703 words) - 02:33, 17 May 2024
- ===Reduction to the nilpotent case=== .../math> is a [[nilpotent matrix]], and <math>[D,N]=0</math>, justifying the reduction of <math>N</math> into subblocks <math>N_i</math>. So the problem of reduci ...14 KB (2,096 words) - 00:27, 31 January 2025
- ...ows that the zeta function of {{mvar|X}} is the product of the ones of the reduction of {{mvar|X}} modulo the primes {{mvar|p}}: ...[[bad reduction]]). For almost all primes, namely when {{mvar|X}} has good reduction, the Euler factor is known to agree with the corresponding factor of the [[ ...11 KB (1,734 words) - 08:16, 2 February 2025