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Randomized Model Order Reduction
[article]
2016
arXiv
pre-print
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Singular value decomposition (SVD) has a crucial role in model order reduction. ...
The aim of this work is to provide efficient computation of the basis functions via randomized matrix decompositions. ...
Randomized Linear Algebra in Model Order Reduction Randomized linear algebra is of growing importance for the analysis of highdimensional data [24] . ...
arXiv:1611.02316v1
fatcat:s6xmikzixjfvtbez5acgz6x65e
Reducts of random hypergraphs
1996
Annals of Pure and Applied Logic
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We shall also show that each of the associated reducts of rk is homogeneous with respect to a finite relational language. ...
In [ 121, I studied the reducts of the random graph r= (V;E); i.e. the countable universal homogeneous graph. ...
For each k B 1, rk will denote the countable universal homogeneous k-graph. r, is also called the random k-graph. ...
doi:10.1016/0168-0072(95)00061-5
fatcat:fk4h4km2brc7zaizt44ijlftae
Random Abstract Simplicial Complexes Reduction
[article]
2017
arXiv
pre-print
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Random abstract simplicial complex representation provides a mathematical description of wireless networks and their topology. ...
In this paper, we present a reduction algorithm that lower the number of points of an abstract simplicial complex in an optimal order while maintaining its topology. ...
Then the reduction algorithm and its properties are described in Section III. The complexity of the algorithm is investigated for a random set of points in Section IV. ...
arXiv:1312.1658v3
fatcat:flniuixbjrh6rjms322ek4zdoa
Randomized Dimension Reduction for Monte Carlo Simulations
[article]
2018
arXiv
pre-print
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We present a new unbiased algorithm that estimates the expected value of f(U) via Monte Carlo simulation, where U is a vector of d independent random variables, and f is a function of d variables. ...
Deterministic dimension reduction This section studies a deterministic dimension reduction algorithm that performs the same steps as the generic randomized dimension reduction algorithm of §2.1, but uses ...
The sequence (N k ) can thus be considered as a deterministic counterpart to the random sequence (N k ) generated by the randomized dimension reduction algorithm when q =q. ...
arXiv:1708.07466v3
fatcat:yo7bvac36nbzbaxnejvn3uuteu
Random Ensembles of Lattices from Generalized Reductions
[article]
2018
arXiv
pre-print
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In this work we investigate general random lattices obtained from error correcting codes. ...
CONSTRUCTIONS FROM NUMBER FIELDS From now on we consider constructions of random ensembles based on algebraic number theory. ...
arXiv:1702.00608v3
fatcat:pizujefcwbccvnkrx4qmlc7uni
Langevin Monte Carlo: random coordinate descent and variance reduction
[article]
2021
arXiv
pre-print
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2021 pre-print arXiv:2007.14209v7 fatcat:lsdusi3e3jd2pgirrfc3nf6zw4Other Versions
In this paper, we investigate how to enhance computational efficiency through the application of RCD (random coordinate descent) on LMC. ...
Ultimately there is no computational gain; 2 We then incorporate variance reduction techniques, such as SAGA (stochastic average gradient) and SVRG (stochastic variance reduced gradient), into RCD-LMC. ...
Any new variance reduction method, when cast into the random coordinate LMC framework, can be analyzed in a similar fashion. ...
arXiv:2007.14209v8
fatcat:sbfj4m7dwzg3te26ary2s7ghfi
Randomized Local Model Order Reduction
2018
SIAM Journal on Scientific Computing
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In this paper, we propose an adaptive randomized algorithm based on methods from randomized linear algebra [N. ...
In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. ...
Jonas Ballani of Akselos for the fruitful discussion on randomized linear algebra at the MoRePaS workshop 2015 in Trieste. Moreover, we are grateful to Dr. ...
doi:10.1137/17m1138480
fatcat:v73ewv7rtncz7adpeejaz75rgm
Theory of Dual-sparse Regularized Randomized Reduction
[article]
2015
arXiv
pre-print
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In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale ...
To address these limitations, we propose dual-sparse regularized randomized reduction methods that introduce a sparse regularizer into the reduced dual problem. ...
In this paper, we focus on the latter technique and refer to randomized feature reduction as randomized reduction for short. ...
arXiv:1504.03991v4
fatcat:iobaemmvl5c4fchsvamkfw2wpq
Strong reductions in effective randomness
2012
Theoretical Computer Science
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We study generalizations of Demuth's Theorem, which states that the image of a Martin-Löf random real under a tt-reduction is either computable or Turing equivalent to a Martin-Löf random real. ...
We show that Demuth's Theorem holds for Schnorr randomness and computable randomness (answering a question of Franklin), but that it cannot be strengthened by replacing the Turing equivalence in the statement ...
Strong reductions and induced measures Strong reductions play a central role in the discussion that follows, and more generally in the study of effective randomness. ...
doi:10.1016/j.tcs.2012.06.031
fatcat:xvctlday7zaubplrx2pmklgzwu
Random projection in dimensionality reduction
2001
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '01
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Random projections have recently emerged as a powerful method for dimensionality reduction. ...
We present experimental results on using random projection as a dimensionality reduction tool in a number of cases, where the high dimensionality of the data would otherwise lead to burdensome computations ...
In both application areas, random projection is compared to well known dimensionality reduction methods. ...
doi:10.1145/502512.502546
fatcat:q3ifxgmpnfe35mpvbvcdfvdgky
Randomizing reductions of search problems
[chapter]
1991
Lecture Notes in Computer Science
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All reductions of search problems to search problems in the literature on average case complexity can be viewed as such m a n y-one randomizing reductions this includes those reductions in the literature ...
Second, we give a general and usable notion of many-one randomizing reductions of search problems and prove that it has desirable properties. ...
Randomizing Many-One Reductions. Let us clarify the notion of composition M = M 2 M 1 of randomizing algorithms. ...
doi:10.1007/3-540-54967-6_58
fatcat:offpyqtfdrc7neqnmz4retqjxa
Random Projections and Dimension Reduction
[article]
2020
arXiv
pre-print
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One solution to these problems is the use of random projections. ...
Compared to standard approaches, random algorithms are often faster and more robust. With these randomized algorithms, analyzing massive data sets becomes tractable. ...
Conclusion Randomization is a powerful tool in low-rank matrix factorization and dimension reduction. ...
arXiv:2008.04552v1
fatcat:3gxsrk374fekroyln4sg3duewi
Randomizing Reductions of Search Problems
1993
SIAM journal on computing (Print)
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All reductions of search problems to search problems in the literature on average case complexity can be viewed as such m a n y-one randomizing reductions this includes those reductions in the literature ...
Second, we give a general and usable notion of many-one randomizing reductions of search problems and prove that it has desirable properties. ...
Randomizing Many-One Reductions. Let us clarify the notion of composition M = M 2 M 1 of randomizing algorithms. ...
doi:10.1137/0222059
fatcat:5qpcba5x55fbveiiyrlevo4jsa
Dimension reduction by random hyperplane tessellations
[article]
2013
arXiv
pre-print
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Since for many sets K one has m = m(K) << n, this yields a new discrete mechanism of dimension reduction for sets in Euclidean spaces. ...
Random hyperplanes prove to be almost ideal for this problem; they achieve the almost optimal bound m = O(w(K)^2) where w(K) is the Gaussian mean width of K. ...
Remark 2.2 (Random matrix formulation). One can state Lemma 2.1 in terms of random matrices. Indeed, let A be an m×n random matrix with independent N (0, 1) entries. ...
arXiv:1111.4452v2
fatcat:jnisswmfxbey5fl7xssji2so3u
Randomized Dimension Reduction on Massive Data
[article]
2013
arXiv
pre-print
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We adapt recent randomized low-rank approximation algorithms to provide efficient solutions to three dimension reduction methods: Principal Component Analysis (PCA), Sliced Inverse Regression (SIR), and ...
A key observation in this paper is that randomization serves a dual role, improving both computational and statistical performance. ...
Randomized algorithms for dimension reduction We will develop randomized algorithms for four dimension reduction methods: PCA, SIR, LSIR, and LPP. ...
arXiv:1211.1642v2
fatcat:yng6gl63dzc4za37qlvl3ogpwe
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