Filters








2,461,938 Hits in 3.6 sec

Randomized Model Order Reduction [article]

Alessandro Alla, J. Nathan Kutz
2016 arXiv   pre-print
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

Simon Thomas
1996 Annals of Pure and Applied Logic  
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]

Anaïs Vergne, Philippe Martins
2017 arXiv   pre-print
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]

Nabil Kahale
2018 arXiv   pre-print
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]

Antonio Campello
2018 arXiv   pre-print
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]

Zhiyan Ding, Qin Li
2021 arXiv   pre-print
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

Andreas Buhr, Kathrin Smetana
2018 SIAM Journal on Scientific Computing  
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]

Tianbao Yang, Lijun Zhang, Rong Jin, Shenghuo Zhu
2015 arXiv   pre-print
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

Laurent Bienvenu, Christopher Porter
2012 Theoretical Computer Science  
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

Ella Bingham, Heikki Mannila
2001 Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '01  
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]

Andreas Blass, Yuri Gurevich
1991 Lecture Notes in Computer Science  
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]

Rishi Advani, Madison Crim, Sean O'Hagan
2020 arXiv   pre-print
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

Andreas Blass, Yuri Gurevich
1993 SIAM journal on computing (Print)  
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]

Yaniv Plan, Roman Vershynin
2013 arXiv   pre-print
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]

Stoyan Georgiev, Sayan Mukherjee
2013 arXiv   pre-print
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
« Previous Showing results 1 — 15 out of 2,461,938 results