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A Rank-1 Sketch for Matrix Multiplicative Weights [article]

Yair Carmon, John C. Duchi, Aaron Sidford, Kevin Tian
2019 arXiv   pre-print
We show that a simple randomized sketch of the matrix multiplicative weight (MMW) update enjoys (in expectation) the same regret bounds as MMW, up to a small constant factor.  ...  Unlike MMW, where every step requires full matrix exponentiation, our steps require only a single product of the form e^A b, which the Lanczos method approximates efficiently.  ...  A rank-1 sketch of matrix multiplicative weights In this section, we state and prove our main result: regret bounds for a rank-1 sketch of the matrix multiplicative weights method.  ... 
arXiv:1903.02675v2 fatcat:wy6xx3abxbhqlj3xbgixmkdsg4

Multiplicative Perturbation Bounds for Multivariate Multiple Linear Regression in Schatten p-Norms [article]

Jocelyn T. Chi, Ilse C. F. Ipsen
2020 arXiv   pre-print
We also present a geometric interpretation of the action of the sketching matrix in terms of relevant subspaces.  ...  We extend recent MLR analyses to sketched MMLR in general Schatten p-norms by interpreting the sketched problem as a multiplicative perturbation.  ...  becomes the exact MMLR problem in (1). If d = 1 and p = 2 in (2), the oblique projector P appears in [39] if rank(SA) = rank(A) and in [9, Lemma 3.1] for any sketching matrix S.  ... 
arXiv:2007.06099v1 fatcat:vea5vuujrnc3ngjop33b53mcju

SBG-Sketch: A Self-Balanced Sketch for Labeled-Graph Stream Summarization [article]

Mohamed S. Hassan, Bruno Ribeiro, Walid G. Aref
2017 arXiv   pre-print
SBG-Sketch maintains synopsis for both the edge attributes (e.g., edge weight) as well as the topology of the streamed graph.  ...  This paper introduces Self-Balanced Graph Sketch (SBG-Sketch, for short), a graphical sketch for summarizing and querying labeled-graph streams that can cope with all these challenges.  ...  1 for Matrix M2.  ... 
arXiv:1709.06723v1 fatcat:sbmk3vcmrff2fctenfdoggvfra

Regularized Weighted Low Rank Approximation [article]

Frank Ban, David Woodruff, Qiuyi Zhang
2019 arXiv   pre-print
A previous paper of [Razenshteyn et al. '16] derived a polynomial time algorithm for weighted low rank approximation with constant rank.  ...  The classical low rank approximation problem is to find a rank k matrix UV (where U has k columns and V has k rows) that minimizes the Frobenius norm of A - UV.  ...  In one version of this problem, where the parameter r corresponds to the rank of the weight matrix W , we are given a matrix M ∈ R n×d , a weight matrix W ∈ R n×d with rank r, and a target integer k >  ... 
arXiv:1911.06958v2 fatcat:o2nsmiljdradhmzfmbyfsrx2da

Cross-domain correspondence for sketch-based 3D model retrieval using convolutional neural network and manifold ranking

Shichao Jiao, Xie Han, Fengguang Xiong, Fusheng Sun, Rong Zhao, Liqun Kuang
2020 IEEE Access  
To address these problems, we propose cross-domain correspondence method for sketch-based 3D model retrieval based on manifold ranking.  ...  Some stateof-the-art approaches usually extract features from 2D sketches and produce multiple projection views of 3D models, and then select one view of 3D models to match sketch.  ...  For the retrieval result through multiple sketches, it is computed by assigning different weights to the relevance value lists of given sketches.  ... 
doi:10.1109/access.2020.3006585 fatcat:mr5hempqoff4zegqasz73qvor4

Visual Saliency Weighting and Cross-Domain Manifold Ranking for Sketch-Based Image Retrieval [chapter]

Takahiko Furuya, Ryutarou Ohbuchi
2014 Lecture Notes in Computer Science  
To effectively compare the sketch containing stroke noise with database images, we employ Cross-Domain Manifold Ranking (CDMR), a manifold-based distance metric learning algorithm.  ...  A Sketch-Based Image Retrieval (SBIR) algorithm compares a linedrawing sketch with images. The comparison is made difficult by image background clutter.  ...  We normalize W for S by using the following equation; 2 1 2 1    WD D S (3) where D is a diagonal matrix whose diagonal element is   j ij ii W D .  ... 
doi:10.1007/978-3-319-04114-8_4 fatcat:wnqnzuu5eja5tabf6zrn7aq7vq

Probabilistic Tensors and Opportunistic Boolean Matrix Multiplication [chapter]

Matti Karppa, Petteri Kaski
2019 Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms  
While this enables an approach to obtaining asymptotically faster algorithm designs for matrix multiplication via the Cohn-Umans inequality ω ≤ 3 2 ω s − 1, the main motivation for the present paper is  ...  Asymptotically, we use Adleman's argument to show that, over the complex field, the support rank exponent ω s of matrix multiplication [H. Cohn and C.  ...  We are grateful to Andreas Björklund for useful discussions and to the anonymous reviewers for their remarks that helped to improve this paper.  ... 
doi:10.1137/1.9781611975482.31 dblp:conf/soda/KarppaK19 fatcat:wizpl45yo5g67kztzcnf33lhji

Fast Matrix Multiplication with Sketching [article]

Huan Wang, Christos Boutsidis, Edo Liberty, Daniel Hsu
2014 arXiv   pre-print
We present an approximate algorithm for matrix multiplication based on matrix sketching techniques.  ...  First one of the matrix is chosen and sparsified using the online matrix sketching algorithm, and then the matrix product is calculated using the sparsified matrix.  ...  In [4] [6] , the matrix product is decomposed into the sum of a series of rank-1 matrices AB T = m i=1 a i b T i (18) Then a weighted non-uniform sampling procedure is designed to sample the rank-1  ... 
arXiv:1406.2648v2 fatcat:xktps5ojcjds7kalswidkasgam

Weighted low rank approximations with provable guarantees

Ilya Razenshteyn, Zhao Song, David P. Woodruff
2016 Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2016  
Inspired by practical applications, we consider a weighted version of low rank approximation: for a non-negative weight matrix W we seek to minimize i,j (Wi,j ·(Ai,j −Bi,j)) 2 .  ...  The classical problem is a special case of this problem when all weights are 1.  ...  Landsberg, Ankur Moitra, Daniel Perrucci, Eric Price, James Renegar, Tselil Schramm, Elias Tsigaridas, Ryan Williams, and David Zuckerman for useful discussions.  ... 
doi:10.1145/2897518.2897639 dblp:conf/stoc/RazenshteynSW16 fatcat:pt66crfa45ertiljzqyteejma4

Sparse PCA via Bipartite Matchings [article]

Megasthenis Asteris, Dimitris Papailiopoulos, Anastasios Kyrillidis, Alexandros G. Dimakis
2015 arXiv   pre-print
We present a novel algorithm for sparse PCA that jointly optimizes multiple disjoint components.  ...  Its complexity grows as a low order polynomial in the ambient dimension of the input data matrix, but exponentially in its rank.  ...  This research has been supported by NSF Grants CCF 1344179, 1344364, 1407278, 1422549 and ARO YIP W911NF-14-1-0258.  ... 
arXiv:1508.00625v1 fatcat:pni54bdl3ffxpfju4xcfan6tsm

Deterministic algorithms for skewed matrix products [article]

Konstantin Kutzkov
2012 arXiv   pre-print
j |C_ij| is the entrywise 1-norm of a matrix C and Sort(n) is the time required to sort n real numbers in linear space.  ...  The algorithm is clearly outperformed by randomized matrix multiplication algorithms, but as a byproduct we obtain the first O(n^2 + ε)-time deterministic algorithm for matrix products with O(√(n)) nonzero  ...  I would like to thank my supervisor Rasmus Pagh for his continuous support and many valuable comments and suggestions.  ... 
arXiv:1209.4508v1 fatcat:bkbwpion4naffpabo2evlfbini

Ranking on Cross-Domain Manifold for Sketch-Based 3D Model Retrieval

Takahiko Furuya, Ryutarou Ohbuchi
2013 2013 International Conference on Cyberworlds  
Sketch-based 3D model retrieval algorithms compare a query, a line drawing sketch, and 3D models for similarity by rendering the 3D models into line drawing-like images.  ...  Given a query sketch, similarity ranks of 3D models are computed by diffusing relevance value from the sketch over the CDM.  ...  We normalize W by using the following equation; (4) where D is a diagonal matrix whose diagonal element is 2 1 2 1    WD D S . ii ij j   D W We use the following equation to find rank values in  ... 
doi:10.1109/cw.2013.60 dblp:conf/cw/FuruyaO13 fatcat:ubho53um2rg47kxo7nal5gea3e

Sketching Curvature for Efficient Out-of-Distribution Detection for Deep Neural Networks [article]

Apoorva Sharma and Navid Azizan and Marco Pavone
2021 arXiv   pre-print
Offline, given a trained model and its training data, SCOD employs tools from matrix sketching to tractably compute a low-rank approximation of the Fisher information matrix, which characterizes which  ...  Building on recent work leveraging the local curvature of DNNs to reason about epistemic uncertainty, we propose Sketching Curvature of OoD Detection (SCOD), an architecture-agnostic framework for equipping  ...  The authors wish to thank Robin Brown and Edward Schmerling for helpful input and discussions during the development of these ideas.  ... 
arXiv:2102.12567v1 fatcat:5qbmsmiornhlbehj7l56wnabna

Sharper Bounds for Regularized Data Fitting [article]

Haim Avron and Kenneth L. Clarkson and David P. Woodruff
2017 arXiv   pre-print
We study matrix sketching methods for regularized variants of linear regression, low rank approximation, and canonical correlation analysis.  ...  For example, we obtain sketching-based algorithms for the low-rank approximation problem _X,Y YX - A _F^2 + f(Y,X) where f(·,·) is a regularizing function satisfying some very general conditions (chiefly  ...  Here for matrix A, its sketch is SA, where S is a sketching matrix.  ... 
arXiv:1611.03225v2 fatcat:gawk6jc7fzafdhvi5nvbtdk3x4

Approximate Weighted CR Coded Matrix Multiplication [article]

Neophytos Charalambides, Mert Pilanci, Alfred Hero
2020 arXiv   pre-print
We present a novel approximate weighted CR coded matrix multiplication scheme, that achieves improved performance for distributed matrix multiplication.  ...  With the rapid development of machine learning and increases in data volume, performing fast matrix intensive multiplications has become a major hurdle.  ...  The CR-multiplication scheme produces a low-rank approximate matrix product [8] [9] [10] .  ... 
arXiv:2011.09709v1 fatcat:q7vmkei5nra5nkwzvapo6oipuu
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