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Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…

Machine Learning · Statistics 2015-12-31 Ravi Ganti , Laura Balzano , Rebecca Willett

Due to challenging applications such as collaborative filtering, the matrix completion problem has been widely studied in the past few years. Different approaches rely on different structure assumptions on the matrix in hand. Here, we focus…

Machine Learning · Statistics 2019-10-14 Vincent Cottet , Pierre Alquier

In this work we propose a nonconvex two-stage \underline{s}tochastic \underline{a}lternating \underline{m}inimizing (SAM) method for sparse phase retrieval. The proposed algorithm is guaranteed to have an exact recovery from $O(s\log n)$…

Numerical Analysis · Mathematics 2022-11-23 Jian-Feng Cai , Yuling Jiao , Xiliang Lu , Juntao You

Fast matrix multiplication algorithms may be useful, provided that their running time is good in practice. Particularly, the leading coefficient of their arithmetic complexity needs to be small. Many sub-cubic algorithms have large leading…

Data Structures and Algorithms · Computer Science 2020-08-11 Gal Beniamini , Nathan Cheng , Olga Holtz , Elaye Karstadt , Oded Schwartz

The problem of low-rank matrix completion has recently generated a lot of interest leading to several results that offer exact solutions to the problem. However, in order to do so, these methods make assumptions that can be quite…

Machine Learning · Statistics 2014-07-14 Srinadh Bhojanapalli , Prateek Jain

The recovery of a low rank matrix from a subset of noisy low-precision quantized samples arises in several applications such as collaborative filtering, intelligent recommendation and millimeter wave channel estimation with few bit ADCs. In…

Information Theory · Computer Science 2019-11-25 Jiang Zhu , Zhennan Liu , Qi Zhang , Chunyi Song , Zhiwei Xu

Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…

Computational Complexity · Computer Science 2014-04-11 Moritz Hardt , Raghu Meka , Prasad Raghavendra , Benjamin Weitz

This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…

Information Theory · Computer Science 2016-11-15 Yudong Chen

This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…

Numerical Analysis · Computer Science 2018-10-03 Shashanka Ubaru , Yousef Saad

In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for…

Machine Learning · Statistics 2020-06-18 Lijun Ding , Yudong Chen

Matrix completion is often applied to data with entries missing not at random (MNAR). For example, consider a recommendation system where users tend to only reveal ratings for items they like. In this case, a matrix completion method that…

Machine Learning · Statistics 2019-10-30 Wei Ma , George H. Chen

We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm…

Data Structures and Algorithms · Computer Science 2015-04-30 Vitaly Feldman , Will Perkins , Santosh Vempala

In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…

Numerical Analysis · Mathematics 2008-08-03 Davod Khojasteh Salkuyeh , Faezeh Toutounian

This paper describes a novel approach of packing sparse convolutional neural networks for their efficient systolic array implementations. By combining subsets of columns in the original filter matrix associated with a convolutional layer,…

Machine Learning · Computer Science 2018-11-13 H. T. Kung , Bradley McDanel , Sai Qian Zhang

For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…

Optimization and Control · Mathematics 2020-12-02 Dongkai Li , Li Wang , Yuying Liu

In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…

Numerical Analysis · Mathematics 2024-03-12 Hongyaoxing Gu

Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…

Machine Learning · Statistics 2026-05-13 Jin Zhu , Junxian Zhu , Zezhi Wang , Borui Tang , Hongmei Lin , Xueqin Wang

Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…

Machine Learning · Computer Science 2021-09-20 Ruslan Khalitov , Tong Yu , Lei Cheng , Zhirong Yang

We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…

Numerical Analysis · Computer Science 2016-07-19 Yoshiyuki Kabashima , Florent Krzakala , Marc Mézard , Ayaka Sakata , Lenka Zdeborová

In prior work, Gupta et al. (SPAA 2022) presented a distributed algorithm for multiplying sparse $n \times n$ matrices, using $n$ computers. They assumed that the input matrices are uniformly sparse--there are at most $d$ non-zeros in each…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-05-24 Chetan Gupta , Janne H. Korhonen , Jan Studený , Jukka Suomela , Hossein Vahidi