Nonconvex optimization meets low-rank matrix factorization: An overview
Substantial progress has been made recently on develo** provably accurate and efficient
algorithms for low-rank matrix factorization via nonconvex optimization. While conventional …
algorithms for low-rank matrix factorization via nonconvex optimization. While conventional …
Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
Low-rank matrix approximations, such as the truncated singular value decomposition and
the rank-revealing QR decomposition, play a central role in data analysis and scientific …
the rank-revealing QR decomposition, play a central role in data analysis and scientific …
Recovering gene interactions from single-cell data using data diffusion
Single-cell RNA sequencing technologies suffer from many sources of technical noise,
including under-sampling of mRNA molecules, often termed" dropout," which can severely …
including under-sampling of mRNA molecules, often termed" dropout," which can severely …
Randomized numerical linear algebra: Foundations and algorithms
This survey describes probabilistic algorithms for linear algebraic computations, such as
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …
Spectral methods for data science: A statistical perspective
Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …
A quantum-inspired classical algorithm for recommendation systems
We give a classical analogue to Kerenidis and Prakash's quantum recommendation system,
previously believed to be one of the strongest candidates for provably exponential speedups …
previously believed to be one of the strongest candidates for provably exponential speedups …
An introduction to matrix concentration inequalities
Random matrices now play a role in many areas of theoretical, applied, and computational
mathematics. Therefore, it is desirable to have tools for studying random matrices that are …
mathematics. Therefore, it is desirable to have tools for studying random matrices that are …
Quantum recommendation systems
A recommendation system uses the past purchases or ratings of $ n $ products by a group of
$ m $ users, in order to provide personalized recommendations to individual users. The …
$ m $ users, in order to provide personalized recommendations to individual users. The …
q-means: A quantum algorithm for unsupervised machine learning
Quantum information is a promising new paradigm for fast computations that can provide
substantial speedups for many algorithms we use today. Among them, quantum machine …
substantial speedups for many algorithms we use today. Among them, quantum machine …
The Optimal Hard Threshold for Singular Values is
We consider recovery of low-rank matrices from noisy data by hard thresholding of singular
values, in which empirical singular values below a threshold λ are set to 0. We study the …
values, in which empirical singular values below a threshold λ are set to 0. We study the …