Yuchen Zhou,Anru R Zhang,Lili Zheng et al.
Yuchen Zhou et al.
This paper studies a general framework for high-order tensor SVD. We propose a new computationally efficient algorithm, tensor-train orthogonal iteration (TTOI), that aims to estimate the low tensor-train rank structure from the noisy high-...
Fan Yang,Sifan Liu,Edgar Dobriban et al.
Fan Yang et al.
In our "big data" age, the size and complexity of data is steadily increasing. Methods for dimension reduction are ever more popular and useful. Two distinct types of dimension reduction are "data-oblivious" methods such as random projectio...
Levenshtein Distance, Sequence Comparison and Biological Database Search [0.03%]
列汶斯坦距离、序列比较及生物学数据库搜索
Bonnie Berger,Michael S Waterman,Yun William Yu
Bonnie Berger
Levenshtein edit distance has played a central role-both past and present-in sequence alignment in particular and biological database similarity search in general. We start our review with a history of dynamic programming algorithms for com...
Vinnu Bhardwaj,Pavel A Pevzner,Cyrus Rashtchian et al.
Vinnu Bhardwaj et al.
The problem of reconstructing a string from its error-prone copies, the trace reconstruction problem, was introduced by Vladimir Levenshtein two decades ago. While there has been considerable theoretical work on trace reconstruction, practi...
Botao Hao,Anru Zhang,Guang Cheng
Botao Hao
In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings. A two-stage non-convex implementation is developed based on sparse tensor decomposition and thresholded gradient descent, which e...
Randomized Linear Algebra Approaches to Estimate the Von Neumann Entropy of Density Matrices [0.03%]
随机线性代数方法估计密度矩阵的冯·诺伊曼熵
Eugenia-Maria Kontopoulou,Gregory-Paul Dexter,Wojciech Szpankowski et al.
Eugenia-Maria Kontopoulou et al.
The von Neumann entropy, named after John von Neumann, is an extension of the classical concept of entropy to the field of quantum mechanics. From a numerical perspective, von Neumann entropy can be computed simply by computing all eigenval...
Anru Zhang,Mengdi Wang
Anru Zhang
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain f...
Yoshimasa Uematsu,Yingying Fan,Kun Chen et al.
Yoshimasa Uematsu et al.
Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network ...
Rahul Jain,Carl A Miller,Yaoyun Shi
Rahul Jain
A prominent application of quantum cryptography is the distribution of cryptographic keys that are provably secure. Recently, such security proofs were extended by Vazirani and Vidick (Physical Review Letters, 113, 140501, 2014) to the devi...
Sparse Recovery Beyond Compressed Sensing: Separable Nonlinear Inverse Problems [0.03%]
压缩感知之外的稀疏恢复：可分离非线性逆问题
Brett Bernstein,Sheng Liu,Chrysa Papadaniil et al.
Brett Bernstein et al.
Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly on...