wanyu/IteraTeR_v2 huggingface dataset:
Original:  This problem is also known as matrix completion and, depending on the choice of W, captures low-rank plus diagonal decomposition, robust PCA,  low-rank recovery from monotone missing data, and a number of other important problems.
Revised:  This problem is also known as matrix completion and, depending on the choice of W, captures low-rank plus diagonal decomposition, robust PCA, matrix completion, low-rank recovery from monotone missing data, and a number of other important problems.
Edit intent: coherence
Original:  This problem is also known as matrix completion and, depending on the choice of W, captures low-rank plus diagonal decomposition, robust PCA,  low-rank recovery from monotone missing data, and a number of other important problems.
Revised:  This problem is also known as matrix completion and, depending on the choice of W, captures low-rank plus diagonal decomposition, robust PCA, low-rank recovery from monotone missing data, and many other problems.
Edit intent: clarity
Original:  Many of these problems are NP-hard, and while  algorithms with provable guarantees are known in some cases , they either 1) run in time n^{\Omega(k^2/\epsilon)}, or 2) make strong assumptions, e.g., that A is incoherent or that W is random.
Revised:  Many of these problems are NP-hard, and while some algorithms with provable guarantees are known in some cases , they either 1) run in time n^{\Omega(k^2/\epsilon)}, or 2) make strong assumptions, e.g., that A is incoherent or that W is random.
Edit intent: clarity
Original:  Many of these problems are NP-hard, and while  algorithms with provable guarantees are known in some cases , they either 1) run in time n^{\Omega(k^2/\epsilon)}, or 2) make strong assumptions, e.g., that A is incoherent or that W is random.
Revised:  Many of these problems are NP-hard, and while algorithms with provable guarantees are known , they either 1) run in time n^{\Omega(k^2/\epsilon)}, or 2) make strong assumptions, e.g., that A is incoherent or that W is random.
Edit intent: clarity
Original:  In this work, we consider bicriteria\ algorithms, which output L with rank k' > k.
Revised:  We consider bicriteria\ algorithms, which output L with rank k' > k.
Edit intent: clarity
Original:  We prove a similar bound using the randomized communication complexity with 2-sided error.
Edit intent: coherence
Original: In masked  low-rank approximation, given A \in R^{n \times n} and binary  W \in \{0,1\}^{n \times n} , the goal is to find a rank-k matrix L for which: cost(L) = i=1^{n} j = 1^{n} W_{i,j} \cdot (A_{i,j} - L_{i,j} )^2 %DIFDELCMD < \le %%%  OPT + \epsilon \|A\|_F^2 , where OPT = rank-k\ \hat{L} cost(\hat L) .
Revised: In masked \ low-rank approximation, given A \in R^{n \times n} and binary W \in \{0,1\}^{n \times n} , the goal is to find a rank-k matrix L for which: cost(L) = i=1^{n} j = 1^{n} W_{i,j} \cdot (A_{i,j} - L_{i,j} )^2 %DIFDELCMD < \le %%% OPT + \epsilon \|A\|_F^2 , where OPT = rank-k\ \hat{L} cost(\hat L) .
Edit intent: fluency
Original: In masked  low-rank approximation, given A \in R^{n \times n} and binary  W \in \{0,1\}^{n \times n} , the goal is to find a rank-k matrix L for which: cost(L) = i=1^{n} j = 1^{n} W_{i,j} \cdot (A_{i,j} - L_{i,j} )^2 %DIFDELCMD < \le %%%  OPT + \epsilon \|A\|_F^2 , where OPT = rank-k\ \hat{L} cost(\hat L) .
Revised: In masked low-rank \ approximation, one is given A \in R^{n \times n} and binary W \in \{0,1\}^{n \times n} , the goal is to find a rank-k matrix L for which: cost(L) = i=1^{n} j = 1^{n} W_{i,j} \cdot (A_{i,j} - L_{i,j} )^2 %DIFDELCMD < \le %%% OPT + \epsilon \|A\|_F^2 , where OPT = rank-k\ \hat{L} cost(\hat L) .
Edit intent: clarity
Original: In masked  low-rank approximation, given A \in R^{n \times n} and binary  W \in \{0,1\}^{n \times n} , the goal is to find a rank-k matrix L for which: cost(L) = i=1^{n} j = 1^{n} W_{i,j} \cdot (A_{i,j} - L_{i,j} )^2 %DIFDELCMD < \le %%%  OPT + \epsilon \|A\|_F^2 , where OPT = rank-k\ \hat{L} cost(\hat L) .
Revised: In masked low-rank approximation, given A \in R^{n \times n} and binary mask W \in \{0,1\}^{n \times n} , the goal is to find a rank-k matrix L for which: cost(L) = i=1^{n} j = 1^{n} W_{i,j} \cdot (A_{i,j} - L_{i,j} )^2 %DIFDELCMD < \le %%% OPT + \epsilon \|A\|_F^2 , where OPT = rank-k\ \hat{L} cost(\hat L) .
Edit intent: fluency
Original: In masked  low-rank approximation, given A \in R^{n \times n} and binary  W \in \{0,1\}^{n \times n} , the goal is to find a rank-k matrix L for which: cost(L) = i=1^{n} j = 1^{n} W_{i,j} \cdot (A_{i,j} - L_{i,j} )^2 %DIFDELCMD < \le %%%  OPT + \epsilon \|A\|_F^2 , where OPT = rank-k\ \hat{L} cost(\hat L) .
Revised: In masked low-rank approximation, given A \in R^{n \times n} and binary W \in \{0,1\}^{n \times n} . The goal is to find a rank-k matrix L for which: cost(L) = i=1^{n} j = 1^{n} W_{i,j} \cdot (A_{i,j} - L_{i,j} )^2 %DIFDELCMD < \le %%% OPT + \epsilon \|A\|_F^2 , where OPT = rank-k\ \hat{L} cost(\hat L) .
Edit intent: fluency
Original:  This problem is a special case of weighted low-rank approximation and captures low-rank plus diagonal decomposition, robust PCA,  matrix completion, low-rank recovery from monotone missing data , and many other problems.
Revised:  This problem is a special case of weighted low-rank plus diagonal decomposition, robust PCA, matrix completion, low-rank recovery from monotone missing data , and many other problems.
Edit intent: clarity
Original:  This problem is a special case of weighted low-rank approximation and captures low-rank plus diagonal decomposition, robust PCA,  matrix completion, low-rank recovery from monotone missing data , and many other problems.
Revised:  This problem is a special case of weighted low-rank approximation and captures low-rank plus diagonal decomposition, robust PCA, low-rank matrix completion, low-rank recovery from monotone missing data , and many other problems.
Edit intent: fluency
Original:  This problem is a special case of weighted low-rank approximation and captures low-rank plus diagonal decomposition, robust PCA,  matrix completion, low-rank recovery from monotone missing data , and many other problems.
Revised:  This problem is a special case of weighted low-rank approximation and captures low-rank plus diagonal decomposition, robust PCA, matrix completion, low-rank recovery from monotone missing data , and many problems.
Edit intent: fluency
Original:  Many of these problems are NP-hard, and while some algorithms with provable guarantees are known, they either 1) run in time n^{\Omega(k^2/\epsilon)} , or 2) make strong assumptions, e.g., that A is incoherent or that W is random.
Revised:  Many of these problems are NP-hard, and while some algorithms with provable guarantees are known, they either 1) run in time n^{\Omega(k^2/\epsilon)} or 2) make strong assumptions, e.g., that A is incoherent or that W is random.
Edit intent: fluency
Original:  We consider bicriteria\ algorithms, which output L with rank k'
Revised:  We consider bicriteria\ algorithms, which output a rank-k' matrix L, with k'
Edit intent: clarity
Original:  > k . We prove that a common  heuristic, which simply sets A to 0 where W is 0, and then computes a standard low-rank approximation, achieves the above approximation bound with rank k'
Revised:  > k . We prove that a common heuristic, which simply sets A to 0 where W is 0, and then finds a standard low-rank approximation, achieves the above approximation bound with rank k'
Edit intent: clarity
Original:  > k . We prove that a common  heuristic, which simply sets A to 0 where W is 0, and then computes a standard low-rank approximation, achieves the above approximation bound with rank k'
Revised:  > k . We prove that a common heuristic, which simply sets A to 0 where W is 0, and then computes a standard low-rank approximation, achieves this error bound with rank k'
Edit intent: clarity
Original:  depending on the communication\ complexity of W . Namely, interpreting W as the communication matrix of a Boolean function f(x,y) with x,y\in \{0 , 1\}^{\log n, it suffices to set k'=O(k\cdot 2^{R^{1-sided}_{\epsilon}(f)}), where R^{1-sided}_{\epsilon}(f) is the randomized communication complexity of f with 1-sided error probability \epsilon}  .
Revised:  depending on the communication\ complexity of W , 1\}^{\log n, it suffices to set k'=O(k\cdot 2^{R^{1-sided}_{\epsilon}(f)}), where R^{1-sided}_{\epsilon}(f) is the randomized communication complexity of f with 1-sided error probability \epsilon} .
Edit intent: coherence
Original:  depending on the communication\ complexity of W . Namely, interpreting W as the communication matrix of a Boolean function f(x,y) with x,y\in \{0 , 1\}^{\log n, it suffices to set k'=O(k\cdot 2^{R^{1-sided}_{\epsilon}(f)}), where R^{1-sided}_{\epsilon}(f) is the randomized communication complexity of f with 1-sided error probability \epsilon}  .
Revised:  depending on the communication\ complexity of W . Namely, interpreting W as the communication matrix of a Boolean function f(x,y) with x,y\in \{0 , , it suffices to set k'=O(k\cdot 2^{R^{1-sided}_{\epsilon}(f)}), where R^{1-sided}_{\epsilon}(f) is the randomized communication complexity of f with 1-sided error probability \epsilon} .
Edit intent: clarity
Original:  For many problems, this yields bicriteria algorithms with k' = k \cdot poly( (\log n) /\epsilon).
Revised:  For many problems, this yields bicriteria algorithms with k' = k \cdot poly( \log n /\epsilon).
Edit intent: fluency
Original:  E.g. , multi-player  communication complexity connects to  tensor decomposition and non-deterministic communication complexity to  Boolean low-rank factorization .
Revised:  E.g. , multi-player communication complexity connects to tensor decomposition and non-deterministic communication complexity to masked Boolean low-rank factorization .
Edit intent: fluency
Original: In masked\ low-rank\ approximation, one is given A \in R^{n \times n} and binary mask  W \in \{0,1\}^{n \times n}.
Revised: In masked\ low-rank\ approximation, one is given A \in R^{n \times n} and binary mask matrix W \in \{0,1\}^{n \times n}.
Edit intent: clarity
Original: Many questions that we have about the history and dynamics of organisms have a geographical component: How many are there, and where  ?
Revised: Many questions that we have about the history and dynamics of organisms have a geographical component: How many are there, and where do they live ?
Edit intent: clarity
Original:  How were they moving a thousand years ago, and where did the ancestors of an individual today live ?
Revised:  How were they moving a thousand years ago, and where were the ancestors of an individual today live ?
Edit intent: fluency
Original:  How were they moving a thousand years ago, and where did the ancestors of an individual today live ?
Revised:  How were they moving a thousand years ago, and where did the ancestors of a particular individual alive today ?
Edit intent: clarity
Original:  The code is publicly available at URL and URL .
Revised:  The code is publicly available at URL and URL 
Edit intent: fluency
Original: In this paper, we investigate  impacts of three main aspects of visual tracking, i.e., the backbone network, the attentional mechanism  and the detection component, and propose a Siamese Attentional Keypoint Network, dubbed SATIN, to achieve efficient tracking and accurate localization.
Revised: In this paper, we investigate the impacts of three main aspects of visual tracking, i.e., the backbone network, the attentional mechanism and the detection component, and propose a Siamese Attentional Keypoint Network, dubbed SATIN, to achieve efficient tracking and accurate localization.
Edit intent: fluency
Original: In this paper, we investigate  impacts of three main aspects of visual tracking, i.e., the backbone network, the attentional mechanism  and the detection component, and propose a Siamese Attentional Keypoint Network, dubbed SATIN, to achieve efficient tracking and accurate localization.
Revised: In this paper, we investigate impacts of three main aspects of visual tracking, i.e., the backbone network, the attentional mechanism , and the detection component, and propose a Siamese Attentional Keypoint Network, dubbed SATIN, to achieve efficient tracking and accurate localization.
Edit intent: fluency
Original: In this paper, we investigate  impacts of three main aspects of visual tracking, i.e., the backbone network, the attentional mechanism  and the detection component, and propose a Siamese Attentional Keypoint Network, dubbed SATIN, to achieve efficient tracking and accurate localization.
Revised: In this paper, we investigate impacts of three main aspects of visual tracking, i.e., the backbone network, the attentional mechanism and the detection component, and propose a Siamese Attentional Keypoint Network, dubbed SATIN, for efficient tracking and accurate localization.
Edit intent: clarity
Original:  Firstly, a new Siamese lightweight hourglass network is specifically designed for visual tracking.
Revised:  Firstly, a new Siamese lightweight hourglass network is specially designed for visual tracking.
Edit intent: fluency
Original:  Secondly, a novel cross-attentional module is utilized to leverage both channel-wise and spatial intermediate attentional information, which  enhance both discriminative and localization capabilities of feature maps.
Revised:  Secondly, a novel cross-attentional module is utilized to leverage both channel-wise and spatial intermediate attentional information, which can enhance both discriminative and localization capabilities of feature maps.
Edit intent: coherence
Original:  Thirdly, a keypoints detection approach is invented to track any target object by detecting the top-left corner point, the centroid point  and the bottom-right corner point of its bounding box.
Revised:  Thirdly, a keypoints detection approach is invented to trace any target object by detecting the top-left corner point, the centroid point and the bottom-right corner point of its bounding box.
Edit intent: fluency
Original:  Thirdly, a keypoints detection approach is invented to track any target object by detecting the top-left corner point, the centroid point  and the bottom-right corner point of its bounding box.
Revised:  Thirdly, a keypoints detection approach is invented to track any target object by detecting the top-left corner point, the centroid point , and the bottom-right corner point of its bounding box.
Edit intent: fluency
Original:  To the best of our knowledge, we are the first to propose this approach.
Edit intent: coherence
Original:  Therefore, our SATIN tracker not only has a strong capability to learn more effective object representations, but also  computational and memory storage efficiency, either during the training or testing stage.
Revised:  Therefore, our SATIN tracker not only has a strong capability to learn more effective object representations, but also is computational and memory storage efficiency, either during the training or testing stage.
Edit intent: coherence
Original:  39 (2017):B424-B441" that free-form curves used in CAGD ( computer aided geometric design ) can usually be represented as the solutions of linear differential systems and points and derivatives on the curves can be evaluated dynamically by solving the differential systems numerically.
Revised:  39 (2017):B424-B441" that free-form curves used in computer aided geometric design ) can usually be represented as the solutions of linear differential systems and points and derivatives on the curves can be evaluated dynamically by solving the differential systems numerically.
Edit intent: clarity
Original:  39 (2017):B424-B441" that free-form curves used in CAGD ( computer aided geometric design ) can usually be represented as the solutions of linear differential systems and points and derivatives on the curves can be evaluated dynamically by solving the differential systems numerically.
Revised:  39 (2017):B424-B441" that free-form curves used in CAGD ( computer aided geometric design can usually be represented as the solutions of linear differential systems and points and derivatives on the curves can be evaluated dynamically by solving the differential systems numerically.
Edit intent: fluency
Original:  In this work we consider the problem of finding the largest number of given subtrees of a tree that satisfy given load constraints.
Revised:  In this paper, we consider the problem of finding the largest number of given subtrees of a tree that satisfy given load constraints.
Edit intent: clarity
Original:  We extend a greedy algorithm that solves the latter problem for interval graphs, and obtain an M-approximation for chordal graphs where M is the maximum number of leaves of the subtrees in the representation of the chordal graph.
Revised:  We extend a greedy algorithm that solves the latter problem for interval graphs, and obtain an M-approximation where M is the maximum number of leaves of the subtrees in the representation of the chordal graph.
Edit intent: fluency
Original:  This implies a 2-approximation forVpt graphs (vertex-intersection graphs of paths in a tree), and an optimal algorithm for the class of directed path graphs (vertex-intersection graphs of paths in a directed tree) which in turn extends the class of interval graphs.
Revised:  This implies a 2-approximation for graphs (vertex-intersection graphs of paths in a tree), and an optimal algorithm for the class of directed path graphs (vertex-intersection graphs of paths in a directed tree) which in turn extends the class of interval graphs.
Edit intent: fluency
Original:  This model gained a lot of attention in ~ 2012 when Haase et al. showed its connections with timed automata.
Revised:  This model gained a lot of attention in 2012 when Haase et al. showed its connections with timed automata.
Edit intent: fluency
Original:  Later in ~ 2013 Fearnley and Jurdzi\'{n}ski proved that the reachability problem in this model is PSPACE-complete even in dimension ~ 1. Here, we investigate the complexity of the reachability problem when the model is extended with branching transitions, and we prove that the problem is EXPTIME-complete when the dimension is ~ 2 or larger.
Revised:  Later in 2013 Fearnley and Jurdzi\'{n}ski proved that the reachability problem in this model is PSPACE-complete even in dimension ~ 1. Here, we investigate the complexity of the reachability problem when the model is extended with branching transitions, and we prove that the problem is EXPTIME-complete when the dimension is ~ 2 or larger.
Edit intent: fluency
Original:  Later in ~ 2013 Fearnley and Jurdzi\'{n}ski proved that the reachability problem in this model is PSPACE-complete even in dimension ~ 1. Here, we investigate the complexity of the reachability problem when the model is extended with branching transitions, and we prove that the problem is EXPTIME-complete when the dimension is ~ 2 or larger.
Revised:  Later in ~ 2013 Fearnley and Jurdzi\'{n}ski proved that the reachability problem in this model is PSPACE-complete even in dimension 1. Here, we investigate the complexity of the reachability problem when the model is extended with branching transitions, and we prove that the problem is EXPTIME-complete when the dimension is ~ 2 or larger.
Edit intent: fluency
Original:  Later in ~ 2013 Fearnley and Jurdzi\'{n}ski proved that the reachability problem in this model is PSPACE-complete even in dimension ~ 1. Here, we investigate the complexity of the reachability problem when the model is extended with branching transitions, and we prove that the problem is EXPTIME-complete when the dimension is ~ 2 or larger.
Revised:  Later in ~ 2013 Fearnley and Jurdzi\'{n}ski proved that the reachability problem in this model is PSPACE-complete even in dimension ~ 1. Here, we investigate the complexity of the reachability problem when the model is extended with branching transitions, and we prove that the problem is EXPTIME-complete when the dimension is 2 or larger.
Edit intent: fluency
Original: Automatic estimation of piano fingering is important for computationally understanding the process of music performance and applicable to performance assistance and education systems.
Revised: Automatic estimation of piano fingering is important for understanding the computational process of music performance and applicable to performance assistance and education systems.
Edit intent: fluency
Original:  Here we study an alternative data-driven approach based on statistical modeling in which the naturalness of a given fingering is described by probabilities.
Revised:  Here we study an alternative data-driven approach based on statistical modeling in which the appropriateness of a given fingering is described by probabilities.
Edit intent: clarity
Original:  Using a newly released dataset of fingering annotations, we conduct systematic evaluations of these models as well as a representative constraint-based method and find that the methods based on high-order HMMs outperform others in terms of estimation accuracies.
Revised:  Using a newly released dataset of fingering annotations, we conduct systematic evaluations of these models as well as a representative constraint-based method . We find that the methods based on high-order HMMs outperform others in terms of estimation accuracies.
Edit intent: coherence
Original:  Using a newly released dataset of fingering annotations, we conduct systematic evaluations of these models as well as a representative constraint-based method and find that the methods based on high-order HMMs outperform others in terms of estimation accuracies.
Revised:  Using a newly released dataset of fingering annotations, we conduct systematic evaluations of these models as well as a representative constraint-based method and find that the methods based on high-order HMMs outperform the other methods in terms of estimation accuracies.
Edit intent: clarity
Original:  In this paper, we show the decidability of one interesting decidable fragment, that of two variable TML.
Revised:  In this paper, we show the decidability of one interesting fragment, that of two variable TML.
Edit intent: clarity
Original: In this paper, we propose a new  algorithm for solving  phase retrieval problem, i.e., the reconstruction of a signal \vx\in\H^n (\H=\R or \C) from phaseless samples b_j=\langle \va_j, \vx\rangle , j=1,\ldots,m . The proposed algorithm solves a  perturbed amplitude-based model  for phase retrieval and is correspondingly named as {\em Perturbed Amplitude Flow} (PAF).
Revised: In this paper, we propose a new algorithm for solving the phase retrieval problem, i.e., the reconstruction of a signal \vx\in\H^n (\H=\R or \C) from phaseless samples b_j=\langle \va_j, \vx\rangle , j=1,\ldots,m . The proposed algorithm solves a perturbed amplitude-based model for phase retrieval and is correspondingly named as {\em Perturbed Amplitude Flow} (PAF).
Edit intent: fluency
Original: In this paper, we propose a new  algorithm for solving  phase retrieval problem, i.e., the reconstruction of a signal \vx\in\H^n (\H=\R or \C) from phaseless samples b_j=\langle \va_j, \vx\rangle , j=1,\ldots,m . The proposed algorithm solves a  perturbed amplitude-based model  for phase retrieval and is correspondingly named as {\em Perturbed Amplitude Flow} (PAF).
Revised: In this paper, we propose a new algorithm for solving phase retrieval problem, i.e., the reconstruction of a signal \vx\in\H^n (\H=\R or \C) from phaseless samples b_j=\langle \va_j, \vx\rangle , j=1,\ldots,m . The proposed algorithm solves a perturbed amplitude-based model , for phase retrieval and is correspondingly named as {\em Perturbed Amplitude Flow} (PAF).
Edit intent: fluency
Original:  Unlike several existing O(n) algorithms that can be theoretically proven to recover only real signals, our algorithm works for both real and complex signals.
Edit intent: coherence
Original:  The effectiveness and benefit of the proposed method can be validated by both the simulation studies and the experiment of recovering natural image .
Revised:  The effectiveness and benefit of the proposed method are validated by both the simulation studies and the experiment of recovering natural image .
Edit intent: clarity