wanyu/IteraTeR_v2 huggingface dataset:
Original:   Median graphs constitute the principal class of graphs investigated in metric graph theory  , due to their bijections with other discrete and geometric structures ( CAT(0) cube complexes , domains of event structures , and solution sets of 2-SAT formulas) .
Revised:  Median graphs constitute the principal class of graphs investigated in metric graph theory , due to their bijections with other discrete and geometric structures ( CAT(0) cube complexes and domains of event structures , and solution sets of 2-SAT formulas) .
Edit intent: coherence
Original:   Median graphs constitute the principal class of graphs investigated in metric graph theory  , due to their bijections with other discrete and geometric structures ( CAT(0) cube complexes , domains of event structures , and solution sets of 2-SAT formulas) .
Revised:  Median graphs constitute the principal class of graphs investigated in metric graph theory , due to their bijections with other discrete and geometric structures ( CAT(0) cube complexes , domains of event structures .
Edit intent: clarity
Original:  Our algorithm is based on the known majority rule characterization of medians in a median graph G and on a fast computation of parallelism classes of edges (\Theta-classes ) of G. The main technical contribution of the paper is a linear time algorithm for computing the \Theta-classes of a median graph G using Lexicographic Breadth First Search (LexBFS).
Revised:  Our algorithm is based on the majority rule characterization of medians in a median graph G and on a fast computation of parallelism classes of edges (\Theta-classes ) of G. The main technical contribution of the paper is a linear time algorithm for computing the \Theta-classes of a median graph G using Lexicographic Breadth First Search (LexBFS).
Edit intent: clarity
Original:  Our algorithm is based on the known majority rule characterization of medians in a median graph G and on a fast computation of parallelism classes of edges (\Theta-classes ) of G. The main technical contribution of the paper is a linear time algorithm for computing the \Theta-classes of a median graph G using Lexicographic Breadth First Search (LexBFS).
Revised:  Our algorithm is based on the known majority rule characterization of medians in median graphs and on a fast computation of parallelism classes of edges (\Theta-classes ) of G. The main technical contribution of the paper is a linear time algorithm for computing the \Theta-classes of a median graph G using Lexicographic Breadth First Search (LexBFS).
Edit intent: fluency
Original:  Namely , we show that any LexBFS ordering of the vertices of a median graph G has the following\emph{fellow traveler property : the fathers of any two adjacent vertices of G are also adjacent.
Revised:  Namely , we show that any LexBFS ordering of the vertices of \emph{fellow traveler property : the fathers of any two adjacent vertices of G are also adjacent.
Edit intent: clarity
Original:  Namely , we show that any LexBFS ordering of the vertices of a median graph G has the following\emph{fellow traveler property : the fathers of any two adjacent vertices of G are also adjacent.
Revised:  Namely , we show that any LexBFS ordering of the vertices of a median graph G has the following\emph{ : the fathers of any two adjacent vertices of G are also adjacent.
Edit intent: clarity
Original:  Using the fast computation of the \Theta-classes of a median graph G , we also compute the Wiener index (total distance) of G in linear  time.
Revised:  Using the fast computation of the \Theta-classes , we also compute the Wiener index (total distance) of G in linear time.
Edit intent: clarity
Original:  In real commercial scenarios, getting such judgments poses an immense challenge in application of LTR algorithms.
Revised:  In commercial scenarios, getting such judgments poses an immense challenge in application of LTR algorithms.
Edit intent: clarity
Original:  It is done by aggregating the logged data and calculating click rate , order rate etc of products , for each query in the logs.
Revised:  It is done by aggregating the logged data and calculating click rate etc of products , for each query in the logs.
Edit intent: clarity
Original:  It is done by aggregating the logged data and calculating click rate , order rate etc of products , for each query in the logs.
Revised:  It is done by aggregating the logged data and calculating click rate , order rate etc of products for the queries in the logs.
Edit intent: clarity
Original:  Our method outperforms full-information loss on deep neural network model as well as traditional ranking models like LambdaMART.
Revised:  Our method outperforms full-information loss on deep neural network models as well as traditional ranking models like LambdaMART.
Edit intent: fluency
Original:  Our method outperforms full-information loss on deep neural network model as well as traditional ranking models like LambdaMART.
Revised:  Our method outperforms full-information loss on deep neural network model as well as traditional models like LambdaMART.
Edit intent: clarity
Original:   Learning to Rank (LTR) algorithms require relevance judgments (labels) on productsfor learning.
Revised:  Traditional Learning to Rank (LTR) algorithms require relevance judgments (labels) on productsfor learning.
Edit intent: fluency
Original:  In commercial scenarios , getting such judgments poses an immense challenge in application of LTR algorithms .
Revised:  In commercial scenarios , getting such judgments poses an immense challenge .
Edit intent: clarity
Original:  In the literature, it is proposed to employ user feedback signals such as clicks, orders etc  to generate relevance judgments.
Revised:  In the literature, it is proposed to employ user feedback signals such as clicks, orders etc ) to generate relevance judgments.
Edit intent: fluency
Original:  It is done by aggregating the logged data and calculating click rate etc of products for the queries in the logs.
Revised:  It is done in two steps: first, query-product pair data are aggregated from the logs and then order rate etc are calculated for each pair in the logs.
Edit intent: clarity
Original:  Due to unavailability of public E-Com LTR dataset, we provide Commercial dataset from our E-Com platform.
Revised:  Due to unavailability of public E-Com LTR dataset, we provide Commercial dataset from our platform.
Edit intent: fluency
Original:  Our empirical evaluation shows that CRM approach not only learns effectively from logged contextual-bandit feedback but also that our CRM based method outperforms full-information  (e.g. cross-entropy) loss on various deep neural network models as well as traditional models like LambdaMART . These findings show that by adopting CRM learning approach, E-Com platforms can get better product search quality compared to full-information approach, without artificially mending the data  .
Revised:  Our empirical evaluation shows that CRM approach learns effectively from logged contextual-bandit feedback but also that our CRM based method outperforms full-information (e.g. cross-entropy) loss on various deep neural network models as well as traditional models like LambdaMART . These findings show that by adopting CRM learning approach, E-Com platforms can get better product search quality compared to full-information approach, without artificially mending the data .
Edit intent: clarity
Original:  Our empirical evaluation shows that CRM approach not only learns effectively from logged contextual-bandit feedback but also that our CRM based method outperforms full-information  (e.g. cross-entropy) loss on various deep neural network models as well as traditional models like LambdaMART . These findings show that by adopting CRM learning approach, E-Com platforms can get better product search quality compared to full-information approach, without artificially mending the data  .
Revised:  Our empirical evaluation shows that CRM approach not only learns effectively from logged contextual-bandit feedback but also that our CRM based method outperforms full-information (e.g. cross-entropy) on various deep neural network models as well as traditional models like LambdaMART . These findings show that by adopting CRM learning approach, E-Com platforms can get better product search quality compared to full-information approach, without artificially mending the data .
Edit intent: clarity
Original:  Our empirical evaluation shows that CRM approach not only learns effectively from logged contextual-bandit feedback but also that our CRM based method outperforms full-information  (e.g. cross-entropy) loss on various deep neural network models as well as traditional models like LambdaMART . These findings show that by adopting CRM learning approach, E-Com platforms can get better product search quality compared to full-information approach, without artificially mending the data  .
Revised:  Our empirical evaluation shows that CRM approach not only learns effectively from logged contextual-bandit feedback but also that our CRM based method outperforms full-information (e.g. cross-entropy) loss on various deep neural network models . These findings show that by adopting CRM learning approach, E-Com platforms can get better product search quality compared to full-information approach, without artificially mending the data .
Edit intent: coherence
Original:  Our empirical evaluation shows that CRM approach not only learns effectively from logged contextual-bandit feedback but also that our CRM based method outperforms full-information  (e.g. cross-entropy) loss on various deep neural network models as well as traditional models like LambdaMART . These findings show that by adopting CRM learning approach, E-Com platforms can get better product search quality compared to full-information approach, without artificially mending the data  .
Revised:  Our empirical evaluation shows that CRM approach not only learns effectively from logged contextual-bandit feedback but also that our CRM based method outperforms full-information (e.g. cross-entropy) loss on various deep neural network models as well as traditional models like LambdaMART . These findings show that by adopting CRM approach, E-Com platforms can get better product search quality compared to full-information approach, without artificially mending the data .
Edit intent: clarity
Original:  Our empirical evaluation shows that CRM approach not only learns effectively from logged contextual-bandit feedback but also that our CRM based method outperforms full-information  (e.g. cross-entropy) loss on various deep neural network models as well as traditional models like LambdaMART . These findings show that by adopting CRM learning approach, E-Com platforms can get better product search quality compared to full-information approach, without artificially mending the data  .
Revised:  Our empirical evaluation shows that CRM approach not only learns effectively from logged contextual-bandit feedback but also that our CRM based method outperforms full-information (e.g. cross-entropy) loss on various deep neural network models as well as traditional models like LambdaMART . These findings show that by adopting CRM learning approach, E-Com platforms can improve product search quality compared to full-information approach, without artificially mending the data .
Edit intent: clarity
Original:  Our empirical evaluation shows that CRM approach not only learns effectively from logged contextual-bandit feedback but also that our CRM based method outperforms full-information  (e.g. cross-entropy) loss on various deep neural network models as well as traditional models like LambdaMART . These findings show that by adopting CRM learning approach, E-Com platforms can get better product search quality compared to full-information approach, without artificially mending the data  .
Revised:  Our empirical evaluation shows that CRM approach not only learns effectively from logged contextual-bandit feedback but also that our CRM based method outperforms full-information (e.g. cross-entropy) loss on various deep neural network models as well as traditional models like LambdaMART . These findings show that by adopting CRM learning approach, E-Com platforms can get better product search quality without artificially mending the data .
Edit intent: coherence
Original:  Our empirical evaluation shows that  CRM approach learns effectively from logged data and beats  strong baseline ranker (\lambda-MART) by a huge margin.
Revised:  Our empirical evaluation shows that our CRM approach learns effectively from logged data and beats strong baseline ranker (\lambda-MART) by a huge margin.
Edit intent: fluency
Original:  Our empirical evaluation shows that  CRM approach learns effectively from logged data and beats  strong baseline ranker (\lambda-MART) by a huge margin.
Revised:  Our empirical evaluation shows that CRM approach learns effectively from logged data and beats a strong baseline ranker (\lambda-MART) by a huge margin.
Edit intent: fluency
Original:  These findings show that by adopting CRM approach, E-Com platforms can improve product search quality without artificially mending the data to fit in the traditional LTR algorithms .
Revised:  These findings demonstrate that by adopting CRM approach, E-Com platforms can improve product search quality without artificially mending the data to fit in the traditional LTR algorithms .
Edit intent: coherence
Original:  These findings show that by adopting CRM approach, E-Com platforms can improve product search quality without artificially mending the data to fit in the traditional LTR algorithms .
Revised:  These findings show that by adopting CRM approach, E-Com platforms can get better product search quality without artificially mending the data to fit in the traditional LTR algorithms .
Edit intent: clarity
Original: A matrix algorithm performs at sub-linear cost if it uses much fewer flops and memory cells than the input matrix has entries.
Revised: A matrix algorithm runs at sublinear cost if it uses much fewer flops and memory cells than the input matrix has entries.
Edit intent: clarity
Original: A matrix algorithm performs at sub-linear cost if it uses much fewer flops and memory cells than the input matrix has entries.
Revised: A matrix algorithm performs at sub-linear cost if it uses much fewer arithmetic operations than the input matrix has entries.
Edit intent: clarity
Original:  Using such algorithms is indispensable for Big Data Mining and Analysis, where the input matrices are so immense that one can only access a small fraction of all their entries.
Revised:  Such algorithms are indispensable for Big Data Mining and Analysis, where the input matrices are so immense that one can only access a small fraction of all their entries.
Edit intent: clarity
Original:  Using such algorithms is indispensable for Big Data Mining and Analysis, where the input matrices are so immense that one can only access a small fraction of all their entries.
Revised:  Using such algorithms is indispensable for Big Data Mining and Analysis, where input matrices are so immense that one can only access a small fraction of all their entries.
Edit intent: fluency
Original:  Typically, however, these matrices admit their LRA ( Low Rank Approximation  ), which one can access and process at sub-linear arithmetic cost, that is, by involving much fewer memory cells and arithmetic operations than an input matrix has entries.
Revised:  Typically, however, such matrices admit their LRA ( Low Rank Approximation ), which one can access and process at sub-linear arithmetic cost, that is, by involving much fewer memory cells and arithmetic operations than an input matrix has entries.
Edit intent: clarity
Original:  Typically, however, these matrices admit their LRA ( Low Rank Approximation  ), which one can access and process at sub-linear arithmetic cost, that is, by involving much fewer memory cells and arithmetic operations than an input matrix has entries.
Revised:  Typically, however, these matrices admit their Low Rank Approximation ), which one can access and process at sub-linear arithmetic cost, that is, by involving much fewer memory cells and arithmetic operations than an input matrix has entries.
Edit intent: clarity
Original:  Adversary argument shows that no algorithm running at sub-linear cost can output accurate LRA of the worst case input matrices , or even of the matrices of small families of our Appendix, but for more than a decade Cross-Approximation iterations, running at sub-linear cost, have routinely been computing accurate LRA.
Revised:  Adversary argument shows that no algorithm running at sublinear cost can output accurate LRA of the worst case input matrices , or even of the matrices of small families of our Appendix, but for more than a decade Cross-Approximation iterations, running at sub-linear cost, have routinely been computing accurate LRA.
Edit intent: fluency
Original:  Adversary argument shows that no algorithm running at sub-linear cost can output accurate LRA of the worst case input matrices , or even of the matrices of small families of our Appendix, but for more than a decade Cross-Approximation iterations, running at sub-linear cost, have routinely been computing accurate LRA.
Revised:  Adversary argument shows that no algorithm running at sub-linear cost can output accurate LRA of worst case input matrices , or even of the matrices of small families of our Appendix, but for more than a decade Cross-Approximation iterations, running at sub-linear cost, have routinely been computing accurate LRA.
Edit intent: fluency
Original:  Adversary argument shows that no algorithm running at sublinear cost can output accurate LRA of worst case input matrices but we prove that some sublinear cost algorithms output a reasonably close LRA of a matrix M if it  (i) is sufficiently close to a low rank matrix or (ii) is a Symmetric Positive Semidefinite (SPSD) matrix that admits LRA.
Revised:  Adversary argument shows that no algorithm running at sublinear cost can output accurate LRA of worst case input matrices but we prove that some sublinear cost algorithms output a reasonably close LRA of a matrix M if it either (i) is sufficiently close to a low rank matrix or (ii) is a Symmetric Positive Semidefinite (SPSD) matrix that admits LRA.
Edit intent: clarity
Original:  In both cases supporting algorithms are deterministic and output LRA in its special form of CUR LRA, memory efficient and built on a submatrix of M, called CUR generator , having maximal volume among all submatrices of the same size.
Revised:  In both cases supporting algorithms are deterministic and output LRA in its special form of CUR LRA, memory efficient and built on a submatrix of M, called CUR generator and having maximal volume among all submatrices of the same size.
Edit intent: fluency
Original:  We provide  first limited formal support for this long-known empirical efficiency where we assume non-degeneracy of the initial submatrix of at least one C-A iteration.
Revised:  We provide the first limited formal support for this long-known empirical efficiency where we assume non-degeneracy of the initial submatrix of at least one C-A iteration.
Edit intent: fluency
Original:  Typically , however, such matrices admit their Low Rank Approximation (LRA), which one can access and process at sublinear cost.
Revised:  Quite typically , however, such matrices admit their Low Rank Approximation (LRA), which one can access and process at sublinear cost.
Edit intent: coherence
Original:   Adversary argument shows that no algorithm running at sublinear cost can output accurate LRA of worst case input matrices but we prove that some  sublinear cost algorithms output a reasonably close LRA of a matrix M if it either (i) is sufficiently close to a low rank matrix or (ii) is a Symmetric Positive Semidefinite (SPSD) matrix that admits LRA.
Revised:  Adversary argument shows that no algorithm running at sublinear cost can output accurate LRA of worst case input matrices but we prove that some sublinear cost algorithms output reasonably close LRA of a matrix M if it either (i) is sufficiently close to a low rank matrix or (ii) is a Symmetric Positive Semidefinite (SPSD) matrix that admits LRA.
Edit intent: coherence
Original: A matrix algorithm runs at sublinear cost {\em  if it uses much fewer memory cells and arithmetic operations than the input matrix has entries.
Revised: A matrix algorithm runs at {\em if it uses much fewer memory cells and arithmetic operations than the input matrix has entries.
Edit intent: clarity
Original:  Quite typically, however, such matrices admit their Low Rank Approximation (LRA), which one can access and process at sublinear cost {\em  . Can, however, we compute LRA at sublinear cost?
Revised:  Quite typically, however, such matrices admit their Low Rank Approximation (LRA), which one can access and process at sublinear cost {\em (LRA) . Can, however, we compute LRA at sublinear cost?
Edit intent: clarity
Original:  Adversary argument shows that no algorithm running at sublinear cost can output accurate LRA even of the matrices of small families of our Appendix, but we prove that some deterministic sublinear cost algorithms output reasonably close LRA in a special form of CUR LRA , which is particularly memory efficient, as long as an input matrix admits LRA and is Symmetric Positive Semidefinite or is sufficiently close to a low rank matrix.
Revised:  Adversary argument shows that the output of any algorithm running at sublinear cost can output accurate LRA even of the matrices of small families of our Appendix, but we prove that some deterministic sublinear cost algorithms output reasonably close LRA in a special form of CUR LRA , which is particularly memory efficient, as long as an input matrix admits LRA and is Symmetric Positive Semidefinite or is sufficiently close to a low rank matrix.
Edit intent: clarity
Original:  Adversary argument shows that no algorithm running at sublinear cost can output accurate LRA even of the matrices of small families of our Appendix, but we prove that some deterministic sublinear cost algorithms output reasonably close LRA in a special form of CUR LRA , which is particularly memory efficient, as long as an input matrix admits LRA and is Symmetric Positive Semidefinite or is sufficiently close to a low rank matrix.
Revised:  Adversary argument shows that no algorithm running at sublinear cost can output accurate LRA even of the matrices of small families of our Appendix, but we prove that some deterministic sublinear cost algorithms output reasonably close LRA in a memory efficient form of CUR LRA , which is particularly memory efficient, as long as an input matrix admits LRA and is Symmetric Positive Semidefinite or is sufficiently close to a low rank matrix.
Edit intent: clarity
Original:  Adversary argument shows that no algorithm running at sublinear cost can output accurate LRA even of the matrices of small families of our Appendix, but we prove that some deterministic sublinear cost algorithms output reasonably close LRA in a special form of CUR LRA , which is particularly memory efficient, as long as an input matrix admits LRA and is Symmetric Positive Semidefinite or is sufficiently close to a low rank matrix.
Revised:  Adversary argument shows that no algorithm running at sublinear cost can output accurate LRA even of the matrices of small families of our Appendix, but we prove that some deterministic sublinear cost algorithms output reasonably close LRA in a special form of CUR LRA if an input matrix admits LRA and is Symmetric Positive Semidefinite or is sufficiently close to a low rank matrix.
Edit intent: clarity