wanyu/IteraTeR_full_sent huggingface dataset:
Original:  The results suggest that all VB variants  perform as well as MCMC and MSLE at prediction and recovery of all model parameters with the exception of the covariance matrix of the multivariate normal mixing distribution .
Revised:  The results suggest that all VB variants with the exception of the ones relying on an alternative variational lower bound constructed with the help of the modified Jensen's inequality perform as well as MCMC and MSLE at prediction and recovery of all model parameters with the exception of the covariance matrix of the multivariate normal mixing distribution .
Edit intent: meaning-changed
Original:  In particular, VB with nonconjugate variational message passing and the delta-method (VB-NCVMP-Delta) is relatively accurate and up to 15 times faster than MCMC and MSLE. On the whole , VB-NCVMP-Delta is most suitable for applications in which fastpredictions are paramount, while MCMC should be preferred in applications in which accurate inferences are most important .
Revised:  In particular, VB with nonconjugate variational message passing and the delta-method (VB-NCVMP-Delta) is up to 16 times faster than MCMC and MSLE. On the whole , VB-NCVMP-Delta is most suitable for applications in which fastpredictions are paramount, while MCMC should be preferred in applications in which accurate inferences are most important .
Edit intent: meaning-changed
Original:  In particular, VB with nonconjugate variational message passing and the delta-method (VB-NCVMP-Delta) is relatively accurate and up to 15 times faster than MCMC and MSLE. On the whole , VB-NCVMP-Delta is most suitable for applications in which fastpredictions are paramount, while MCMC should be preferred in applications in which accurate inferences are most important .
Revised:  In particular, VB with nonconjugate variational message passing and the delta-method (VB-NCVMP-Delta) is relatively accurate and up to 15 times faster than MCMC and MSLE. Thus , VB-NCVMP-Delta is most suitable for applications in which fastpredictions are paramount, while MCMC should be preferred in applications in which accurate inferences are most important .
Edit intent: coherence
Original:  In particular, VB with nonconjugate variational message passing and the delta-method (VB-NCVMP-Delta) is relatively accurate and up to 15 times faster than MCMC and MSLE. On the whole , VB-NCVMP-Delta is most suitable for applications in which fastpredictions are paramount, while MCMC should be preferred in applications in which accurate inferences are most important .
Revised:  In particular, VB with nonconjugate variational message passing and the delta-method (VB-NCVMP-Delta) is relatively accurate and up to 15 times faster than MCMC and MSLE. On the whole , VB-NCVMP-Delta can be an attractive alternative to MCMC and MSLE for fast, scalable and accurate estimation of MMNL models .
Edit intent: clarity
Original:  The Meataxe algorithm, the only known one for computing such a decomposition  runs in O(n^{6(d+1)}) time where n is the size of  input module.
Revised:  The Meataxe algorithm, a popular one known for computing such a decomposition runs in O(n^{6(d+1)}) time where n is the size of input module.
Edit intent: meaning-changed
Original:  The Meataxe algorithm, the only known one for computing such a decomposition  runs in O(n^{6(d+1)}) time where n is the size of  input module.
Revised:  The Meataxe algorithm, the only known one for computing such a decomposition , runs in O(n^{6(d+1)}) time where n is the size of input module.
Edit intent: fluency
Original:  The Meataxe algorithm, the only known one for computing such a decomposition  runs in O(n^{6(d+1)}) time where n is the size of  input module.
Revised:  The Meataxe algorithm, the only known one for computing such a decomposition runs in O(n^{6(d+1)}) time where n is the size of the input module.
Edit intent: fluency
Original:  The Meataxe algorithm, a popular one known for computing such a decomposition , runs in O(n^{ 6(d+1) }) time where n is the size of the input module .
Revised:  The Meataxe algorithm, a popular one known for computing such a decomposition runs in O(n^{ 6(d+1) }) time where n is the size of the input module .
Edit intent: fluency
Original:  The Meataxe algorithm, a popular one known for computing such a decomposition , runs in O(n^{ 6(d+1) }) time where n is the size of the input module .
Revised:  The Meataxe algorithm, a popular one known for computing such a decomposition , runs in O(n^{ 12d }) time where n is the size of the input module .
Edit intent: meaning-changed
Original:  The Meataxe algorithm, a popular one known for computing such a decomposition , runs in O(n^{ 6(d+1) }) time where n is the size of the input module .
Revised:  The Meataxe algorithm, a popular one known for computing such a decomposition , runs in O(n^{ 6(d+1) }) time where n is the size of the input filtration .
Edit intent: clarity
Original:  We present for the first time a generalization of the persistence algorithm based on a generalized matrix reduction technique that runs in O(n^{2\omega  }) time  where \omega<2.
Revised:  We present for the first time a generalization of the persistence algorithm based on a generalized matrix reduction technique that runs in O(n^{2\omega }) time for d=2 and in O(n^{d(2\omega +1) where \omega<2.
Edit intent: meaning-changed
Original: 373 is the exponent for matrix multiplication . We also show how a recent algorithm of Lesnick and Wright can be adapted to convert the input filtration in O(n^{2d+1 presentation matrix %DIFAUXCMD which is ultimately decomposed . Various structural and computational results connecting the graded modules from commutative algebra to matrix reductions are established through the course.
Revised: 373 is the exponent for matrix multiplication presentation matrix %DIFAUXCMD which is ultimately decomposed . Various structural and computational results connecting the graded modules from commutative algebra to matrix reductions are established through the course.
Edit intent: coherence
Original:  We also show how a recent algorithm of Lesnick and Wright can be adapted to convert the input filtration in O(n^{2d+1 presentation matrix %DIFAUXCMD which is ultimately decomposed . Various structural and computational results connecting the graded modules from commutative algebra to matrix reductions are established through the course.
Revised:  We also show how a recent algorithm of Lesnick and Wright can be adapted to convert the input filtration in O(n^{2d+1 %DIFAUXCMD which is ultimately decomposed . Various structural and computational results connecting the graded modules from commutative algebra to matrix reductions are established through the course.
Edit intent: clarity
Original:  We also show how a recent algorithm of Lesnick and Wright can be adapted to convert the input filtration in O(n^{2d+1 presentation matrix %DIFAUXCMD which is ultimately decomposed . Various structural and computational results connecting the graded modules from commutative algebra to matrix reductions are established through the course.
Revised:  We also show how a recent algorithm of Lesnick and Wright can be adapted to convert the input filtration in O(n^{2d+1 presentation matrix %DIFAUXCMD . Various structural and computational results connecting the graded modules from commutative algebra to matrix reductions are established through the course.
Edit intent: coherence
Original:  The Meataxe algorithm, a popular one known for computing such a decomposition runs in O(n^{ 12d }) time where n is the size of the input filtration.
Revised:  The Meataxe algorithm, a popular one known for computing such a decomposition runs in O(n^{ 6(d+1) }) time where n is the size of the input filtration.
Edit intent: meaning-changed
Original:  However, in the multi-parameter setting, one of the main bottlenecks is that topological summaries such as barcodes and distances among them cannot be as efficiently computed as in the 1-parameter case because there is no known generalization of the persistence algorithm for computing the decomposition of multi-parameter persistence modules.
Revised:  However, in the multi-parameter setting, one of the main challenges is that topological summaries such as barcodes and distances among them cannot be as efficiently computed as in the 1-parameter case because there is no known generalization of the persistence algorithm for computing the decomposition of multi-parameter persistence modules.
Edit intent: clarity
Original:  However, in the multi-parameter setting, one of the main bottlenecks is that topological summaries such as barcodes and distances among them cannot be as efficiently computed as in the 1-parameter case because there is no known generalization of the persistence algorithm for computing the decomposition of multi-parameter persistence modules.
Revised:  However, in the multi-parameter setting, one of the main bottlenecks is that topological summaries based on algebraic structure such as decompositions and bottleneck distances cannot be as efficiently computed as in the 1-parameter case because there is no known generalization of the persistence algorithm for computing the decomposition of multi-parameter persistence modules.
Edit intent: meaning-changed
Original:  However, in the multi-parameter setting, one of the main bottlenecks is that topological summaries such as barcodes and distances among them cannot be as efficiently computed as in the 1-parameter case because there is no known generalization of the persistence algorithm for computing the decomposition of multi-parameter persistence modules.
Revised:  However, in the multi-parameter setting, one of the main bottlenecks is that topological summaries such as barcodes and distances among them cannot be as efficiently computed as in the 1-parameter case because there is no known extension of the persistence algorithm for computing the decomposition of multi-parameter persistence modules.
Edit intent: clarity
Original:  However, in the multi-parameter setting, one of the main bottlenecks is that topological summaries such as barcodes and distances among them cannot be as efficiently computed as in the 1-parameter case because there is no known generalization of the persistence algorithm for computing the decomposition of multi-parameter persistence modules.
Revised:  However, in the multi-parameter setting, one of the main bottlenecks is that topological summaries such as barcodes and distances among them cannot be as efficiently computed as in the 1-parameter case because there is no known generalization of the persistence algorithm to multi-parameter persistence modules.
Edit intent: clarity
Original:  The Meataxe algorithm , a popular one known for computing such a decomposition runs in (n^{6(d+1)  on a generalized matrix reduction technique that runs in O( n ^{2\omega+1}) time for d=2 and in O(n^{d(2\omega +1)) time for d>2 where \omega<2.
Revised:  (n^{6(d+1) on a generalized matrix reduction technique that runs in O( n ^{2\omega+1}) time for d=2 and in O(n^{d(2\omega +1)) time for d>2 where \omega<2.
Edit intent: coherence
Original:  The Meataxe algorithm , a popular one known for computing such a decomposition runs in (n^{6(d+1)  on a generalized matrix reduction technique that runs in O( n ^{2\omega+1}) time for d=2 and in O(n^{d(2\omega +1)) time for d>2 where \omega<2.
Revised:  The Meataxe algorithm , a popular one known for computing such a decomposition runs in We present an efficient algorithm to compute the unique decomposition of a finitely presented persistence module M defined over the multiparameter \mathbb{Z on a generalized matrix reduction technique that runs in O( n ^{2\omega+1}) time for d=2 and in O(n^{d(2\omega +1)) time for d>2 where \omega<2.
Edit intent: meaning-changed
Original:  The Meataxe algorithm , a popular one known for computing such a decomposition runs in (n^{6(d+1)  on a generalized matrix reduction technique that runs in O( n ^{2\omega+1}) time for d=2 and in O(n^{d(2\omega +1)) time for d>2 where \omega<2.
Revised:  The Meataxe algorithm , a popular one known for computing such a decomposition runs in (n^{6(d+1) distinctly graded on a generalized matrix reduction technique that runs in O( n ^{2\omega+1}) time for d=2 and in O(n^{d(2\omega +1)) time for d>2 where \omega<2.
Edit intent: meaning-changed
Original:  The Meataxe algorithm , a popular one known for computing such a decomposition runs in (n^{6(d+1)  on a generalized matrix reduction technique that runs in O( n ^{2\omega+1}) time for d=2 and in O(n^{d(2\omega +1)) time for d>2 where \omega<2.
Revised:  The Meataxe algorithm , a popular one known for computing such a decomposition runs in (n^{6(d+1) . Based on a generalized matrix reduction technique that runs in O( n ^{2\omega+1}) time for d=2 and in O(n^{d(2\omega +1)) time for d>2 where \omega<2.
Edit intent: coherence
Original:  The Meataxe algorithm , a popular one known for computing such a decomposition runs in (n^{6(d+1)  on a generalized matrix reduction technique that runs in O( n ^{2\omega+1}) time for d=2 and in O(n^{d(2\omega +1)) time for d>2 where \omega<2.
Revised:  The Meataxe algorithm , a popular one known for computing such a decomposition runs in (n^{6(d+1) on a generalized matrix reduction technique it runs in O( n ^{2\omega+1}) time for d=2 and in O(n^{d(2\omega +1)) time for d>2 where \omega<2.
Edit intent: coherence
Original:  The Meataxe algorithm , a popular one known for computing such a decomposition runs in (n^{6(d+1)  on a generalized matrix reduction technique that runs in O( n ^{2\omega+1}) time for d=2 and in O(n^{d(2\omega +1)) time for d>2 where \omega<2.
Revised:  The Meataxe algorithm , a popular one known for computing such a decomposition runs in (n^{6(d+1) on a generalized matrix reduction technique that runs in O( N ^{2\omega+1}) time for d=2 and in O(n^{d(2\omega +1)) time for d>2 where \omega<2.
Edit intent: fluency
Original:  The Meataxe algorithm , a popular one known for computing such a decomposition runs in (n^{6(d+1)  on a generalized matrix reduction technique that runs in O( n ^{2\omega+1}) time for d=2 and in O(n^{d(2\omega +1)) time for d>2 where \omega<2.
Revised:  The Meataxe algorithm , a popular one known for computing such a decomposition runs in (n^{6(d+1) on a generalized matrix reduction technique that runs in O( n ^{2\omega+1}) time ) time for d>2 where \omega<2.
Edit intent: coherence
Original:  Under the stability assumption, we present two sampling algorithms for computing approximate MEB with sample complexities independent of the number of input points . Further , we achieve the first sub-linear time  approximation algorithm for  MEB with outliers .
Revised:  Under the stability assumption, we present two sampling algorithms for computing approximate MEB with sample complexities independent of the number of input points ; further , we achieve the first sub-linear time approximation algorithm for MEB with outliers .
Edit intent: fluency
Original:  We also show that our idea can be extended to  the general case of MEB with outliers ({\em i.e.,} without the stability assumption) , and obtain a sub-linear time bi-criteria approximation algorithm.
Revised:  We also show that our ideas can be extended to the general case of MEB with outliers ({\em i.e.,} without the stability assumption) , and obtain a sub-linear time bi-criteria approximation algorithm.
Edit intent: fluency
Original:  We also show that our idea can be extended to  the general case of MEB with outliers ({\em i.e.,} without the stability assumption) , and obtain a sub-linear time bi-criteria approximation algorithm.
Revised:  We also show that our idea can be extended to be more general techniques, a novel uniform-adaptive sampling method and a sandwich lemma, for solving the general case of MEB with outliers ({\em i.e.,} without the stability assumption) , and obtain a sub-linear time bi-criteria approximation algorithm.
Edit intent: meaning-changed
Original:  We also show that our idea can be extended to  the general case of MEB with outliers ({\em i.e.,} without the stability assumption) , and obtain a sub-linear time bi-criteria approximation algorithm.
Revised:  We also show that our idea can be extended to the general case of MEB with outliers ({\em i.e.,} without the stability assumption) and the problem of k-center clustering with outliers. We achieve sub-linear time bi-criteria approximation algorithm.
Edit intent: meaning-changed
Original:  We also show that our idea can be extended to  the general case of MEB with outliers ({\em i.e.,} without the stability assumption) , and obtain a sub-linear time bi-criteria approximation algorithm. Our results can be viewed as a new step along the direction of beyond worst-case analysis .
Revised:  We also show that our idea can be extended to the general case of MEB with outliers ({\em i.e.,} without the stability assumption) , and obtain a sub-linear time bi-criteria approximation algorithms for these problems respectively; the algorithms have sample sizes independent of the number of points n and the dimensionality d, which significantly improve the time complexities of existing algorithms. We expect that our technique will be applicable to design sub-linear time algorithms for other shape fitting with outliers problems .
Edit intent: meaning-changed
Original:   Under the stability assumption, we present two sampling algorithms for computing approximate MEB with sample complexities independent of the number of input points ;
Revised:  Roughly speaking, an instance of MEB is stable, if the radius of the resulting ball cannot be significantly reduced by removing a small fraction of the input points. Under the stability assumption, we present two sampling algorithms for computing approximate MEB with sample complexities independent of the number of input points ;
Edit intent: meaning-changed
Original:   Under the stability assumption, we present two sampling algorithms for computing approximate MEB with sample complexities independent of the number of input points ; further, we achieve the first sub-linear time single-criterion approximation algorithm for the MEB with outliers problem.
Revised:  Under the stability assumption, we present two sampling algorithms for computing approximate MEB with sample complexities independent of the number of input points n. In particular, the second algorithm has the sample complexity even independent of the dimensionality d. Further, we extend the idea to achieve a sub-linear time single-criterion approximation algorithm for the MEB with outliers problem.
Edit intent: meaning-changed
Original:  Our result can be viewed as a new step along the direction of beyond worst-case analysis. We also show that our ideas can be extended to be more general techniques, a novel uniform-adaptive sampling method and a sandwich lemma, for solving the general case of MEB with outliers (%DIFDELCMD < {\em %%% i.e., without the stability assumption) and the problem of k-center clustering with outliers.
Revised:  %DIFDELCMD < {\em %%% i.e., without the stability assumption) and the problem of k-center clustering with outliers.
Edit intent: coherence
Original:  We also show that our ideas can be extended to be more general techniques, a novel uniform-adaptive sampling method and a sandwich lemma, for solving the general case of MEB with outliers (%DIFDELCMD < {\em %%% i.e., without the stability assumption) and the problem of k-center clustering with outliers.
Revised:  We also show that our ideas can be extended to be more general techniques, a novel uniform-adaptive sampling method and a sandwich lemma, for solving the general case of MEB with outliers (%DIFDELCMD < {\em %%% without the stability assumption) and the problem of k-center clustering with outliers.
Edit intent: coherence
Original:  We also show that our ideas can be extended to be more general techniques, a novel uniform-adaptive sampling method and a sandwich lemma, for solving the general case of MEB with outliers (%DIFDELCMD < {\em %%% i.e., without the stability assumption) and the problem of k-center clustering with outliers. We achieve sub-linear time bi-criteria approximation algorithms for these problems respectively;
Revised:  We also show that our ideas can be extended to be more general techniques, a novel uniform-adaptive sampling method and a sandwich lemma, for solving the general case of MEB with outliers (%DIFDELCMD < {\em %%% i.e., Note that most existing sub-linear time bi-criteria approximation algorithms for these problems respectively;
Edit intent: meaning-changed
Original:  We achieve sub-linear time bi-criteria approximation algorithms for these problems respectively; the algorithms have sample sizes independent of the number of points n and the dimensionality d, which significantly improve the time complexities of existing algorithms .
Revised:  We achieve sub-linear time bi-criteria approximations, where the "bi-criteria" means that the solution has to allow the approximations on the radius and the number of covered points. Differently, all the algorithms proposed in this paper yield single-criterion approximations (with respect to radius) .
Edit intent: meaning-changed
Original:  Availability  : The plug-in (running on Windows, Linux, or Mac OS) and its tutorial (both in written and video forms) can be downloaded freely under the terms of the MIT license from: URL  Contact: csermely.peter@med.semmelweis-univ.hu
Revised:  Availability and implementation : The plug-in (running on Windows, Linux, or Mac OS) and its tutorial (both in written and video forms) can be downloaded freely under the terms of the MIT license from: URL Contact: csermely.peter@med.semmelweis-univ.hu
Edit intent: meaning-changed
Original:  Availability  : The plug-in (running on Windows, Linux, or Mac OS) and its tutorial (both in written and video forms) can be downloaded freely under the terms of the MIT license from: URL  Contact: csermely.peter@med.semmelweis-univ.hu
Revised:  Availability : The plug-in (running on Windows, Linux, or Mac OS) and its tutorial (both in written and video forms) can be downloaded freely under the terms of the MIT license from: URL Supplementary data are available at Bioinformatics online. Contact: csermely.peter@med.semmelweis-univ.hu
Edit intent: meaning-changed
Original: We consider the problem of designing Locality Sensitive Filters (LSF)for set overlaps, also known as maximum inner product search on binary data. We give a simple data structure that generalizes and outperforms previous algorithms such as MinHash [J. Discrete Algorithms 1998], SimHash [STOC 2002], Spherical LSF [SODA  2017] and Chosen Path [STOC 2017] ;
Revised: We formulate and optimally solve a new generalized Set Similarity Search problem, which assumes the size of the database and query sets are known in advance. By creating polylog copies of our data-structure, we optimally solve any symmetric Approximate Set Similarity Search problem, including approximate versions of Subset Search, Maximum Inner Product Search (MIPS), Jaccard Similarity Search and Partial Match. Our algorithm can be seen as a natural generalization of previous work on Set as well as Euclidean Similarity Search, but conceptually it differs by optimally exploiting the information present in the sets as well as their complements, and doing so asymmetrically between queries and stored sets. Doing so we improve upon the best previous work: MinHash [J. Discrete Algorithms 1998], SimHash [STOC 2002], Spherical LSF [SODA 2017] and Chosen Path [STOC 2017] ;
Edit intent: meaning-changed
Original:  We give a simple data structure that generalizes and outperforms previous algorithms such as MinHash [J. Discrete Algorithms 1998], SimHash [STOC 2002], Spherical LSF [SODA  2017] and Chosen Path [STOC 2017] ;
Revised:  We give a simple data structure that generalizes and outperforms previous algorithms such as MinHash [J. Discrete Algorithms 1998], SimHash [STOC 2002], Spherical LSF [SODA 2016, 2017] and Chosen Path [STOC 2017] ;
Edit intent: meaning-changed