wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Because of its factored form, the Krylov prior is amenable to low-rank approximation, which produces an efficient BayesCG implementation as a CG method. We also introduce a probabilistic error estimator, the `S-statistic'. Although designed for sampling from BayesCG posteriors, its mean and variance under approximate Krylov priors can be computed with CG. An approximation of the S-statistic by a `95 percent credible interval' avoids the cost of sampling altogether .  Numerical experiments illustrate that the resulting error estimates are competitive with the best existing methods and are easy to compute .
Revised:  Because of its factored form, the Krylov prior is amenable to low-rank and maintained in factored form . Numerical experiments illustrate that the resulting error estimates are competitive with the best existing methods and are easy to compute .
Edit intent: clarity
Original:  Although designed for sampling from BayesCG posteriors, its mean and variance under approximate Krylov priors can be computed with CG. An approximation of the S-statistic by a `95 percent credible interval' avoids the cost of sampling altogether .  Numerical experiments illustrate that the resulting error estimates are competitive with the best existing methods and are easy to compute .
Revised:  Although designed for sampling from BayesCG posteriors, its mean and variance under approximate Krylov priors can be computed with CG. An approximation of the S-statistic by a `95 percent credible interval' avoids the cost of sampling altogether . This allows easy generation of accurate samples to probe uncertainty in subsequent computations. Numerical experiments illustrate that the resulting error estimates are competitive with the best existing methods and are easy to compute .
Edit intent: meaning-changed
Original:  Although designed for sampling from BayesCG posteriors, its mean and variance under approximate Krylov priors can be computed with CG. An approximation of the S-statistic by a `95 percent credible interval' avoids the cost of sampling altogether .  Numerical experiments illustrate that the resulting error estimates are competitive with the best existing methods and are easy to compute .
Revised:  Although designed for sampling from BayesCG posteriors, its mean and variance under approximate Krylov priors can be computed with CG. An approximation of the S-statistic by a `95 percent credible interval' avoids the cost of sampling altogether . Numerical experiments confirm the effectiveness of the posteriors and their low-rank approximations .
Edit intent: clarity
Original: The main focus of this paper is radius-based clustering problems in the two-stage stochastic setting with recourse, where the inherent stochasticity of the model comes in the form of a budget constraint.
Revised: The main focus of this paper is radius-based (supplier) clustering in the two-stage stochastic setting with recourse, where the inherent stochasticity of the model comes in the form of a budget constraint.
Edit intent: meaning-changed
Original:  Further, we show that our problems have natural applications to allocating healthcare testing centers . The eventual goal is to provide results for supplier-like problems in the most general distributional setting, where there is only black-box access to the underlying distribution.
Revised:  We note that the particular family of problems we consider, has natural applications in setting up healthcare facility centers with the intent of emergency planning. Our eventual goal is to provide results for supplier-like problems in the most general distributional setting, where there is only black-box access to the underlying distribution.
Edit intent: meaning-changed
Original:  second, we    exploit structural properties of these algorithms and generalize them to the black-box setting. These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
Revised:  second, we exploit structural properties of (1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
Edit intent: clarity
Original:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
Revised:  These key properties are: the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
Edit intent: fluency
Original:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
Revised:  These key properties are:(1) (2) there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
Edit intent: coherence
Original:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
Revised:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
Edit intent: coherence
Original:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
Revised:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) \emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
Edit intent: coherence
Original:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
Revised:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{ ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
Edit intent: clarity
Original:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
Revised:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{efficient the algorithms developed for the first step of the framework. In this way, we manage to generalize the results of the latter to the black-box case, which also preserve the approximation ratio exactly.
Edit intent: meaning-changed
Original:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly. We note that prior generalization approaches, i.e., variants of the\emph{Sample Average Approximation method , can be used for the problems we consider, however they would yield worse approximation guarantees .
Revised:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{efficient ways to extend their output to the black-box \emph{Sample Average Approximation method , can be used for the problems we consider, however they would yield worse approximation guarantees .
Edit intent: coherence
Original:  We note that prior generalization approaches, i.e., variants of the\emph{Sample Average Approximation method , can be used for the problems we consider, however they would yield worse approximation guarantees .
Revised:  We note that prior generalization approaches, i.e., variants of the\emph{Sample Average Approximation model. Finally, we note that the scenario-discarding modification to the SAA method is necessary in order to optimize over the radius .
Edit intent: meaning-changed
Original:  second, we employ a novel scenario-discarding variant of the standard Sample Average Approximation (SAA) method, in which we also crucially exploit structural properties of the algorithms developed for the first step of the framework.
Revised:  second, we employ a novel scenario-discarding variant of the standard Sample Average Approximation (SAA) method, in which we crucially exploit properties of the algorithms developed for the first step of the framework.
Edit intent: clarity
Original:  second, we employ a novel scenario-discarding variant of the standard Sample Average Approximation (SAA) method, in which we also crucially exploit structural properties of the algorithms developed for the first step of the framework. In this way, we manage to generalize the results of the latter to the black-box model. Finally, we note that the scenario-discarding modification to the SAA method is necessary in order to optimize over the radius.
Revised:  second, we employ a novel scenario-discarding variant of the standard Sample Average Approximation (SAA) method, in which we also crucially exploit structural properties of the restricted-case algorithms. We finally note that the scenario-discarding modification to the SAA method is necessary in order to optimize over the radius.
Edit intent: clarity
Original: Recently, a 4th-order asymptotic preserving multiderivative Implicit-Explicit (IMEX) scheme was developed ( Sch\"uz and Seal 2020, arXiv:2001.08268).
Revised: Recently, a 4th-order asymptotic preserving multiderivative implicit-explicit (IMEX) scheme was developed ( Sch\"uz and Seal 2020, arXiv:2001.08268).
Edit intent: fluency
Original: Recently, a 4th-order asymptotic preserving multiderivative Implicit-Explicit (IMEX) scheme was developed ( Sch\"uz and Seal 2020, arXiv:2001.08268).
Revised: Recently, a 4th-order asymptotic preserving multiderivative Implicit-Explicit (IMEX) scheme was developed ( Sch\"utz and Seal 2020, arXiv:2001.08268).
Edit intent: fluency
Original:  Afterwards, we demonstrate how the method of Sch\"uz and Seal 2020 generalises in a straightforward manner to any of these schemes, and prove convergence properties of the resulting IMEX schemes.
Revised:  Afterwards, we demonstrate how the method of Sch\"utz and Seal 2020 generalises in a straightforward manner to any of these schemes, and prove convergence properties of the resulting IMEX schemes.
Edit intent: fluency
Original: We consider the problem of allocating a set of divisible goods to N agents in an online manner over T periods, with adversarially-chosen normalized valuations in each period. Our goal is to maximize the Nash social welfare, a widely studied objective which provides a balance between fairness and efficiency.
Revised: We consider the problem of allocating a set of divisible goods to N agents in an online manner , aiming to maximize the Nash social welfare, a widely studied objective which provides a balance between fairness and efficiency.
Edit intent: clarity
Original:  On the positive side, we provide an online algorithm that achieves a competitive ratio of O(\log N) and O(\log T) , but also a stronger competitive ratio of O(\log k) in settings where the value of any agent for her most preferred item is no more than k times her average value .
Revised:  The goods arrive in a sequence of T periods and the value of each agent for a good is adversarially chosen when the good arrives. We first observe that no online algorithm can achieve a competitive ratio better than the trivial O(N), unless it is given additional information about the agents' values. Then, in line with the emerging area of "algorithms with predictions", we consider a setting where for each agent, the online algorithm is only given a prediction of her monopolist utility, i.e., her utility if all goods were given to her alone (corresponding to the sum of her values over the T periods). Our main result is an online algorithm that achieves a competitive ratio of O(\log N) and O(\log T) , but also a stronger competitive ratio of O(\log k) in settings where the value of any agent for her most preferred item is no more than k times her average value .
Edit intent: meaning-changed
Original:  On the positive side, we provide an online algorithm that achieves a competitive ratio of O(\log N) and O(\log T) , but also a stronger competitive ratio of O(\log k) in settings where the value of any agent for her most preferred item is no more than k times her average value .
Revised:  On the positive side, we provide an online algorithm whose competitive ratio is parameterized by the multiplicative errors in these predictions. The algorithm achieves a competitive ratio of O(\log N) and O(\log T) , but also a stronger competitive ratio of O(\log k) in settings where the value of any agent for her most preferred item is no more than k times her average value .
Edit intent: meaning-changed
Original:  On the positive side, we provide an online algorithm that achieves a competitive ratio of O(\log N) and O(\log T) , but also a stronger competitive ratio of O(\log k) in settings where the value of any agent for her most preferred item is no more than k times her average value .
Revised:  On the positive side, we provide an online algorithm that achieves a competitive ratio of O(\log N) and O(\log T) if the predictions are perfectly accurate. Moreover, the competitive ratio degrades smoothly with the errors in the predictions, and is surprisingly robust: the logarithmic competitive ratio holds even if the predictions are very inaccurate .
Edit intent: meaning-changed
Original:  We complement this by showing this bound is essentially tight: no online algorithm  can achieve a competitive ratio of O(\log^{1-\epsilon} N) or O(\log^{1-\epsilon} T) for any constant \epsilon>0.
Revised:  We complement this positive result by showing that our bounds are essentially tight: no online algorithm can achieve a competitive ratio of O(\log^{1-\epsilon} N) or O(\log^{1-\epsilon} T) for any constant \epsilon>0.
Edit intent: meaning-changed
Original:  We complement this by showing this bound is essentially tight: no online algorithm  can achieve a competitive ratio of O(\log^{1-\epsilon} N) or O(\log^{1-\epsilon} T) for any constant \epsilon>0.
Revised:  We complement this by showing this bound is essentially tight: no online algorithm , even if provided with perfectly accurate predictions, can achieve a competitive ratio of O(\log^{1-\epsilon} N) or O(\log^{1-\epsilon} T) for any constant \epsilon>0.
Edit intent: meaning-changed
Original:  For text classification, however, the discrete property of the text input space makes it hard to adapt the gradient-based adversarial methods from the image domain. Existing text attack methods, moreover, are effective but not efficient enough to be incorporated into practical text adversarial training.
Revised:  For text classification, however, existing synonym substitution based adversarial attacks are effective but not efficient enough to be incorporated into practical text adversarial training.
Edit intent: meaning-changed
Original:  In this work, we propose a  Fast Gradient Projection Method (FGPM) to generate text adversarial examples based on synonym substitution, where each substitution is scored by the product of gradient magnitude and the projected distance between the original word and the candidate word in the gradient direction.
Revised:  Gradient-based attacks, which are very efficient for images, are hard to be implemented for synonym substitution based text attacks due to the lexical, grammatical and semantic constraints and the discrete text input space. Thereby, we propose a Fast Gradient Projection Method (FGPM) to generate text adversarial examples based on synonym substitution, where each substitution is scored by the product of gradient magnitude and the projected distance between the original word and the candidate word in the gradient direction.
Edit intent: meaning-changed
Original:  In this work, we propose a  Fast Gradient Projection Method (FGPM) to generate text adversarial examples based on synonym substitution, where each substitution is scored by the product of gradient magnitude and the projected distance between the original word and the candidate word in the gradient direction.
Revised:  In this work, we propose a fast text adversarial attack method called Fast Gradient Projection Method (FGPM) to generate text adversarial examples based on synonym substitution, where each substitution is scored by the product of gradient magnitude and the projected distance between the original word and the candidate word in the gradient direction.
Edit intent: meaning-changed
Original:  In this work, we propose a  Fast Gradient Projection Method (FGPM) to generate text adversarial examples based on synonym substitution, where each substitution is scored by the product of gradient magnitude and the projected distance between the original word and the candidate word in the gradient direction.
Revised:  In this work, we propose a Fast Gradient Projection Method (FGPM) based on synonym substitution, where each substitution is scored by the product of gradient magnitude and the projected distance between the original word and the candidate word in the gradient direction.
Edit intent: clarity
Original:  In this work, we propose a  Fast Gradient Projection Method (FGPM) to generate text adversarial examples based on synonym substitution, where each substitution is scored by the product of gradient magnitude and the projected distance between the original word and the candidate word in the gradient direction. Empirical evaluations demonstrate that FGPM achieves similar attack performance and transferability when compared with competitive attack baselines, at the same time it is about 20 times faster than the current fastest text attack method.
Revised:  In this work, we propose a Fast Gradient Projection Method (FGPM) to generate text adversarial examples based on synonym substitution, which is about 20 times faster than the current fastest text attack method.
Edit intent: coherence
Original:  Empirical evaluations demonstrate that FGPM achieves similar attack performance and transferability when compared with competitive attack baselines, at the same time it is about 20 times faster than the current fastest text attack method. Such performanceenables us to incorporate FGPM with adversarial training as an effective defense method , and scale to large neural networks and datasets.
Revised:  Empirical evaluations demonstrate that FGPM achieves similar attack performance and transferability when compared with competitive attack baselines, at the same time it is about 20 times faster than existing text attack methods and could achieve similar attack performance. We then incorporate FGPM with adversarial training as an effective defense method , and scale to large neural networks and datasets.
Edit intent: clarity
Original:  Such performanceenables us to incorporate FGPM with adversarial training as an effective defense method , and scale to large neural networks and datasets. Experiments show that the adversarial training with FGPM (ATF)significantly improves the model robustness , and blocks the transferability of adversarial examples without any decay on the model generalization .
Revised:  Such performanceenables us to incorporate FGPM with adversarial training and propose a text defense method called Adversarial Training with FGPM enhanced by Logit pairing (ATFL). Experiments show that ATFL could significantly improve the model robustness , and blocks the transferability of adversarial examples without any decay on the model generalization .
Edit intent: meaning-changed
Original:  Experiments show that the adversarial training with FGPM (ATF)significantly improves the model robustness , and blocks the transferability of adversarial examples without any decay on the model generalization .
Revised:  Experiments show that the adversarial training with FGPM (ATF)significantly improves the model robustness and block the transferability of adversarial examples without any decay on the model generalization .
Edit intent: fluency
Original:  Significant effort has been committed to harness gene expression data as real-valued matrices for multiple analyses while accounting for time-to-event modeling by including survival times . Traditional biological analysis has focused separately on non-negative matrix factorization (NMF) of the gene expression data matrix and survival regression with Cox proportional hazards model.
Revised:  Significant effort has been committed to harness gene expression data as real-valued matrices for multiple analyses while accounting for time-to-event modeling by including survival times , many traditional analyses have focused separately on non-negative matrix factorization (NMF) of the gene expression data matrix and survival regression with Cox proportional hazards model.
Edit intent: clarity
Original:  We describe the terms ``perfect tracking'', ``perfect monitoring'' and ``perfect reporting'' to indicate that traced contacts will be tracked while incubating, tracked contacts are efficiently monitored so that they do not cause secondary infections, and all infected persons are reported, respectively.
Revised:  We describe the terms "perfect tracking", "perfect monitoring" and "perfect reporting" to indicate that traced contacts will be tracked while incubating, tracked contacts are efficiently monitored so that they do not cause secondary infections, and all infected persons are reported, respectively.
Edit intent: fluency
Original:  Furthermore, we gave a lower bound on the proportion of contacts to be traced to ensure that the effective reproduction, \mathcal{R , is below one and describe \mathcal{R in terms of observable quantities such as the proportion of reported and traced cases.
Revised:  Furthermore, we gave a lower bound on the proportion of contacts to be traced to ensure that the effective reproduction, \mathcal{R , is below one and describe \mathcal{R in terms of observable quantities such as the proportion of reported and traced cases.
Edit intent: fluency
Original:  Model simulations using the Covid-19 data obtained from John Hopkins University for some selected states in the US suggest that even late intervention of CT may reasonably reduce the transmission of Covid-19 and reduce peak hospitalizations and deaths .
Revised:  Model simulations using the COVID-19 data obtained from John Hopkins University for some selected states in the US suggest that even late intervention of CT may reasonably reduce the transmission of Covid-19 and reduce peak hospitalizations and deaths .
Edit intent: clarity
Original:  Model simulations using the Covid-19 data obtained from John Hopkins University for some selected states in the US suggest that even late intervention of CT may reasonably reduce the transmission of Covid-19 and reduce peak hospitalizations and deaths .
Revised:  Model simulations using the Covid-19 data obtained from John Hopkins University for some selected states in the US suggest that even late intervention of CT may reasonably reduce the transmission of COVID-19 and reduce peak hospitalizations and deaths .
Edit intent: clarity