wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi}  ]  - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Revised:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi} ] - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Edit intent: fluency
Original:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi}  ]  - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Revised:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) gave the first efficient algorithm for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi} ] - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Edit intent: clarity
Original:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi}  ]  - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Revised:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem . These results , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi} ] - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Edit intent: coherence
Original:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi}  ]  - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Revised:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, and the error bounds on \|\Pi} ] - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Edit intent: coherence
Original:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi}  ]  - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Revised:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi} obtain an error that grows with the dimension (linearly in ] - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Edit intent: meaning-changed
Original:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi}  ]  - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Revised:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi} RY] - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Edit intent: clarity
Original:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi}  ]  - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Revised:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi} ] and logarithmically in BK) at the cost of quasi-polynomial running time) and rely on - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Edit intent: meaning-changed
Original:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi}  ]  - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Revised:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi} ] certifiable anti-concentration - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Edit intent: meaning-changed
Original:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi}  ]  - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Revised:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever \mathcal{D , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi} ] - a relatively strict condition satisfied essentially only by the Gaussian distribution . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Edit intent: meaning-changed
Original: We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a positive function of a Volterra type continuous Gaussian process that may have extremely rough sample paths.
Revised: We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have extremely rough sample paths.
Edit intent: meaning-changed
Original: We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have extremely rough sample paths.
Revised: We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths.
Edit intent: fluency
Original:  The drift function and the volatility function are assumed to be time-dependent and locally \omega-continuous for some modulus of continuity \omega. The main results obtained in the paper are sample path and small-noise large deviation principles for the log-price process in a  Gaussian model under very mild restrictions.
Revised:  The main results obtained in the paper are sample path and small-noise large deviation principles for the log-price process in a Gaussian model under very mild restrictions.
Edit intent: coherence
Original:  In this work, we utilize the PageRank function on the lower-star filtration of the graph as input to persistent homology to study the problem of graph similarity. By representing each graph as a persistence diagram,we can then compare outputs using the bottleneck distance .
Revised:  In this work, we utilize the PageRank function on the lower-star filtration of the graph as input to persistent homology to obtain a scalable graph descriptor and utilize it to compare the similarities between graphs. For a given graph G(V,E), our descriptor can be computed in O(|E|\alpha(|V|)), where \alpha is the inverse Ackermann function which makes it scalable and computable on massive graphs .
Edit intent: meaning-changed
Original:   If instead the driving policy is a carbon dioxide cap or tax, wind and solar shares can rise without cannibalising their own market revenue, even at penetrations of wind and solar above 80\%.
Revised:  This decline is mathematically guaranteed regardless of whether the subsidised technology is variable or not. If instead the driving policy is a carbon dioxide cap or tax, wind and solar shares can rise without cannibalising their own market revenue, even at penetrations of wind and solar above 80\%.
Edit intent: meaning-changed
Original:  The policy of subsidy is thus the primary factor driving lower market values, and this decline happens even for dispatchable low-emission technologies; the variability of wind and solar is only a secondary factor that accelerates the decline if they are subsidised. The strong dependence of market value on the policy regime means that market value needs to be used with caution as a measure of market integration  .
Revised:  The strong dependence of market value on the policy regime means that market value needs to be used with caution as a measure of market integration .
Edit intent: coherence
Original:  We use visual analysis to support the multi-criteria comparison, enabling the selection of the most logical and intuitive option. We applied the revised cost-benefit measure to two case studies, demonstrating its uses in practical scenarios, while the collected real world data further informs the selection of a bounded measure  .
Revised:  We use visual analysis to support the multi-criteria comparison, narrowing the search down to those options with better mathematical properties. We apply those remaining options to two visualization case studies to instantiate their uses in practical scenarios, while the collected real world data further informs the selection of a bounded measure .
Edit intent: meaning-changed
Original:  We applied the revised cost-benefit measure to two case studies, demonstrating its uses in practical scenarios, while the collected real world data further informs the selection of a bounded measure  .
Revised:  We applied the revised cost-benefit measure to two case studies, demonstrating its uses in practical scenarios, while the collected real world data further informs the selection of a bounded measure , which can be used to estimate the benefit of visualization .
Edit intent: meaning-changed
Original:  We also present proposed model-based strategies on how to prevent the spread of the disease in local setting, such as during large social gatherings  .
Revised:  We also present proposed model-based strategies on how to prevent the spread of the disease in local setting, such as during large social gatherings , are also presented. The model shows that the exposure time is a significant factor in spreading the disease. With a basic reproduction number equal to 2, and 14-day infectious period, an infected person staying more than 9 hours in the event could infect other people. Assuming the exposure time is 18 hours, the model recommends that attendees of the social gathering should have a protection with more than 70 percent effectiveness .
Edit intent: meaning-changed
Original:  In this paper, we consider a situation called adaptive experimental design where research subjects sequentially visit a researcher, and the researcher assigns a treatment. For estimating the ATE efficiently, we consider changing the probability of assigning a treatment at a period by using past information obtained until the period .
Revised:  In this paper, we consider a situation called adaptive experimental design where research subjects sequentially . In adaptive experimental design, the experimenter is allowed to change the probability of assigning a treatment at a period by using past information obtained until the period .
Edit intent: clarity
Original:  In this paper, to construct an efficient estimator, we overcome this conventional problem by using an algorithm of the multi-armed bandit problem and the theory of martingale. In the proposed method, we use the probability of assigning a treatment that minimizes the asymptotic variance of an estimator of the ATE. We also elucidate the theoretical properties of an estimatorobtained from the proposed algorithm for both infinite and finite samples .
Revised:  We thus propose an algorithm for efficient experiments with estimators constructed from dependent samples. We also introduce a sequential testing framework using the proposed estimator. To justify our proposed approach, we provide finite and infinite sample analyses .
Edit intent: clarity
Original:  Analogous to other domains in AI , there are specific tasks of AIEd for which labels are scarce . For instance, labels like exam score and grade are considered important in educational and social context. However, obtaining the labels is costly as they require student actions taken outside the system. Likewise, while student events like course dropout and review correctnessare automatically recorded by IESs, they are few in number as the events occur sporadically in practice .
Revised:  Analogous to other domains in AI , there are specific tasks of AIEd for which labels are scarce and expensive, such as predicting exam score or review correctness .
Edit intent: clarity
Original:  To this end, we propose assessment modeling, fundamental pre-training tasks for IESs . An assessment is a feature of student-system interactions which can act as pedagogical evaluation, such as student response correctness or timeliness .
Revised:  To this end, we propose Assessment Modeling, a class of fundamental pre-training tasks for IESs . An assessment is a feature of student-system interactions which can act as pedagogical evaluation, such as student response correctness or timeliness .
Edit intent: clarity
Original:  To this end, we propose assessment modeling, fundamental pre-training tasks for IESs . An assessment is a feature of student-system interactions which can act as pedagogical evaluation, such as student response correctness or timeliness .
Revised:  To this end, we propose assessment modeling, fundamental pre-training tasks for general interactive educational systems . An assessment is a feature of student-system interactions which can act as pedagogical evaluation, such as student response correctness or timeliness .
Edit intent: clarity
Original:  To this end, we propose assessment modeling, fundamental pre-training tasks for IESs . An assessment is a feature of student-system interactions which can act as pedagogical evaluation, such as student response correctness or timeliness . Assessment modeling is the prediction of assessments conditioned on the surrounding context of interactions.
Revised:  To this end, we propose assessment modeling, fundamental pre-training tasks for IESs . An assessment is a feature of student-system interactions which can serve as a pedagogical evaluation. Examples include the correctness and timeliness of a student's answer. Assessment Modeling is the prediction of assessments conditioned on the surrounding context of interactions.
Edit intent: clarity
Original:  Although it is natural to pre-train  interactive features available in large amount, narrowing down the prediction targets to assessments holds relevance to the label-scarce educational problems while reducing irrelevant noises.
Revised:  Although it is natural to pre-train on interactive features available in large amount, narrowing down the prediction targets to assessments holds relevance to the label-scarce educational problems while reducing irrelevant noises.
Edit intent: fluency
Original:  Although it is natural to pre-train  interactive features available in large amount, narrowing down the prediction targets to assessments holds relevance to the label-scarce educational problems while reducing irrelevant noises.
Revised:  Although it is natural to pre-train interactive features available in large amount, narrowing down the prediction targets to assessments focuses the tasks' relevance to the label-scarce educational problems while reducing irrelevant noises.
Edit intent: clarity
Original:  Although it is natural to pre-train  interactive features available in large amount, narrowing down the prediction targets to assessments holds relevance to the label-scarce educational problems while reducing irrelevant noises. To the best of our knowledge, this is the first work investigating appropriate pre-training method of predicting educational features from student-system interactions.
Revised:  Although it is natural to pre-train interactive features available in large amount, narrowing down the prediction targets to assessments holds relevance to the label-scarce educational problems and reduces less-relevant noise.
Edit intent: clarity
Original:  In this paper, we study one aspect of nonconvexity relevant for modern machine learning applications: existence of invariances (symmetries) in the function f, as a result of which the distribution p will have manifolds of points with equal probability.
Revised:  In this paper, we focus on an aspect of nonconvexity relevant for modern machine learning applications: existence of invariances (symmetries) in the function f, as a result of which the distribution p will have manifolds of points with equal probability.
Edit intent: clarity
Original:  We give a recipe for proving mixing time bounds of Langevin dynamics in order to sample from manifolds of local optima of the function f in settings where the distribution is well-concentrated around them. We specialize our arguments to classic matrix factorization-like Bayesian inference problems where we get noisy measurements A(XX^T), X \in R^{d \times k} of a low-rank matrix, i.e. f(X) = \|A(XX^T) - b\|^2_2, X \in R^{d \times k}, and \beta the inverse of the variance of the noise.
Revised:  We give a recipe for proving mixing time bounds for Langevin diffusion as a function of the geometry of these manifolds. Second, we specialize our arguments to classic matrix factorization-like Bayesian inference problems where we get noisy measurements A(XX^T), X \in R^{d \times k} of a low-rank matrix, i.e. f(X) = \|A(XX^T) - b\|^2_2, X \in R^{d \times k}, and \beta the inverse of the variance of the noise.
Edit intent: clarity
Original:  In particular, by plugging in the algorithm of M\k{a [ FOCS 2013 ], we obtain an O(n^{ 10 / 7 }) time algorithm for computing the permutation distance between two trees on n nodes.
Revised:  In particular, by plugging in the algorithm of Liu and Sidford [ FOCS 2013 ], we obtain an O(n^{ 10 / 7 }) time algorithm for computing the permutation distance between two trees on n nodes.
Edit intent: meaning-changed
Original:  In particular, by plugging in the algorithm of M\k{a [ FOCS 2013 ], we obtain an O(n^{ 10 / 7 }) time algorithm for computing the permutation distance between two trees on n nodes.
Revised:  In particular, by plugging in the algorithm of M\k{a [ ArXiv 2019 ], we obtain an O(n^{ 10 / 7 }) time algorithm for computing the permutation distance between two trees on n nodes.
Edit intent: meaning-changed
Original:  In particular, by plugging in the algorithm of M\k{a [ FOCS 2013 ], we obtain an O(n^{ 10 / 7 }) time algorithm for computing the permutation distance between two trees on n nodes.
Revised:  In particular, by plugging in the algorithm of M\k{a [ FOCS 2013 ], we obtain an O(n^{ 11 / 7 }) time algorithm for computing the permutation distance between two trees on n nodes.
Edit intent: meaning-changed
Original:  In particular, by plugging in the algorithm of M\k{a [ FOCS 2013 ], we obtain an O(n^{ 10 / 7 }) time algorithm for computing the permutation distance between two trees on n nodes.
Revised:  In particular, by plugging in the algorithm of M\k{a [ FOCS 2013 ], we obtain an O(n^{ 10 / 8 }) time algorithm for computing the permutation distance between two trees on n nodes.
Edit intent: meaning-changed
Original:  In particular, by plugging in the algorithm of Liu and Sidford [ArXiv 2019 ], we obtain an O(n^{ 11 / 8 }) time algorithm for computing the permutation distance between two trees on n nodes.
Revised:  In particular, by plugging in the algorithm of Liu and Sidford [ArXiv 2020 ], we obtain an O(n^{ 11 / 8 }) time algorithm for computing the permutation distance between two trees on n nodes.
Edit intent: meaning-changed
Original:  In particular, by plugging in the algorithm of Liu and Sidford [ArXiv 2019 ], we obtain an O(n^{ 11 / 8 }) time algorithm for computing the permutation distance between two trees on n nodes.
Revised:  In particular, by plugging in the algorithm of Liu and Sidford [ArXiv 2019 ], we obtain an O(n^{ 4 / 8 }) time algorithm for computing the permutation distance between two trees on n nodes.
Edit intent: meaning-changed
Original:  In particular, by plugging in the algorithm of Liu and Sidford [ArXiv 2019 ], we obtain an O(n^{ 11 / 8 }) time algorithm for computing the permutation distance between two trees on n nodes.
Revised:  In particular, by plugging in the algorithm of Liu and Sidford [ArXiv 2019 ], we obtain an O(n^{ 11 / 3+o(1) }) time algorithm for computing the permutation distance between two trees on n nodes.
Edit intent: meaning-changed