wanyu/IteraTeR_full_sent huggingface dataset:
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: fluency
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: fluency
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: fluency
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that computes such polynomials efficiently -- the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: coherence
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: clarity
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: fluency
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: coherence
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of quantifier elimination combined with that of " \epsilon-samples ".
Edit intent: fluency
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of \epsilon-samples ".
Edit intent: fluency
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ". We present four applications of our result.
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~\mathcal{S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples . We also present an extension of our construction to multi-level polynomial partitioning for semi-algebraic sets in \mathbb{R applications of our result.
Edit intent: meaning-changed
Original:  The first is a data structure for answering point-location queries among a family of semi-algebraic sets in \mathbb{R}^d in O(\log n) time ; the second is data structure for answering range search queries with semi-algebraic ranges in  O(\log n) time ;
Revised:  The first is a data structure for answering point-location queries among a family of semi-algebraic sets in \mathbb{R}^d in O(\log n) time , with storage complexity and expected preprocessing time of O(n^{d+\epsilon data structure for answering range search queries with semi-algebraic ranges in O(\log n) time ;
Edit intent: meaning-changed
Original:  the second is data structure for answering range search queries with semi-algebraic ranges in  O(\log n) time ; the third is a data structure for answering vertical ray-shooting queries among semi-algebraic sets in \mathbb{R}^{d} in O(\log^2 n) time ;
Revised:  the second is data structure for answering range search queries with semi-algebraic ranges in O(\log n) time , with O(n^{t+\epsilon third is a data structure for answering vertical ray-shooting queries among semi-algebraic sets in \mathbb{R}^{d} in O(\log^2 n) time ;
Edit intent: meaning-changed
Original:  the third is a data structure for answering vertical ray-shooting queries among semi-algebraic sets in \mathbb{R}^{d} in O(\log^2 n) time ; and the fourth is an efficient algorithm for cutting algebraic planar curves into pseudo-segments , i. e., into Jordan arcs, each pair of which intersect at most once^3, where we show a nearly-optimal algorithm to cut n pairwise disjoint non-vertical triangles in \mathbb{R}^3 into pieces that form a depth order} .
Revised:  the third is a data structure for answering vertical ray-shooting queries among semi-algebraic sets in \mathbb{R}^{d} in O(\log^2 n) time , with O(n^{d+\epsilon fourth is an efficient algorithm for cutting algebraic planar curves into pseudo-segments , i. e., into Jordan arcs, each pair of which intersect at most once^3, where we show a nearly-optimal algorithm to cut n pairwise disjoint non-vertical triangles in \mathbb{R}^3 into pieces that form a depth order} .
Edit intent: meaning-changed
Original:  and the fourth is an efficient algorithm for cutting algebraic planar curves into pseudo-segments , i. e., into Jordan arcs, each pair of which intersect at most once^3, where we show a nearly-optimal algorithm to cut n pairwise disjoint non-vertical triangles in \mathbb{R}^3 into pieces that form a depth order} .
Revised:  and the fourth is an efficient algorithm for cutting algebraic curves in \mathbb{R into pseudo-segments , i. e., into Jordan arcs, each pair of which intersect at most once^3, where we show a nearly-optimal algorithm to cut n pairwise disjoint non-vertical triangles in \mathbb{R}^3 into pieces that form a depth order} .
Edit intent: clarity
Original:  and the fourth is an efficient algorithm for cutting algebraic planar curves into pseudo-segments , i. e., into Jordan arcs, each pair of which intersect at most once^3, where we show a nearly-optimal algorithm to cut n pairwise disjoint non-vertical triangles in \mathbb{R}^3 into pieces that form a depth order} .
Revised:  and the fourth is an efficient algorithm for cutting algebraic planar curves into pseudo-segments . The fifth application is for eliminating depth cycles among triangles in \mathbb{R^3, where we show a nearly-optimal algorithm to cut n pairwise disjoint non-vertical triangles in \mathbb{R}^3 into pieces that form a depth order} .
Edit intent: meaning-changed
Original: This paper studies inference on treatment effects in aggregate panel data settings with a single treated unit and many control units. We propose new methods for making inference on average treatment effects in settings where both the number of pre-treatment and the number of post-treatment periods are large.
Revised: This paper proposes a practical and robust method for making inference on average treatment effects in settings where both the number of pre-treatment and the number of post-treatment periods are large.
Edit intent: clarity
Original:  We propose new methods for making inference on average treatment effects in settings where both the number of pre-treatment and the number of post-treatment periods are large. We use linear models to approximate the counterfactual mean outcomes in the absence of the treatment. The counterfactuals are estimated using constrained Lasso, an essentially tuning free regression approach that nests difference-in-differences and synthetic control as special cases. We propose a K-fold cross-fitting procedure to remove the bias induced by regularization .
Revised:  We propose new methods for making inference on average treatment effects estimated by synthetic control and related methods. We develop a K-fold cross-fitting procedure to remove the bias induced by regularization .
Edit intent: clarity
Original:  To avoid the  estimation of the long run variance, we construct a self-normalized t-statistic. The test statistic has an asymptotically pivotal distribution (a student t-distribution with K-1 degrees of freedom) , which makes our procedure very easy to implement .
Revised:  To avoid the estimation of the long run variance, we construct a self-normalized t-test statistic, which has an asymptotically pivotal distribution (a student t-distribution with K-1 degrees of freedom) , which makes our procedure very easy to implement .
Edit intent: coherence
Original:  The test statistic has an asymptotically pivotal distribution (a student t-distribution with K-1 degrees of freedom) , which makes our procedure very easy to implement .
Revised:  The test statistic has an asymptotically pivotal distribution (a student t-distribution . Our procedure only requires consistent (in \ell_2-norm) estimation of the parameters, which can be verified for many popular estimators. The proposed method is easy to implement .
Edit intent: meaning-changed
Original:  The test statistic has an asymptotically pivotal distribution (a student t-distribution with K-1 degrees of freedom) , which makes our procedure very easy to implement . Our approach has several theoretical advantages. First, it does not rely on any sparsity assumptions. Second, it is fully robust against misspecification of the linear model.
Revised:  The test statistic has an asymptotically pivotal distribution (a student t-distribution with K-1 degrees of freedom) , which makes our procedure very easy to implement , provably robust against misspecification of the linear model.
Edit intent: clarity
Original:  Second, it is fully robust against misspecification of the linear model. Third, it is more efficient than difference-in-means and difference-in-differences estimators. The proposed method demonstrates an excellent performance in simulation experiments, and is taken to a data application, where we re-evaluate the economic consequences of terrorism .
Revised:  Second, it is fully robust against misspecification , and demonstrates an excellent performance in simulation experiments, and is taken to a data application, where we re-evaluate the economic consequences of terrorism .
Edit intent: coherence
Original:  Our procedure only requires consistent (in \ell_2-norm) estimation of the parameters, which can be verified for synthetic control and many other popular estimators. The proposed method is easy to implement, provably robust against misspecification, more efficient than difference-in-differences, valid with non-stationary data, and demonstrates an excellent small sample performance  .
Revised:  Our t-test is easy to implement, provably robust against misspecification, more efficient than difference-in-differences, valid with non-stationary data, and demonstrates an excellent small sample performance .
Edit intent: clarity
Original:  The proposed method is easy to implement, provably robust against misspecification, more efficient than difference-in-differences, valid with non-stationary data, and demonstrates an excellent small sample performance  .
Revised:  The proposed method is easy to implement, provably robust against misspecification, more efficient than difference-in-differences, valid with non-stationary data, and demonstrates an excellent small sample performance . Compared to difference-in-differences, our method often yields more than 50\% shorter confidence intervals and is robust to violations of parallel trends assumptions. An R-package for implementing our methods is available .
Edit intent: meaning-changed
Original: The instrumental variable quantile regression (IVQR) model of Chernozhukov and Hansen (2005, 2006 ) is a flexible and powerful tool for evaluating the impact of endogenous covariateson the whole distribution of the outcome of interest.
Revised: The instrumental variable quantile regression (IVQR) model ( Chernozhukov and Hansen (2005, 2006 ) is a flexible and powerful tool for evaluating the impact of endogenous covariateson the whole distribution of the outcome of interest.
Edit intent: clarity
Original: The instrumental variable quantile regression (IVQR) model of Chernozhukov and Hansen (2005, 2006 ) is a flexible and powerful tool for evaluating the impact of endogenous covariateson the whole distribution of the outcome of interest.
Revised: The instrumental variable quantile regression (IVQR) model of Chernozhukov and Hansen , 2005 ) is a flexible and powerful tool for evaluating the impact of endogenous covariateson the whole distribution of the outcome of interest.
Edit intent: coherence
Original: The instrumental variable quantile regression (IVQR) model of Chernozhukov and Hansen (2005, 2006 ) is a flexible and powerful tool for evaluating the impact of endogenous covariateson the whole distribution of the outcome of interest. Estimation, however, is computationally burdensome because the GMM objective function is non-smooth and non-convex .
Revised: The instrumental variable quantile regression (IVQR) model of Chernozhukov and Hansen (2005, 2006 ) is a popular tool for estimating causal quantile effects with endogenous covariates. However, estimation is complicated by the non-smoothness and non-convexity of the IVQR GMM objective function is non-smooth and non-convex .
Edit intent: clarity
Original:  This reformulation leads to new identification results and , most importantly, to practical , easy to implement, and computationally tractable estimators . We explore estimation algorithms based on the contraction mapping theorem and algorithms based on root-finding methods. We prove consistency and asymptotic normality of our estimators and establish the validity of a bootstrap procedure for estimating the limiting laws. Monte Carlo simulations support the estimator's enhanced computational tractability and demonstrate desirable finite sample properties .
Revised:  This reformulation leads to new identification results and , most importantly, to practical , easy to implement, and tuning-free estimators that do not require the availability of high-level black box optimization routines .
Edit intent: clarity
Original: A deep convolutional fuzzy system (DCFS) on a high-dimensional input space is a multi-layer connection of many low-dimensional fuzzy systems, where the input variables to the low-dimensional fuzzy systems are selected through a moving window (a convolution operator) across the input spaces of the layers.
Revised: A deep convolutional fuzzy system (DCFS) on a high-dimensional input space is a multi-layer connection of many low-dimensional fuzzy systems, where the input variables to the low-dimensional fuzzy systems are selected through a moving window across the input spaces of the layers.
Edit intent: clarity
Original:  Specifically, by viewing each of the first-layer fuzzy systems as a weak estimator of the output based only on a very small portion of the input variables, we can design these fuzzy systems using the WM Method.
Revised:  Specifically, by viewing each of the first-layer fuzzy systems as a weak estimator of the output based only on a very small portion of the input variables, we design these fuzzy systems using the WM Method.
Edit intent: coherence
Original:  After the first-layer fuzzy systems are designed, we pass the data through the first layer and replace the inputs in the original data set by the corresponding outputs of the first layer to form a new data set , then we design the second-layer fuzzy systems based on this new data set in the same way as designing the first-layer fuzzy systems.
Revised:  After the first-layer fuzzy systems are designed, we pass the data through the first layer to form a new data set , then we design the second-layer fuzzy systems based on this new data set in the same way as designing the first-layer fuzzy systems.
Edit intent: coherence
Original:  After the first-layer fuzzy systems are designed, we pass the data through the first layer and replace the inputs in the original data set by the corresponding outputs of the first layer to form a new data set , then we design the second-layer fuzzy systems based on this new data set in the same way as designing the first-layer fuzzy systems.
Revised:  After the first-layer fuzzy systems are designed, we pass the data through the first layer and replace the inputs in the original data set by the corresponding outputs of the first layer to form a new data set and design the second-layer fuzzy systems based on this new data set in the same way as designing the first-layer fuzzy systems.
Edit intent: coherence
Original:  Then, we propose a data structure with \tau levels %DIFDELCMD < \bigds %%% _{\tau} } that stores all snap-roundings of each persistence diagram in \Gamma at each resolution.
Revised:  Then, we propose a data structure with \tau levels %DIFDELCMD < \bigds %%% \mathbb{D_{\tau} } that stores all snap-roundings of each persistence diagram in \Gamma at each resolution.
Edit intent: meaning-changed