wanyu/IteraTeR_full_sent huggingface dataset:
Original:  The players in ensemble games are pre-trained binary classifiers that collaborate in an ensemble to correctly label points from a dataset. We design Troupe a scalable algorithm that designates payoffs to individual models based on the Shapley value of those in the ensemble game. We show that the approximate  Shapley value of classifiers in these games is an adequate measure for selecting a subgroup of highly predictive models .
Revised:  The players in ensemble games are pre-trained models cooperate to make classification decisions. To quantify the importance of models in these ensemble games, we define Shapley value of classifiers in these games is an adequate measure for selecting a subgroup of highly predictive models .
Edit intent: clarity
Original:  We show that the approximate  Shapley value of classifiers in these games is an adequate measure for selecting a subgroup of highly predictive models .
Revised:  We show that the approximate -- an efficient algorithm which allocates payoffs based on approximate Shapley values of the classifiers. We argue that the Shapley value of classifiers in these games is an adequate measure for selecting a subgroup of highly predictive models .
Edit intent: meaning-changed
Original:  We show that the approximate  Shapley value of classifiers in these games is an adequate measure for selecting a subgroup of highly predictive models . In addition, we introduce the Shapley entropy a new metric to quantify the heterogeneity of machine learning ensembles when it comes to model quality. We analytically prove that our Shapley value approximation algorithm is accurate and scales to large ensembles and big data.
Revised:  We show that the approximate Shapley value of classifiers in these games is an effective decision metric for choosing a high performing subset of models from the ensemble. Our analytical findings prove that our Shapley value approximation algorithm is accurate and scales to large ensembles and big data.
Edit intent: clarity
Original:  We analytically prove that our Shapley value approximation algorithm is accurate and scales to large ensembles and big data. Experimental results on graph classification tasks establish that Troupe gives precise estimates of the Shapley value in ensemble games.
Revised:  We analytically prove that our Shapley value estimation scheme is precise and scalable; its performance increases with size of the dataset and ensemble. Empirical results on real world graph classification tasks establish that Troupe gives precise estimates of the Shapley value in ensemble games.
Edit intent: clarity
Original:  Experimental results on graph classification tasks establish that Troupe gives precise estimates of the Shapley value in ensemble games. We demonstrate that the Shapley value can be used for pruning large ensembles, show that complex classifiers have a prime role in correct and incorrect classification decisions, and provide evidence that adversarial models receive a low valuation  .
Revised:  Experimental results on graph classification tasks establish that Troupe gives precise estimates of the Shapley value . We find that Shapley values can be utilized for ensemble pruning, and that adversarial models receive a low valuation .
Edit intent: clarity
Original:  We demonstrate that the Shapley value can be used for pruning large ensembles, show that complex classifiers have a prime role in correct and incorrect classification decisions, and provide evidence that adversarial models receive a low valuation  .
Revised:  We demonstrate that the Shapley value can be used for pruning large ensembles, show that complex classifiers have a prime role in correct and incorrect classification decisions, and provide evidence that adversarial models receive a low valuation . Complex classifiers are frequently found to be responsible for both correct and incorrect classification decisions .
Edit intent: meaning-changed
Original: Node attributes are ubiquitous in real-world networks, whose fusion with graph topology raises new challenges for the detection and understanding of community structure. Due to their principled characterization and interpretation , probabilistic generative models (PGMs) have become the mainstream methods for community detection in attributed networks.
Revised: Node attributes are ubiquitous in real-world networks, communities can be reflected by abundant node attributes with the fusion of graph topology. In attribute-aware community detection , probabilistic generative models (PGMs) have become the mainstream methods for community detection in attributed networks.
Edit intent: meaning-changed
Original:  Due to their principled characterization and interpretation , probabilistic generative models (PGMs) have become the mainstream methods for community detection in attributed networks. Most existing PGMs require the attributes to be categorical or Gaussian distributed.
Revised:  Due to their principled characterization and interpretation , probabilistic generative models (PGMs) have become the mainstream fusion method due to their principled characterization and interpretation. Here, we propose a novel PGM without imposing any distributional assumptions on attributes, which is superior to existing PGMs that require attributes to be categorical or Gaussian distributed.
Edit intent: coherence
Original:  For the generality of our model, we consider the impact of the distances between attributes on node popularity , whose description raises the model selection problem in statistical inference. We present a novel scheme to address this issue by analyzing the detectability of communities for our model , which is also a quantitative description on the effect of node attributes with respect to communities .
Revised:  For the generality of our model, we consider the impact of the distances between attributes on node popularity using an additional term. To characterize the effect quantitatively, we analyze the detectability of communities for our model , which is also a quantitative description on the effect of node attributes with respect to communities .
Edit intent: meaning-changed
Original:  We present a novel scheme to address this issue by analyzing the detectability of communities for our model , which is also a quantitative description on the effect of node attributes with respect to communities .
Revised:  We present a novel scheme to address this issue by analyzing the detectability of communities for the proposed model and then establish the requirements of the attribute-popularity term, which leads to a new scheme for the model selection problem in attribute-aware community detection .
Edit intent: meaning-changed
Original: We revisit the randomized incremental construction of the Trapezoidal Search DAG (TSD) for a set of{\cal   n non-crossing segments, e.g. edges from planar subdivisions.
Revised: The Randomized Incremental Construction (RIC) of search DAGs for point location in planar subdivisions, nearest-neighbor search in 2D points, and extreme point search in 3D convex hulls, are well known to take{\cal n non-crossing segments, e.g. edges from planar subdivisions.
Edit intent: meaning-changed
Original: We revisit the randomized incremental construction of the Trapezoidal Search DAG (TSD) for a set of{\cal   n non-crossing segments, e.g. edges from planar subdivisions.
Revised: We revisit the randomized incremental construction of the Trapezoidal Search DAG (TSD) for a set of{\cal O n non-crossing segments, e.g. edges from planar subdivisions.
Edit intent: fluency
Original: We revisit the randomized incremental construction of the Trapezoidal Search DAG (TSD) for a set of{\cal   n non-crossing segments, e.g. edges from planar subdivisions.
Revised: We revisit the randomized incremental construction of the Trapezoidal Search DAG (TSD) for a set of{\cal ( n non-crossing segments, e.g. edges from planar subdivisions.
Edit intent: fluency
Original: We revisit the randomized incremental construction of the Trapezoidal Search DAG (TSD) for a set of{\cal   n non-crossing segments, e.g. edges from planar subdivisions. It is well known that this point location structure has {\cal O}(n) expected size and {\cal O} (n \ln n) expected construction time.
Revised: We revisit the randomized incremental construction of the Trapezoidal Search DAG (TSD) for a set of{\cal n \log n) expected time for structures of {\cal O}(n) expected size and {\cal O} (n \ln n) expected construction time.
Edit intent: clarity
Original:  It is well known that this point location structure has {\cal O}(n) expected size and {\cal O} (n \ln n) expected construction time. Our main result is an improved tail bound, with exponential decay, for the size of the TSD: There is a constant such that the probability for a TSD to exceed its expected size by more than this factor is at most 1/e^n.This yields improved bounds on the TSD construction and their maintenance.I.e. TSD construction takes with high probability {\cal O}( n \ln n) time and TSD size can be made worst case {\cal O}(n) with an expected rebuild cost of {\cal O}( 1).
Revised:  It is well known that this point location structure has {\cal O}(n) expected size and {\cal O} (\log n) comparisons in the first and w.h.p. {\cal O}( n \ln n) time and TSD size can be made worst case {\cal O}(n) with an expected rebuild cost of {\cal O}( 1).
Edit intent: meaning-changed
Original: I.e. TSD construction takes with high probability {\cal O}( n \ln n) time and TSD size can be made worst case {\cal O}(n) with an expected rebuild cost of {\cal O}( 1).
Revised: I.e. TSD construction takes with high probability {\cal O}( \log^2 n) comparisons in the latter two DAGs. However, the expected depth of the DAGs and high probability bounds for their size are unknown. Using a novel analysis technique, we show that the three DAGs have w.h.p. i) a size of {\cal O}(n) with an expected rebuild cost of {\cal O}( 1).
Edit intent: meaning-changed
Original: I.e. TSD construction takes with high probability {\cal O}( n \ln n) time and TSD size can be made worst case {\cal O}(n) with an expected rebuild cost of {\cal O}( 1).
Revised: I.e. TSD construction takes with high probability {\cal O}( n \ln n) time and TSD size can be made worst case {\cal O}(n) , ii) a depth of {\cal O}( 1).
Edit intent: meaning-changed
Original: I.e. TSD construction takes with high probability {\cal O}( n \ln n) time and TSD size can be made worst case {\cal O}(n) with an expected rebuild cost of {\cal O}( 1). The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [  Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Revised: I.e. TSD construction takes with high probability {\cal O}( n \ln n) time and TSD size can be made worst case {\cal O}(n) with an expected rebuild cost of {\cal O}( \log n), and iii) a construction time of {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [ Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Edit intent: meaning-changed
Original:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [  Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Revised:  The proposed analysis technique also shows that the expected depth is {\cal O}( n \log n). One application of these new and improved results are\emph{ [ Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Edit intent: meaning-changed
Original:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [  Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Revised:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{remarkably simple [ Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Edit intent: meaning-changed
Original:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [  Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Revised:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ Las Vegas verifiers to obtain search DAGs with optimal worst-case bounds. This positively answers the conjectured logarithmic search cost in the DAG of Delaunay triangulations[ Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Edit intent: meaning-changed
Original:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [  Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Revised:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [Guibas et al.; ICALP 1990 Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Edit intent: meaning-changed
Original:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [  Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Revised:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [ and a conjecture on the depth of the DAG of Trapezoidal subdivisions Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Edit intent: meaning-changed
Original:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [  Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Revised:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [ Hemmer et al. ; ESA 2012 [ .
Edit intent: meaning-changed
Original:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [  Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Revised:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [ Hemmer et al. that is used in the CGAL implementation of the TSD . It also shows that history-based RIC circumvents a lower bound on runtime tail estimates of conflict-graph RICs[ .
Edit intent: meaning-changed
Original:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [  Hemmer et al. that is used in the CGAL implementation of the TSD [ .
Revised:  The proposed analysis technique also shows that the expected depth is {\cal O}( \ln n ), which partially solves a recent conjecture by\emph{ [ Hemmer et al. that is used in the CGAL implementation of the TSD [Sen; STACS 2019 .
Edit intent: meaning-changed
Original: The computation of probability density functions (PDF) using approximate maps (surrogate models) is a building block in such diverse fields as forward uncertainty quantification (UQ), sampling algorithms, learning, and inverse problems. In these settings, the probability measure of interest is induced by an unknown map from a known probability space to the real line, i. e., the measure of interest is a pushforward of another known measure.
Revised: The computation of probability density functions (PDF) using approximate maps (surrogate models) is a building block in computational probability. We consider forward problems in uncertainty quantification: the inputs or the parameters of an otherwise deterministic model are random with a known distribution. The scalar quantity of interest is a pushforward of another known measure.
Edit intent: clarity
Original:  In these settings, the probability measure of interest is induced by an unknown map from a known probability space to the real line, i. e., the measure of interest is a pushforward of another known measure. In computation, we do not know the true map , but only an approximate one. In the field of UQ, the{\em   generalized Polynomial Chaos (gPC) method is widely popular and yields excellent approximations of the map and its moment .
Revised:  In these settings, the probability measure of interest is induced by an unknown map from a known probability space to the real line, i. e., the measure of interest is a fixed function of the parameters, and can therefore be considered as a random variable as a well. Often, the quantity of interest map is not explicitly known, and so the computational problem is to find its ``right'' approximation (surrogate model). For the goal of approximating the{\em generalized Polynomial Chaos (gPC) method is widely popular and yields excellent approximations of the map and its moment .
Edit intent: meaning-changed
Original:  In the field of UQ, the{\em   generalized Polynomial Chaos (gPC) method is widely popular and yields excellent approximations of the map and its moment .
Revised:  In the field of UQ, the{\em of the quantity of interest, there is a developed body of research. One widely popular approach is generalized Polynomial Chaos (gPC) method is widely popular and yields excellent approximations of the map and its moment .
Edit intent: meaning-changed
Original: A highly desirable property of networks is robustness to failures. Consider a metric space (X, d_X ]  ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Revised: Chan, Har-Peled, and Jones ] ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Edit intent: meaning-changed
Original:  Consider a metric space (X, d_X ]  ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Revised:  Consider a metric space (X, d_X 2020] ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Edit intent: meaning-changed
Original:  Consider a metric space (X, d_X ]  ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Revised:  Consider a metric space (X, d_X ] recently developed locality-sensitive ordering (LSO ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Edit intent: meaning-changed
Original:  Consider a metric space (X, d_X ]  ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Revised:  Consider a metric space (X, d_X ] ), a new tool that allows one to reduce problems in the Euclidean space \mathbb{R }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Edit intent: meaning-changed
Original:  Consider a metric space (X, d_X ]  ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Revised:  Consider a metric space (X, d_X ] ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H \'{a}} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Edit intent: meaning-changed
Original:  Consider a metric space (X, d_X ]  ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Revised:  Consider a metric space (X, d_X ] ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }}h [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Edit intent: meaning-changed
Original:  Consider a metric space (X, d_X ]  ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Revised:  Consider a metric space (X, d_X ] ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ 2019,2020 ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|.
Edit intent: meaning-changed
Original:  Consider a metric space (X, d_X ]  ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] preserves all the distances between points in X\setminus B^+ up to a stretch factor t, while the expected size of B^+ is as most (1+\vartheta)|B|. Such a spanner could withstand a catastrophe: failureof even{\em    90\\%DIF < of the network.
Revised:  Consider a metric space (X, d_X ] ), a graph H over X is a \vartheta-reliable t-spanner if, for every set of failed vertices B\subset X, there is a superset B^+\supseteq B such that the induced subgraph H }} [ X\setminus B ] used the LSO of Chan{\em 90\\%DIF < of the network.
Edit intent: meaning-changed