wanyu/IteraTeR_v2 huggingface dataset:
Original:  Concretely, our algorithm takes input an \epsilon-corrupted sample from a k-GMM and  outputs an approximate clustering that misclassifies at most O(k\epsilon)(\epsilon} +\eta  fraction of the points whenever every pair of components is separated by 1-\exp(- poly (k/\eta)  ) in total variation distance.
Revised:  Concretely, our algorithm takes input an \epsilon-corrupted sample from a k-GMM and outputs an approximate clustering that misclassifies at most O(k\epsilon)(\epsilon} +\eta ) fraction of the points whenever every pair of components is separated by 1-\exp(- poly (k/\eta) ) in total variation distance.
Edit intent: fluency
Original:  For k=2, our algorithms run in time and samples }poly (d) with no dependence on the spread \kappa.
Revised:  For k=2, our algorithms run in time and samples } (d) with no dependence on the spread \kappa.
Edit intent: fluency
Original:  More generally, our algorithm succeeds for mixtures of any distribution that satisfies two well-studied analytic assumptions - certifiable hypercontractivity and anti-concentration .
Revised:  More generally, our algorithm succeeds for mixtures of any distribution that satisfies two well-studied analytic assumptions - (certifiable) hypercontractivity and anti-concentration .
Edit intent: fluency
Original:  Even the information theoretic clusterability of distributions satisfying our analytic assumptions was not known  and is likely to be of independent interest.
Revised:  Even the information theoretic clusterability of distributions satisfying our analytic assumptions was not known prior to our work and is likely to be of independent interest.
Edit intent: clarity
Original:  Our algorithms build on the recent flurry of work relying on certifiable anti-concentration , first introduced in [KKK'19,RY'20].
Revised:  Our algorithms build on the recent sequence of works relying on certifiable anti-concentration , first introduced in [KKK'19,RY'20].
Edit intent: clarity
Original:  Our algorithms build on the recent flurry of work relying on certifiable anti-concentration , first introduced in [KKK'19,RY'20].
Revised:  Our algorithms build on the recent flurry of work relying on certifiable anti-concentration first introduced in [KKK'19,RY'20].
Edit intent: fluency
Original:  This involves  a low-degree sum-of-squares proof of statements that relate parameter  distance to total variation distance simply relying on hypercontractivity and anti-concentration.
Revised:  This involves giving a low-degree sum-of-squares proof of statements that relate parameter distance to total variation distance simply relying on hypercontractivity and anti-concentration.
Edit intent: clarity
Original:  This involves  a low-degree sum-of-squares proof of statements that relate parameter  distance to total variation distance simply relying on hypercontractivity and anti-concentration.
Revised:  This involves a low-degree sum-of-squares proof of statements that relate parameter distance to total variation distance by relying only on hypercontractivity and anti-concentration.
Edit intent: clarity
Original:  Even the information theoretic clusterability of separated distributions satisfying these two analytic assumptions was not known prior to our work and is likely to be of independent interest.
Revised:  Even the information-theoretic clusterability of separated distributions satisfying these two analytic assumptions was not known prior to our work and is likely to be of independent interest.
Edit intent: fluency
Original: We propose a new paradigm---called PK-clustering---to help social scientists create meaningful clusters in social networks.
Revised: We propose a new approach -- called PK-clustering -- to help social scientists create meaningful clusters in social networks.
Edit intent: clarity
Original:  Our work introduces a new clustering paradigm and a visual analytics user interface that address this issue.
Revised:  Our work introduces a new clustering approach and a visual analytics user interface that address this issue.
Edit intent: clarity
Original:  We describe our paradigm using an initial functional prototype, then provide two examples of use and early feedback from social scientists.
Revised:  We describe our approach using an initial functional prototype, then provide two examples of use and early feedback from social scientists.
Edit intent: clarity
Original:  We believe our clustering paradigm offers a novel constructive method to iteratively build knowledge while avoiding being overly influenced by the results of often-randomly selected black-box clustering algorithms.
Revised:  We believe our clustering approach offers a novel constructive method to iteratively build knowledge while avoiding being overly influenced by the results of often-randomly selected black-box clustering algorithms.
Edit intent: clarity
Original:  We believe our clustering paradigm offers a novel constructive method to iteratively build knowledge while avoiding being overly influenced by the results of often-randomly selected black-box clustering algorithms.
Revised:  We believe our clustering paradigm offers a novel constructive method to iteratively build knowledge while avoiding being overly influenced by the results of often randomly selected black-box clustering algorithms.
Edit intent: fluency
Original:  Given flow induced by non-receiving agents, we cast the optimal information design problem for the receiving agents as an instance of the generalized problem of moments .
Revised:  Given flow induced by non-receiving agents, design of an optimal private signal is shown to be a generalized problem of moments .
Edit intent: clarity
Original:  All the agents have the same prior belief about the state, but only a fixed fraction receive private route recommendations or a common message, which are generated by a known randomization, referred to as private or public signal respectively.
Revised:  The agents have the same prior belief about the state, but only a fixed fraction receive private route recommendations or a common message, which are generated by a known randomization, referred to as private or public signal respectively.
Edit intent: coherence
Original:  All the agents have the same prior belief about the state, but only a fixed fraction receive private route recommendations or a common message, which are generated by a known randomization, referred to as private or public signal respectively.
Revised:  All the agents have the same prior belief about the state, but only a fixed fraction receive private route recommendations or a common message, which are generated by a known randomization, referred to as private or public signaling policy respectively.
Edit intent: clarity
Original:  The remaining non-receiving agents choose route according to Bayes Nash flow with respect to the prior.
Revised:  The remaining agents choose route according to Bayes Nash flow with respect to the prior.
Edit intent: clarity
Original:  We develop a computational approach to solve the optimal information design problem, i.e., to minimize expected social latency cost over all public or obedient private signals .
Revised:  We develop a computational approach to solve the optimal information design problem, i.e., to minimize expected social latency over all public or obedient private signals .
Edit intent: clarity
Original:  We develop a computational approach to solve the optimal information design problem, i.e., to minimize expected social latency cost over all public or obedient private signals .
Revised:  We develop a computational approach to solve the optimal information design problem, i.e., to minimize expected social latency cost over all public or obedient private signaling policies .
Edit intent: clarity
Original:  For a fixed flow induced by non-receiving agents, design of an optimal private signal is shown to be a generalized problem of moments for affine link latency functions, and to admit an atomic solution for the basic two link case.
Revised:  For a fixed flow induced by non-participating agents, design of an optimal private signal is shown to be a generalized problem of moments for affine link latency functions, and to admit an atomic solution for the basic two link case.
Edit intent: clarity
Original:  For a fixed flow induced by non-receiving agents, design of an optimal private signal is shown to be a generalized problem of moments for affine link latency functions, and to admit an atomic solution for the basic two link case.
Revised:  For a fixed flow induced by non-receiving agents, design of an optimal private signaling policy is shown to be a generalized problem of moments for affine link latency functions, and to admit an atomic solution for the basic two link case.
Edit intent: clarity
Original: An important component of every country's COVID-19 response is fast and efficient testing -- to identify and isolate cases, as well as for early detection of local hotspots.
Revised: An important component of every country's COVID-19 response is fast and efficient testing - to identify and isolate cases, as well as for early detection of local hotspots.
Edit intent: fluency
Original:  In this note, we compare several well-established group testing schemes in the context of qPCR testing for COVID-19.
Revised:  In this note, we compare several popular group testing schemes in the context of qPCR testing for COVID-19.
Edit intent: clarity
Original:  We present Monte Carlo simulation results of a Susceptible- Infected-Removed (SIR) model on a network, where individuals are limited in the number of other people they can interact with  .
Revised:  We present Monte Carlo simulation results of a Susceptible- Infected-Removed (SIR) model on a network, where individuals are limited in the number of acquaintances that they can interact with .
Edit intent: clarity
Original:  While increased social distancing always reduces the spread of an infectious disease, the magnitude varies greatly depending on the topology of the social network.
Revised:  While increased social distancing always reduces the spread of an infectious disease, the magnitude varies greatly depending on the topology of the network.
Edit intent: fluency
Original:  In particular, the public health benefits from social distancing to a group (e.g., a country) may be completely undone if that group maintains connections with outside groups that are not social distancing .
Revised:  In particular, the public health benefits from social distancing to a group (e.g., a country) may be completely undone if that group maintains connections with outside groups that are not following suit .
Edit intent: clarity
Original:  The effectiveness of the concrete interpretations are evaluated via a disambiguation task, on an extension of a sentence disambiguation dataset to parasitic gap phrase one , using BERT, Word2Vec, and FastText vectors and Relational tensors.
Revised:  The effectiveness of the concrete interpretations are evaluated via a disambiguation task, on an extension of a sentence disambiguation dataset to parasitic gap phrases , using BERT, Word2Vec, and FastText vectors and Relational tensors.
Edit intent: clarity
Original:  This results in an "AND" gate logic for the dynamics of TFs.
Revised:  This results in an ``AND'' gate logic for the dynamics of TFs.
Edit intent: fluency
Original:  Finally, we investigate the resilience of global gene expression against node elimination protocols which mimic gene knockout experiments.
Revised:  Finally, we consider perturbations involving single node removal that mimic gene knockout experiments.
Edit intent: clarity
Original:  Results reveal that gene regulatory networks inferred from gene knockout experiments may substantially differ from the network of effective gene-gene interactions extracted from the underlying bipartite graph .
Revised:  Results reveal the strong dependence of the gene knockout cascade on the logic implemented in the underlying network dynamics, highlighting in particular that avalanche sizes cannot be easily related to gene-gene interactions extracted from the underlying bipartite graph .
Edit intent: clarity
Original:  Results reveal that gene regulatory networks inferred from gene knockout experiments may substantially differ from the network of effective gene-gene interactions extracted from the underlying bipartite graph .
Revised:  Results reveal that gene regulatory networks inferred from gene knockout experiments may substantially differ from the network of effective gene-gene interaction networks .
Edit intent: clarity
Original:  Numerically we demonstrate the effectiveness of the method on a class of parametric elliptic PDE problems , showing convergence and robustness of the approximation scheme with respect to the size of the discretization, and compare our method with existing algorithms from the literature  .
Revised:  We also include numerical experiments which demonstrate the effectiveness of the method on a class of parametric elliptic PDE problems , showing convergence and robustness of the approximation scheme with respect to the size of the discretization, and compare our method with existing algorithms from the literature .
Edit intent: clarity
Original:  Numerically we demonstrate the effectiveness of the method on a class of parametric elliptic PDE problems , showing convergence and robustness of the approximation scheme with respect to the size of the discretization, and compare our method with existing algorithms from the literature  .
Revised:  Numerically we demonstrate the effectiveness of the method , showing convergence and robustness of the approximation scheme with respect to the size of the discretization, and compare our method with existing algorithms from the literature .
Edit intent: clarity
Original:  Numerically we demonstrate the effectiveness of the method on a class of parametric elliptic PDE problems , showing convergence and robustness of the approximation scheme with respect to the size of the discretization, and compare our method with existing algorithms from the literature  .
Revised:  Numerically we demonstrate the effectiveness of the method on a class of parametric elliptic PDE problems , showing convergence and robustness of the approximation scheme with respect to the size of the discretization, and compare it with existing algorithms from the literature .
Edit intent: clarity
Original: We investigate whether sophisticated volatility estimation improves the out-of-sample performance of mean-variance portfolio strategies relative to the na\"{\i 1/N strategy.
Revised: We investigate whether sophisticated volatility estimation improves the out-of-sample performance of mean-variance portfolio strategies relative to the naive 1/N strategy.
Edit intent: fluency
Original: Avikainen proved the estimate \mathbb{E[|f(X)-f(X)|^{q}]
Revised: Avikainen [|f(X)-f(X)|^{q}]
Edit intent: clarity
Original: q \in [1,\infty), one-dimensional random variables X with the bounded density function and , and a function f of bounded variation in R ]\leq C(p,q)E[|X-X|^{p}]^{1{p+1}}, where X is a one-dimensional random variable with a bounded density, and }X  . In this article, we will provide multi-dimensional analogues of this estimate for functions of bounded variation in \mathbb{R}^{d}, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents  and fractional Sobolev spaces.
Revised: q \in [1,\infty), , and a function f of bounded variation in R ]\leq C(p,q)E[|X-X|^{p}]^{1{p+1}}, where X is a one-dimensional random variable with a bounded density, and }X . In this article, we will provide multi-dimensional analogues of this estimate for functions of bounded variation in \mathbb{R}^{d}, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents and fractional Sobolev spaces.
Edit intent: clarity
Original: q \in [1,\infty), one-dimensional random variables X with the bounded density function and , and a function f of bounded variation in R ]\leq C(p,q)E[|X-X|^{p}]^{1{p+1}}, where X is a one-dimensional random variable with a bounded density, and }X  . In this article, we will provide multi-dimensional analogues of this estimate for functions of bounded variation in \mathbb{R}^{d}, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents  and fractional Sobolev spaces.
Revised: q \in [1,\infty), one-dimensional random variables X with the bounded density function and and any function f of bounded variation in R ]\leq C(p,q)E[|X-X|^{p}]^{1{p+1}}, where X is a one-dimensional random variable with a bounded density, and }X . In this article, we will provide multi-dimensional analogues of this estimate for functions of bounded variation in \mathbb{R}^{d}, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents and fractional Sobolev spaces.
Edit intent: clarity
Original: q \in [1,\infty), one-dimensional random variables X with the bounded density function and , and a function f of bounded variation in R ]\leq C(p,q)E[|X-X|^{p}]^{1{p+1}}, where X is a one-dimensional random variable with a bounded density, and }X  . In this article, we will provide multi-dimensional analogues of this estimate for functions of bounded variation in \mathbb{R}^{d}, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents  and fractional Sobolev spaces.
Revised: q \in [1,\infty), one-dimensional random variables X with the bounded density function and , and a function f of bounded variation in R ]\leq C(p,q)E[|X-X|^{p}]^{1{p+1}}, where X is a one-dimensional random variable with a bounded density, and }X is an arbitrary random variable . In this article, we will provide multi-dimensional analogues of this estimate for functions of bounded variation in \mathbb{R}^{d}, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents and fractional Sobolev spaces.
Edit intent: clarity
Original: q \in [1,\infty), one-dimensional random variables X with the bounded density function and , and a function f of bounded variation in R ]\leq C(p,q)E[|X-X|^{p}]^{1{p+1}}, where X is a one-dimensional random variable with a bounded density, and }X  . In this article, we will provide multi-dimensional analogues of this estimate for functions of bounded variation in \mathbb{R}^{d}, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents  and fractional Sobolev spaces.
Revised: q \in [1,\infty), one-dimensional random variables X with the bounded density function and , and a function f of bounded variation in R ]\leq C(p,q)E[|X-X|^{p}]^{1{p+1}}, where X is a one-dimensional random variable with a bounded density, and }X . In this article, we will provide multi-dimensional versions of this estimate for functions of bounded variation in \mathbb{R}^{d}, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents and fractional Sobolev spaces.
Edit intent: clarity
Original: q \in [1,\infty), one-dimensional random variables X with the bounded density function and , and a function f of bounded variation in R ]\leq C(p,q)E[|X-X|^{p}]^{1{p+1}}, where X is a one-dimensional random variable with a bounded density, and }X  . In this article, we will provide multi-dimensional analogues of this estimate for functions of bounded variation in \mathbb{R}^{d}, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents  and fractional Sobolev spaces.
Revised: q \in [1,\infty), one-dimensional random variables X with the bounded density function and , and a function f of bounded variation in R ]\leq C(p,q)E[|X-X|^{p}]^{1{p+1}}, where X is a one-dimensional random variable with a bounded density, and }X . In this article, we will provide multi-dimensional analogues of this estimate for functions of bounded variation in \mathbb{R}^{d}, Orlicz--Sobolev spaces, Sobolev spaces with variable exponents and fractional Sobolev spaces.
Edit intent: fluency
Original: q \in [1,\infty), one-dimensional random variables X with the bounded density function and , and a function f of bounded variation in R ]\leq C(p,q)E[|X-X|^{p}]^{1{p+1}}, where X is a one-dimensional random variable with a bounded density, and }X  . In this article, we will provide multi-dimensional analogues of this estimate for functions of bounded variation in \mathbb{R}^{d}, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents  and fractional Sobolev spaces.
Revised: q \in [1,\infty), one-dimensional random variables X with the bounded density function and , and a function f of bounded variation in R ]\leq C(p,q)E[|X-X|^{p}]^{1{p+1}}, where X is a one-dimensional random variable with a bounded density, and }X . In this article, we will provide multi-dimensional analogues of this estimate for functions of bounded variation in \mathbb{R}^{d}, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents , and fractional Sobolev spaces.
Edit intent: fluency
Original:  The main idea of our arguments is to use Hardy-Littlewood maximal estimates and pointwise characterizations of these function spaces.
Revised:  The main idea of our arguments is to use the Hardy--Littlewood maximal estimates and pointwise characterizations of these function spaces.
Edit intent: fluency
Original:  We will apply main statements to numerical analysis on irregular functionals of a solution to stochastic differential equations based on the Euler-Maruyama scheme and the multilevel Monte Carlo method , and to estimates of the L^{2}-time regularity of decoupled forward-backward stochastic differential equations with irregular terminal conditions.
Revised:  We will apply main statements to numerical analysis on irregular functionals of the solution of stochastic differential equations based on the Euler-Maruyama scheme and the multilevel Monte Carlo method , and to estimates of the L^{2}-time regularity of decoupled forward-backward stochastic differential equations with irregular terminal conditions.
Edit intent: fluency
Original:  We will apply main statements to numerical analysis on irregular functionals of a solution to stochastic differential equations based on the Euler-Maruyama scheme and the multilevel Monte Carlo method , and to estimates of the L^{2}-time regularity of decoupled forward-backward stochastic differential equations with irregular terminal conditions.
Revised:  We will apply main statements to numerical analysis on irregular functionals of a solution to stochastic differential equations , and to estimates of the L^{2}-time regularity of decoupled forward-backward stochastic differential equations with irregular terminal conditions.
Edit intent: clarity
Original:  We will apply main statements to numerical analysis on irregular functionals of a solution to stochastic differential equations based on the Euler-Maruyama scheme and the multilevel Monte Carlo method , and to estimates of the L^{2}-time regularity of decoupled forward-backward stochastic differential equations with irregular terminal conditions.
Revised:  We will apply main statements to numerical analysis on irregular functionals of a solution to stochastic differential equations based on the Euler-Maruyama scheme and the multilevel Monte Carlo method , and to estimate the L^{2}-time regularity of decoupled forward-backward stochastic differential equations with irregular terminal conditions.
Edit intent: fluency
Original:  We will apply main statements to numerical analysis on irregular functionals of a solution to stochastic differential equations based on the Euler-Maruyama scheme and the multilevel Monte Carlo method , and to estimates of the L^{2}-time regularity of decoupled forward-backward stochastic differential equations with irregular terminal conditions.
Revised:  We will apply main statements to numerical analysis on irregular functionals of a solution to stochastic differential equations based on the Euler-Maruyama scheme and the multilevel Monte Carlo method , and to estimates of the L^{2}-time regularity of decoupled forward--backward stochastic differential equations with irregular terminal conditions.
Edit intent: fluency
Original:  We apply our main results to analyze the numerical approximation for some irregular functionals of the solution of stochastic differential equations , and to estimate the L^{2 .
Revised:  We apply our main results to analyze the numerical approximation for some irregular functionals of the solution of stochastic differential equations .
Edit intent: coherence