wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Our main technical contribution is an approach to handle the correlation that builds due to interactivity and quantifies how effectively one can exploit this correlation in spite of the local constraints. Using this, we fill gaps in some prior works and characterize the optimal sample complexity of learning and testing discrete distributions under total variation distance, for both communication and local differential privacy constraints. Prior to our work, this was known only for the problem of testing under local privacy constraints (Amin, Joseph, and Mao (2020);
Revised:  Our main technical contribution is an approach to handle the correlation that builds due to interactivity ; in fact, gaps can be found in prior claims of tight bounds of distribution estimation using interactive protocols. We propose a new approach to handle this correlation and establish a unified method to establish lower bounds for both tasks. As an application, we obtain optimal bounds for both estimation and testing under local privacy constraints (Amin, Joseph, and Mao (2020);
Edit intent: clarity
Original:  Prior to our work, this was known only for the problem of testing under local privacy constraints (Amin, Joseph, and Mao (2020); Berrett and Butucea (2020)). Our results show that interactivity does not help for learning or testing under these two constraints. Finally, we provide the first instance of a natural family of "leaky query" local constraints under which interactive protocols strictly outperform the noninteractive ones for distribution testing .
Revised:  Prior to our work, this was known only for the problem of testing under local differential privacy and communication constraints. We also provide an example of a natural family of "leaky query" local constraints under which interactive protocols strictly outperform the noninteractive ones for distribution testing .
Edit intent: clarity
Original: We study the effects of rounding on the moments of a random variable . Specifically, given a random variable X and its rounded counterpart rd(X), we study | \mathbf{E - \mathbf{E | for non-negative integer k.
Revised: We study the effects of rounding on the moments of random variables . Specifically, given a random variable X and its rounded counterpart rd(X), we study | \mathbf{E - \mathbf{E | for non-negative integer k.
Edit intent: fluency
Original: We study the effects of rounding on the moments of a random variable . Specifically, given a random variable X and its rounded counterpart rd(X), we study | \mathbf{E - \mathbf{E | for non-negative integer k.
Revised: We study the effects of rounding on the moments of a random variable . Specifically, given a random variable X and its rounded counterpart rd(X), we study | \mathbb{E - \mathbf{E | for non-negative integer k.
Edit intent: fluency
Original: We study the effects of rounding on the moments of a random variable . Specifically, given a random variable X and its rounded counterpart rd(X), we study | \mathbf{E - \mathbf{E | for non-negative integer k.
Revised: We study the effects of rounding on the moments of a random variable . Specifically, given a random variable X and its rounded counterpart rd(X), we study | \mathbf{E - \mathbb{E | for non-negative integer k.
Edit intent: clarity
Original:  In both cases, we show, under reasonable assumptions on the density function of X, how to compute a constant C such that |E[X^k] - E[rd(X)^{k}]| < C\epsilon^2, provided  \operatorname{rd}(x) - x| \leq \epsilon  E(x) . Asymptotic and non-asymptotic }\to _{\geq 0} is some fixed positive piecewise linear function.
Revised:  In both cases, we show, under reasonable assumptions on the density function of X, how to compute a constant C such that |E[X^k] - E[rd(X)^{k}]| < C\epsilon^2, provided | \operatorname{rd}(x) - x| \leq \epsilon E(x) . Asymptotic and non-asymptotic }\to _{\geq 0} is some fixed positive piecewise linear function.
Edit intent: fluency
Original:  In both cases, we show, under reasonable assumptions on the density function of X, how to compute a constant C such that |E[X^k] - E[rd(X)^{k}]| < C\epsilon^2, provided  \operatorname{rd}(x) - x| \leq \epsilon  E(x) . Asymptotic and non-asymptotic }\to _{\geq 0} is some fixed positive piecewise linear function.
Revised:  In both cases, we show, under reasonable assumptions on the density function of X, how to compute a constant C such that |E[X^k] - E[rd(X)^{k}]| < C\epsilon^2, provided \operatorname{rd}(x) - x| \leq \epsilon \: E(x) . Asymptotic and non-asymptotic }\to _{\geq 0} is some fixed positive piecewise linear function.
Edit intent: meaning-changed
Original:  In both cases, we show, under reasonable assumptions on the density function of X, how to compute a constant C such that |E[X^k] - E[rd(X)^{k}]| < C\epsilon^2, provided  \operatorname{rd}(x) - x| \leq \epsilon  E(x) . Asymptotic and non-asymptotic }\to _{\geq 0} is some fixed positive piecewise linear function.
Revised:  In both cases, we show, under reasonable assumptions on the density function of X, how to compute a constant C such that |E[X^k] - E[rd(X)^{k}]| < C\epsilon^2, provided \operatorname{rd}(x) - x| \leq \epsilon E(x) , where E : \mathbb{R }\to _{\geq 0} is some fixed positive piecewise linear function.
Edit intent: meaning-changed
Original:  In both cases, we show, under reasonable assumptions on the density function of X, how to compute a constant C such that |E[X^k] - E[rd(X)^{k}]| < C\epsilon^2, provided  \operatorname{rd}(x) - x| \leq \epsilon  E(x) . Asymptotic and non-asymptotic }\to _{\geq 0} is some fixed positive piecewise linear function.
Revised:  In both cases, we show, under reasonable assumptions on the density function of X, how to compute a constant C such that |E[X^k] - E[rd(X)^{k}]| < C\epsilon^2, provided \operatorname{rd}(x) - x| \leq \epsilon E(x) . Asymptotic and non-asymptotic }\to \mathbb{R_{\geq 0} is some fixed positive piecewise linear function.
Edit intent: meaning-changed
Original:  Refined } bounds for the absolute moments \mathbb{E[ |X^k-\operatorname{rd}(X)^{k}| ] } [ |X^k-\operatorname{rd}(X)^{k}|] } are also given.
Revised:  Refined } bounds for the absolute moments [ |X^k-\operatorname{rd}(X)^{k}| ] } [ |X^k-\operatorname{rd}(X)^{k}|] } are also given.
Edit intent: meaning-changed
Original:  Refined } bounds for the absolute moments \mathbb{E[ |X^k-\operatorname{rd}(X)^{k}| ] } [ |X^k-\operatorname{rd}(X)^{k}|] } are also given.
Revised:  Refined } bounds for the absolute moments \mathbb{E[ |X^k-\operatorname{rd}(X)^{k}| ] } \mathbb{E[ |X^k-\operatorname{rd}(X)^{k}|] } are also given.
Edit intent: fluency
Original: Anomaly Detection is one of the most important tasks in unsupervised learning as it aims at detecting anomalous behaviours w.r.t. historical data; in particular, multivariate Anomaly Detection has an important role in many applications thanks to the capability of summarizing the status of a complex system or observed phenomenon with a single indicator (typically called `Anomaly Score') and thanks to the unsupervised nature of the task that does not require human tagging.
Revised: Anomaly Detection is one of the most important tasks in unsupervised learning as it aims at detecting anomalous behaviours with respect to historical data. In particular, multivariate Anomaly Detection has an important role in many applications thanks to the capability of summarizing the status of a complex system or observed phenomenon with a single indicator (typically called `Anomaly Score') and thanks to the unsupervised nature of the task that does not require human tagging.
Edit intent: clarity
Original:  Moreover, we define a procedure to perform unsupervised feature selection for Anomaly Detection problems based on our interpretability method . We provide an extensive analysis of the proposed approaches, including comparisons against state-of-the-art interpretability techniques .
Revised:  Moreover, we define a procedure to perform unsupervised feature selection for Anomaly Detection problems based on our interpretability method ; such procedure also serves the purpose of tackling the challenging task of feature importance evaluation in unsupervised anomaly detection .
Edit intent: meaning-changed
Original:  The radial scaling converts the problem of approximation of high frequency contents of PDEs' solutions to one of lower frequency , and the compact support activation functions facilitate the separation of scales to be approximated by corresponding DNNs.
Revised:  The radial scaling converts the problem of approximation of high frequency contents of PDEs' solutions to a problem of learning about lower frequency functions , and the compact support activation functions facilitate the separation of scales to be approximated by corresponding DNNs.
Edit intent: clarity
Original:  The radial scaling converts the problem of approximation of high frequency contents of PDEs' solutions to one of lower frequency , and the compact support activation functions facilitate the separation of scales to be approximated by corresponding DNNs.
Revised:  The radial scaling converts the problem of approximation of high frequency contents of PDEs' solutions to one of lower frequency , and the compact support activation functions facilitate the separation of frequency contents of the target function to be approximated by corresponding DNNs.
Edit intent: clarity
Original: Despite advances in the acquisition of medical imaging and computer-aided support techniques, x-rays due to their low cost, high availability and low radiation levels are still an important diagnostic procedure, constituting the most frequently performed radiographic examination in pediatric patients for disease investigation while researchers are looking for increasingly efficient techniques to support decision-making.
Revised: Several reasons explain the significant role that chest X-rays play on supporting clinical analysis and early disease detection in pediatric patients, such as low cost, high availability and low radiation levels are still an important diagnostic procedure, constituting the most frequently performed radiographic examination in pediatric patients for disease investigation while researchers are looking for increasingly efficient techniques to support decision-making.
Edit intent: meaning-changed
Original: Despite advances in the acquisition of medical imaging and computer-aided support techniques, x-rays due to their low cost, high availability and low radiation levels are still an important diagnostic procedure, constituting the most frequently performed radiographic examination in pediatric patients for disease investigation while researchers are looking for increasingly efficient techniques to support decision-making.
Revised: Despite advances in the acquisition of medical imaging and computer-aided support techniques, x-rays due to their low cost, high resolution, low radiation levels are still an important diagnostic procedure, constituting the most frequently performed radiographic examination in pediatric patients for disease investigation while researchers are looking for increasingly efficient techniques to support decision-making.
Edit intent: clarity
Original: Despite advances in the acquisition of medical imaging and computer-aided support techniques, x-rays due to their low cost, high availability and low radiation levels are still an important diagnostic procedure, constituting the most frequently performed radiographic examination in pediatric patients for disease investigation while researchers are looking for increasingly efficient techniques to support decision-making. Emerging in the last decade as a viable alternative, deep learning (DL) , a technique inspired by neuroscientific and neural connections, has gained much attention from researchers and made significant advances in the field of medical imaging, outperformed the state-of-art of many techniques, including those applied to pediatric chest radiography (PCXR).
Revised: Despite advances in the acquisition of medical imaging and computer-aided support techniques, x-rays due to their low cost, high availability and low radiation levels , and high availability. In the last decade as a viable alternative, deep learning (DL) , a technique inspired by neuroscientific and neural connections, has gained much attention from researchers and made significant advances in the field of medical imaging, outperformed the state-of-art of many techniques, including those applied to pediatric chest radiography (PCXR).
Edit intent: coherence
Original:  Emerging in the last decade as a viable alternative, deep learning (DL) , a technique inspired by neuroscientific and neural connections, has gained much attention from researchers and made significant advances in the field of medical imaging, outperformed the state-of-art of many techniques, including those applied to pediatric chest radiography (PCXR).
Revised:  Emerging in the last decade , Deep Learning (DL) , a technique inspired by neuroscientific and neural connections, has gained much attention from researchers and made significant advances in the field of medical imaging, outperformed the state-of-art of many techniques, including those applied to pediatric chest radiography (PCXR).
Edit intent: clarity
Original:  Emerging in the last decade as a viable alternative, deep learning (DL) , a technique inspired by neuroscientific and neural connections, has gained much attention from researchers and made significant advances in the field of medical imaging, outperformed the state-of-art of many techniques, including those applied to pediatric chest radiography (PCXR).
Revised:  Emerging in the last decade as a viable alternative, deep learning (DL) has been given special attention from the computer-aided diagnosis research community, outperforming the state of the art of many techniques, including those applied to pediatric chest radiography (PCXR).
Edit intent: clarity
Original:  Emerging in the last decade as a viable alternative, deep learning (DL) , a technique inspired by neuroscientific and neural connections, has gained much attention from researchers and made significant advances in the field of medical imaging, outperformed the state-of-art of many techniques, including those applied to pediatric chest radiography (PCXR).
Revised:  Emerging in the last decade as a viable alternative, deep learning (DL) , a technique inspired by neuroscientific and neural connections, has gained much attention from researchers and made significant advances in the field of medical imaging, outperformed the state-of-art of many techniques, including those applied to pediatric chest X-rays (PCXR).
Edit intent: clarity
Original:  Given the scenario and considering the fact that, as far as we know, there is still no mapping study on the application of deep learning techniques in PCXRimages, we propose in this article a "deep radiography" of the last decade in this research topic and a preliminary research agenda that deals with the state of the art of applying DL on PCXR that constitute a collaborative tool for future researchers.
Revised:  Due to this increasing interest, much high-quality secondary research has also arisen, overviewing machine learning and DL algorithms on medical imaging and PCXR, in particular. However, these secondary studies follow different guidelines, hampering their reproduction or improvement by third-parties regarding the identified trends and gaps. This paper proposes a "deep radiography" of the last decade in this research topic and a preliminary research agenda that deals with the state of the art of applying DL on PCXR that constitute a collaborative tool for future researchers.
Edit intent: meaning-changed
Original:  Given the scenario and considering the fact that, as far as we know, there is still no mapping study on the application of deep learning techniques in PCXRimages, we propose in this article a "deep radiography" of the last decade in this research topic and a preliminary research agenda that deals with the state of the art of applying DL on PCXR that constitute a collaborative tool for future researchers. Our goal is to identify primary studies and support the process of choosing and developing DL techniques applied to PCXR images , in addition to pointing out gaps and trends by drawing up a preliminary research agenda.
Revised:  Given the scenario and considering the fact that, as far as we know, there is still no mapping study on the application of deep learning techniques in PCXRimages, we propose in this article a "deep radiography" of primary research on DL techniques applied to PCXR images , in addition to pointing out gaps and trends by drawing up a preliminary research agenda.
Edit intent: coherence
Original:  Our goal is to identify primary studies and support the process of choosing and developing DL techniques applied to PCXR images , in addition to pointing out gaps and trends by drawing up a preliminary research agenda.
Revised:  Our goal is to identify primary studies and support the process of choosing and developing DL techniques applied in PCXR images. We elaborated on a Systematic Literature Mapping (SLM) protocol, including automatic search on six sources for studies published from January 1 , in addition to pointing out gaps and trends by drawing up a preliminary research agenda.
Edit intent: meaning-changed
Original:  Our goal is to identify primary studies and support the process of choosing and developing DL techniques applied to PCXR images , in addition to pointing out gaps and trends by drawing up a preliminary research agenda. A protocol is described in each phase detailing criteria used from selection to extraction and our set of selected studies is subjected to careful analysis to respond to the research form. Six basic sources were used and the synthesis, results, limitations, and conclusions are exposed .
Revised:  Our goal is to identify primary studies and support the process of choosing and developing DL techniques applied to PCXR images , 2010, to May 20, 2020, and selection criteria utilized on a hundred research papers. As a result, this paper categorizes twenty-six relevant studies and provides a research agenda highlighting limitations, gaps, and trends for further investigations on DL usage in PCXR images. Besides the fact that there is no systematic mapping study on this research topic, to the best of authors' knowledge, this URLanizes the process of finding and selecting relevant studies and data gathering and synthesis in a reproducible way .
Edit intent: meaning-changed
Original: We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support , the set of "alternatives that can be chosen," is a choice correspondence that satisfies the Weak Axiom of Revealed Preference,  and random choice  occurs according to a stochastic tie breaking among optimizers that satisfies Renyi's Conditioning Axiom.
Revised: We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support is a choice correspondence that satisfies the Weak Axiom of Revealed Preference, and random choice occurs according to a stochastic tie breaking among optimizers that satisfies Renyi's Conditioning Axiom.
Edit intent: clarity
Original: We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support , the set of "alternatives that can be chosen," is a choice correspondence that satisfies the Weak Axiom of Revealed Preference,  and random choice  occurs according to a stochastic tie breaking among optimizers that satisfies Renyi's Conditioning Axiom.
Revised: We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support , the set of "alternatives that can be chosen," is a choice correspondence that satisfies the Weak Axiom of Revealed Preference, thus it consists of alternatives that are optimal according to some preference, and random choice occurs according to a stochastic tie breaking among optimizers that satisfies Renyi's Conditioning Axiom.
Edit intent: meaning-changed
Original: We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support , the set of "alternatives that can be chosen," is a choice correspondence that satisfies the Weak Axiom of Revealed Preference,  and random choice  occurs according to a stochastic tie breaking among optimizers that satisfies Renyi's Conditioning Axiom.
Revised: We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support , the set of "alternatives that can be chosen," is a choice correspondence that satisfies the Weak Axiom of Revealed Preference, and random choice then occurs according to a stochastic tie breaking among optimizers that satisfies Renyi's Conditioning Axiom.
Edit intent: clarity
Original: We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support , the set of "alternatives that can be chosen," is a choice correspondence that satisfies the Weak Axiom of Revealed Preference,  and random choice  occurs according to a stochastic tie breaking among optimizers that satisfies Renyi's Conditioning Axiom.
Revised: We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support , the set of "alternatives that can be chosen," is a choice correspondence that satisfies the Weak Axiom of Revealed Preference, and random choice occurs according to a tie breaking among optimizers that satisfies Renyi's Conditioning Axiom.
Edit intent: clarity
Original: We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support , the set of "alternatives that can be chosen," is a choice correspondence that satisfies the Weak Axiom of Revealed Preference,  and random choice  occurs according to a stochastic tie breaking among optimizers that satisfies Renyi's Conditioning Axiom.
Revised: We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support , the set of "alternatives that can be chosen," is a choice correspondence that satisfies the Weak Axiom of Revealed Preference, and random choice occurs according to a stochastic tie breaking among such alternatives that satisfies Renyi's Conditioning Axiom.
Edit intent: clarity
Original: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G  does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Revised: For an integer t, a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Edit intent: meaning-changed
Original: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G  does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Revised: We give an algorithm that takes as input a graph G is called does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Edit intent: meaning-changed