wanyu/IteraTeR_full_sent huggingface dataset:
Original:  The complexity of our algorithms is 2^{(\log(1/ \varepsilon \eps )/ \varepsilon \eps )^{O(d^2)}} n \log^4 n + 2^{O(d)} n \log^9 n, making a significant improvement over the state-of-the-art algorithm which runs in time n^{(d/ \varepsilon \eps )^{O(d)}}  .
Revised:  The complexity of our algorithms is 2^{(\log(1/ \varepsilon \eps )/ \varepsilon \eps )^{O(d^2)}} n \log^4 n + 2^{O(d)} n \log^9 n, making a significant improvement over the state-of-the-art algorithms which run in time n^{(d/ \varepsilon \eps )^{O(d)}} .
Edit intent: fluency
Original:  The complexity of our algorithms is 2^{(\log(1/ \varepsilon \eps )/ \varepsilon \eps )^{O(d^2)}} n \log^4 n + 2^{O(d)} n \log^9 n, making a significant improvement over the state-of-the-art algorithm which runs in time n^{(d/ \varepsilon \eps )^{O(d)}}  .
Revised:  The complexity of our algorithms is 2^{(\log(1/ \varepsilon \eps )/ \varepsilon \eps )^{O(d^2)}} n \log^4 n + 2^{O(d)} n \log^9 n, making a significant improvement over the state-of-the-art algorithm which runs in time n^{(d/ \eps )^{O(d)}} .
Edit intent: fluency
Original:  The complexity of our algorithms is 2^{(\log(1/ \varepsilon \eps )/ \varepsilon \eps )^{O(d^2)}} n \log^4 n + 2^{O(d)} n \log^9 n, making a significant improvement over the state-of-the-art algorithm which runs in time n^{(d/ \varepsilon \eps )^{O(d)}}  .
Revised:  The complexity of our algorithms is 2^{(\log(1/ \varepsilon \eps )/ \varepsilon \eps )^{O(d^2)}} n \log^4 n + 2^{O(d)} n \log^9 n, making a significant improvement over the state-of-the-art algorithm which runs in time n^{(d/ \varepsilon \eps )^{O(d)}} . Moreover, we show how to extend the techniques used to get the first efficient approximation schemes for the problems of prize-collecting k-Medians and k-Means, and efficient bicriteria approximation schemes for k-Medians with outliers, k-Means with outliers and k-Center .
Edit intent: meaning-changed
Original:  Although we show that deciding the distances is NP-complete for general embedded graphs, we prove that our approach yields polynomial time algorithms for the distances based on the Fr\'echet distance if the graphs are trees, and for the distances based on the weak Fr\'echet distance if the graphs are trees or if they are plane.
Revised:  Although we show that deciding the distances is NP-hard for general embedded graphs, we prove that our approach yields polynomial time algorithms for the distances based on the Fr\'echet distance if the graphs are trees, and for the distances based on the weak Fr\'echet distance if the graphs are trees or if they are plane.
Edit intent: clarity
Original:  Although we show that deciding the distances is NP-complete for general embedded graphs, we prove that our approach yields polynomial time algorithms for the distances based on the Fr\'echet distance if the graphs are trees, and for the distances based on the weak Fr\'echet distance if the graphs are trees or if they are plane.
Revised:  Although we show that deciding the distances is NP-complete for general embedded graphs, we prove that our approach yields polynomial time algorithms if the graphs are trees, and for the distances based on the weak Fr\'echet distance if the graphs are trees or if they are plane.
Edit intent: fluency
Original:  Although we show that deciding the distances is NP-complete for general embedded graphs, we prove that our approach yields polynomial time algorithms for the distances based on the Fr\'echet distance if the graphs are trees, and for the distances based on the weak Fr\'echet distance if the graphs are trees or if they are plane.
Revised:  Although we show that deciding the distances is NP-complete for general embedded graphs, we prove that our approach yields polynomial time algorithms for the distances based on the Fr\'echet distance if the graphs are trees, and for the distance based on the weak Fr\'echet distance if the graphs are trees or if they are plane.
Edit intent: fluency
Original:  Although we show that deciding the distances is NP-complete for general embedded graphs, we prove that our approach yields polynomial time algorithms for the distances based on the Fr\'echet distance if the graphs are trees, and for the distances based on the weak Fr\'echet distance if the graphs are trees or if they are plane. Furthermore , we prove that deciding the distances based on the Fr\'echet remains NP-complete for plane graphs and show how our general algorithmic approach yields an exponential time algorithm and a polynomial time approximation algorithm for this case.
Revised:  Although we show that deciding the distances is NP-complete for general embedded graphs, we prove that our approach yields polynomial time algorithms for the distances based on the Fr\'echet distance if the graphs are trees, and for the distances based on the weak Fr\'echet distance if the graphs are planar embedded. Moreover , we prove that deciding the distances based on the Fr\'echet remains NP-complete for plane graphs and show how our general algorithmic approach yields an exponential time algorithm and a polynomial time approximation algorithm for this case.
Edit intent: clarity
Original:  Furthermore , we prove that deciding the distances based on the Fr\'echet remains NP-complete for plane graphs and show how our general algorithmic approach yields an exponential time algorithm and a polynomial time approximation algorithm for this case.
Revised:  Furthermore , we prove that deciding the distances based on the Fr\'echet distance remains NP-hard for planar embedded graphs and show how our general algorithmic approach yields an exponential time algorithm and a polynomial time approximation algorithm for this case.
Edit intent: meaning-changed
Original:  We evaluate Quicker ADC with multiple indexes including Inverted Multi-Indexes and IVF HNSW and show that it outperforms FAISS PQ implementation and optimization (i.e., Polysemous codes) for numerous configurations.
Revised:  We evaluate Quicker ADC with multiple indexes including Inverted Multi-Indexes and IVF HNSW and show that it outperforms the reference optimized implementations (i.e., Polysemous codes) for numerous configurations.
Edit intent: meaning-changed
Original:  We evaluate Quicker ADC with multiple indexes including Inverted Multi-Indexes and IVF HNSW and show that it outperforms FAISS PQ implementation and optimization (i.e., Polysemous codes) for numerous configurations.
Revised:  We evaluate Quicker ADC with multiple indexes including Inverted Multi-Indexes and IVF HNSW and show that it outperforms FAISS PQ implementation and optimization (i.e., FAISS and polysemous codes) for numerous configurations.
Edit intent: clarity
Original: A firm is selling a product to different types (based on the features such as education backgrounds, ages, etc. ) of customers over a finite season with non-replenishable initial inventory. The type label of an arriving customer can be observed but the demand function associated with each type is initially unknown.
Revised: We consider the problem of a firm seeking to use personalized pricing to sell an exogenously given stock of a product over a finite selling horizon to different consumer types. We assume that the type of an arriving customer can be observed but the demand function associated with each type is initially unknown.
Edit intent: clarity
Original: Many neural systems display avalanche behavior characterized by uninterrupted sequences of neuronal firing whose distributions of size and durations are heavy-tailed. Theoretical models of such systems suggest that these dynamics support optimal information transmission and storage. However, the unknown role of network structure precludes an understanding of how variations in network topology manifest in neural dynamics and either support or impinge upon information processing.
Revised: Many neural systems display avalanche behavior characterized by uninterrupted sequences of neuronal firing . This gap precludes an understanding of how variations in network topology manifest in neural dynamics and either support or impinge upon information processing.
Edit intent: clarity
Original:  Here, using a generalized spiking model, we develop a mechanistic understanding of how network topology supports information processing through network dynamics . First, we show how network topology determines network dynamics by analytically and numerically demonstrating that network topology can be designed to propagate stimulus patternsfor long durations.
Revised:  Here, using a generalized spiking model, we develop a mechanistic understanding of how network topology supports information processing through network dynamics , and we validate our theory with empirical data. Using a generalized spiking model and mathematical tools from linear systems theory, network control theory, and information theory, we show how network topology determines network dynamics by analytically and numerically demonstrating that network topology can be designed to propagate stimulus patternsfor long durations.
Edit intent: meaning-changed
Original:  First, we show how network topology determines network dynamics by analytically and numerically demonstrating that network topology can be designed to propagate stimulus patternsfor long durations. We then identify strongly connected cycles as empirically observable network motifs that are prevalent in such networks.
Revised:  First, we show how network topology determines network dynamics by analytically and numerically demonstrating that network topology can be designed to temporally extend the propagation and recovery of certain stimulus patterns. Moreover, we observe cycles as structural and dynamic motifs that are prevalent in such networks.
Edit intent: meaning-changed
Original:  Next, we show that within a network, mathematical intuitions from network control theory are tightly linked with dynamics initiated by node-specific stimulation and can identify stimuli that promote long-lasting cascades. Finally, we use these network-based metrics and control-based stimuli to demonstrate that long-lasting cascade dynamics facilitate delayed recovery of stimulus patterns from network activity, as measured by mutual information. Collectively, our results provide evidence that cortical networks are structured with architectural motifs that support long-lasting propagation and recovery of a few crucial patterns of stimulation, especially those consisting of activity in highly controllable neurons.
Edit intent: clarity
Original:  This shift may facilitate a URLanized push towards human WBE, making the goal potentially reachable during the 21st century. By implementing IBE , large-scale scientific infrastructure may shift towards developing more WBEs and move in the direction of comprehensively understanding neural computation .
Revised:  Furthermore, IBE will facilitate dramatic advances in cognitive neuroscience, artificial intelligence, and robotics through studies performed using virtual insects .
Edit intent: meaning-changed
Original:  We propose easy-to-implement algorithms for high-dimensional hypotheses testing and construction of simultaneously valid confidence intervals that are cluster-robust, robust against imperfect model selection and asymptotically non-conservative using a new multiplier cluster bootstrap  .
Revised:  We propose easy-to-implement algorithms for high-dimensional hypotheses testing and construction of simultaneously valid confidence intervals that are cluster-robust, robust against imperfect model selection using a new multiplier cluster bootstrap .
Edit intent: coherence
Original:  We propose easy-to-implement algorithms for high-dimensional hypotheses testing and construction of simultaneously valid confidence intervals that are cluster-robust, robust against imperfect model selection and asymptotically non-conservative using a new multiplier cluster bootstrap  .
Revised:  We propose easy-to-implement algorithms for high-dimensional hypotheses testing and construction of simultaneously valid confidence intervals that are cluster-robust, robust against imperfect model selection and asymptotically non-conservative using a new multiplier cluster bootstrap . We then apply algorithms to study multiple-testing problem of gendered language on the internet .
Edit intent: meaning-changed
Original: This paper studies inferencefor multiple/ many average partial effects when outcome variable is binary or fractional under data rich, cluster sampling environments. The number of average partial effects of interest can be much larger than number of sample clusters. We propose a post-double-selection estimator as well as a Neyman orthogonal moment estimator, both based on \ell_1-penalization, and explore their asymptotic properties.
Revised: This paper studies inferencefor multiple/ many average partial effects of lasso Logit. Focusing on high-dimensional, cluster-sampling environments, we propose a new average partial effect estimator and explore its asymptotic properties.
Edit intent: meaning-changed
Original:  The proposed estimators do not require oracle property for valid inference . We propose easy-to-implement algorithms for  high-dimensional hypotheses testing and construction of simultaneously valid confidence intervals that are cluster-robust, robust against imperfect model selection using a new multiplier cluster bootstrap.
Revised:  The proposed estimators do not require oracle property for valid inference without requiring oracle property. We provide easy-to-implement algorithms for high-dimensional hypotheses testing and construction of simultaneously valid confidence intervals that are cluster-robust, robust against imperfect model selection using a new multiplier cluster bootstrap.
Edit intent: meaning-changed
Original:  We propose easy-to-implement algorithms for  high-dimensional hypotheses testing and construction of simultaneously valid confidence intervals that are cluster-robust, robust against imperfect model selection using a new multiplier cluster bootstrap.
Revised:  We propose easy-to-implement algorithms for cluster-robust high-dimensional hypotheses testing and construction of simultaneously valid confidence intervals that are cluster-robust, robust against imperfect model selection using a new multiplier cluster bootstrap.
Edit intent: meaning-changed
Original: In this paper we study a treatment allocation problem with multiple treatments, in which the individuals to be treated arrive sequentially. The goal of the policy maker is to treat every individual as well as possible. Which treatment is "best" is allowed to depend on various characteristics (functionals) of the individual-specific outcome distribution of each treatment. For example measures of welfare, inequality, or poverty. We propose the Functional Sequential Allocation policy, and provide upper bounds on the regretit incurs compared to the oracle policy that knows the best treatment for each individual.
Revised: Consider a setting in which a policy maker assigns subjects to treatments, observing each outcome before the next subject arrives. The sequential nature of the problem permits learning about the effectiveness of the treatments, which we measure by a functional of the associated outcome distributions, for example an inequality, welfare or poverty measure. We evaluate different assignment policies according to their regret, that is, the sum of all losses incurred due to assigning subjects to suboptimal treatments. All our results are non-asymptotic, in that we provide finite sample lower and upper bounds on the regretit incurs compared to the oracle policy that knows the best treatment for each individual.
Edit intent: meaning-changed
Original:  We propose the Functional Sequential Allocation policy, and provide upper bounds on the regretit incurs compared to the oracle policy that knows the best treatment for each individual. These upper bounds increase sublinearly in the number of treatment assignments and we show that this regret guarantee is minimax optimal. In addition, the assumptions under which this regret guarantee is established are as weak as possible --- even a minimal weakening of them will imply non-existence of policies with regret increasing sub-linearly in the number of assignments.
Revised:  We propose the Functional Sequential Allocation policy, and provide upper bounds on maximal expected regret. We first study explore-then-commit (ETC) policies. These are policies, where one initially explores which treatment is of the highest quality, typically through a randomized controlled trial, and subsequently fully commits to the inferred superior treatment. Then, we introduce and study the Functional Upper Confidence Bound (F-UCB) policy, which interweaves exploration and exploitation and is thus not of the assumptions under which this regret guarantee is established are as weak as possible --- even a minimal weakening of them will imply non-existence of policies with regret increasing sub-linearly in the number of assignments.
Edit intent: meaning-changed
Original:  In addition, the assumptions under which this regret guarantee is established are as weak as possible --- even a minimal weakening of them will imply non-existence of policies with regret increasing sub-linearly in the number of assignments. Furthermore, we provide an upper bound on the number of suboptimal assignments made by the FSA policy and show that every policy must make a number of suboptimal assignments at least of this order .
Revised:  In addition, the ETC type. Our results show, in particular, that the F-UCB policy (i) performs much better than any ETC policy, and (ii) is near minimax optimal. We also show that a suitably adapted F-UCB policy is near minimax optimal under minimal assumptions when covariate information is available .
Edit intent: meaning-changed
Original:  The sequential nature of the problem permits learning about the effectiveness of the treatments, which we measure by a functional of the associated outcome distributions, for example an inequality, welfare or poverty measure.
Revised:  Initially, it is unknown which treatment is best. However, the sequential nature of the problem permits learning about the effectiveness of the treatments, which we measure by a functional of the associated outcome distributions, for example an inequality, welfare or poverty measure.
Edit intent: meaning-changed
Original:  Initially, it is unknown which treatment is best . However, the sequential nature of the problem permits learning about the effectiveness of the treatments , which we measure by a functional of the associated outcome distributions, for example an inequality, welfare or poverty measure .
Revised:  Initially, it is unknown which treatment is best , but the sequential nature of the problem permits learning about the effectiveness of the treatments , which we measure by a functional of the associated outcome distributions, for example an inequality, welfare or poverty measure .
Edit intent: coherence
Original:  However, the sequential nature of the problem permits learning about the effectiveness of the treatments , which we measure by a functional of the associated outcome distributions, for example an inequality, welfare or poverty measure .
Revised:  However, the sequential nature of the problem permits learning about the effectiveness of the treatments . While the multi-armed-bandit literature has shed much light on the situation when the policy maker compares the effectiveness of the treatments through their mean, economic decision making often requires targeting purpose specific characteristics of the outcome distribution, such as its inherent degree of inequality, welfare or poverty measure .
Edit intent: meaning-changed
Original:  In the present article, we evaluate assignment policies according to their regret, that is, the sum of all losses incurred due to assigning subjects to suboptimal treatments. We first study explore-then-commit (ETC) policies. These are policies, where one initially explores which treatment is of the highest quality, typically through a randomized controlled trial, and subsequently fully commits to the ``inferred superior'' (but potentially suboptimal) treatment .
Revised:  In the present paper we introduce and study sequential learning algorithms when the distributional characteristic of interest is a general functional of the outcome distribution. In particular, it turns out that intuitively reasonable approaches, such as first conducting an experiment on an initial group of subjects followed by rolling out the inferred best treatment to the population, are dominated by the policies we develop and of the highest quality, typically through a randomized controlled trial, and subsequently fully commits to the ``inferred superior'' (but potentially suboptimal) treatment .
Edit intent: meaning-changed
Original:  These are policies, where one initially explores which treatment is of the highest quality, typically through a randomized controlled trial, and subsequently fully commits to the ``inferred superior'' (but potentially suboptimal) treatment . Then, we introduce and study the Functional Upper Confidence Bound (F-UCB) policy, which interweaves exploration and exploitation and is thus not of the ETC type. Our results show , in particular, that the F-UCB policy (i) performs much better than any ETC policy, and (ii) is near minimax optimal. We also show that a suitably adapted F-UCB policy is near minimax optimal under minimal assumptions when covariate information is available .
Revised:  These are policies, where one initially explores which treatment is of which we show that they are optimal .
Edit intent: clarity
Original:  While the multi-armed-bandit literature has shed much light on the situation when the policy maker compares the effectiveness of the treatments through their mean, economic decision making often requires targeting purpose specific characteristics of the outcome distribution, such as its inherent degree of inequality, welfare or poverty.
Revised:  While the multi-armed-bandit literature has shed much light on the situation when the policy maker compares the effectiveness of the treatments through their mean, much less is known about other targets. This is relevant, because a cautious decision maker may prefer to target a robust location measure such as a quantile or a trimmed mean. Furthermore, socio-economic decision making often requires targeting purpose specific characteristics of the outcome distribution, such as its inherent degree of inequality, welfare or poverty.
Edit intent: meaning-changed
Original:  In particular, it turns out that intuitively reasonable approaches, such as first conducting an experiment on an initial group of subjects followed by rolling out the inferred best treatment to the population, are dominated by the policies we develop and of which we show that they are optimal .
Revised:  Minimax expected regret optimality results are obtained within the subclass of explore-then-commit policies, and for the unrestricted class of all policies .
Edit intent: meaning-changed
Original:  This paper develops new estimation and inference procedures for multiple treatment models in a selection-on-observables framework by modifying the Causal Forest approach suggested by Wager and Athey (2018)  .
Revised:  This paper develops new estimation and inference procedures for multiple treatment models in a selection-on-observables framework by modifying the Causal Forest approach suggested by Wager and Athey (2018) in several dimensions .
Edit intent: meaning-changed
Original:  An Empirical Monte Carlo study shows that they may outperform previously suggested estimators . Inference tends to be accurate for effects relating to larger groups and conservative for effects relating to fine levels of granularity. An application to the evaluation of an active labour market programme shows the value of the new methods for applied research.
Revised:  An Empirical Monte Carlo study shows that they may outperform previously suggested estimators , an application to the evaluation of an active labour market programme shows the value of the new methods for applied research.
Edit intent: clarity