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Journal articles on the topic 'Distributional'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

Fu, Heman, Jincheng Xiong, and Huoyun Wang. "The Hierarchy of Distributional Chaos." International Journal of Bifurcation and Chaos 25, no. 01 (2015): 1550001. http://dx.doi.org/10.1142/s0218127415500017.

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For each λ ∈ [0, 1], λ-power distributional chaos has been defined via Furstenberg families to strengthen distributional chaos. For the sake of distinguishing them, we present a class of dynamical systems, called wedge-shape systems. Through a thorough analysis of dynamical behaviors of all point-pairs, we show that wedge-shape systems can be λ-power distributionally chaotic and admit no λ′-power distributionally scrambled pairs for any λ′ ∈ [0, λ). Then we unfold a picture of distributional chaos with rich hierarchical structures, which helps to improve our comprehension of the diversity of chaos.

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2

Wang, Lidong, Xiang Wang, Fengchun Lei, and Heng Liu. "Asymptotic average shadowing property, almost specification property and distributional chaos." Modern Physics Letters B 30, no. 03 (2016): 1650001. http://dx.doi.org/10.1142/s0217984916500019.

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It is proved that a nontrivial compact dynamical system with asymptotic average shadowing property (AASP) displays uniformly distributional chaos or distributional chaos in a sequence. Moreover, distributional chaos in a system with AASP can be uniform and dense in the measure center, that is, there is an uncountable uniformly distributionally scrambled set consisting of such points that the orbit closure of every point contains the measure center. As a corollary, the similar results hold for the system with almost specification property.

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3

Wang, Lidong, Yingcui Zhao, Yuelin Gao, and Heng Liu. "Chaos to Multiple Mappings." International Journal of Bifurcation and Chaos 27, no. 08 (2017): 1750119. http://dx.doi.org/10.1142/s021812741750119x.

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Let [Formula: see text] be a compact metric space and [Formula: see text] be an [Formula: see text]-tuple of continuous selfmaps on [Formula: see text]. This paper investigates Hausdorff metric Li–Yorke chaos, distributional chaos and distributional chaos in a sequence from a set-valued view. On the basis of this research, we draw the main conclusions as follows: (i) If [Formula: see text] has a distributionally chaotic pair, especially [Formula: see text] is distributionally chaotic, the strongly nonwandering set [Formula: see text] contains at least two points. (ii) We give a sufficient condition for [Formula: see text] to be distributionally chaotic in a sequence and chaotic in the strong sense of Li–Yorke. Finally, an example to verify (ii) is given.

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4

Weeds, Julie, and David Weir. "Co-occurrence Retrieval: A Flexible Framework for Lexical Distributional Similarity." Computational Linguistics 31, no. 4 (2005): 439–75. http://dx.doi.org/10.1162/089120105775299122.

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Techniques that exploit knowledge of distributional similarity between words have been proposed in many areas of Natural Language Processing. For example, in language modeling, the sparse data problem can be alleviated by estimating the probabilities of unseen co-occurrences of events from the probabilities of seen co-occurrences of similar events. In other applications, distributional similarity is taken to be an approximation to semantic similarity. However, due to the wide range of potential applications and the lack of a strict definition of the concept of distributional similarity, many methods of calculating distributional similarity have been proposed or adopted. In this work, a flexible, parameterized framework for calculating distributional similarity is proposed. Within this framework, the problem of finding distributionally similar words is cast as one of co-occurrence retrieval (CR) for which precision and recall can be measured by analogy with the way they are measured in document retrieval. As will be shown, a number of popular existing measures of distributional similarity are simulated with parameter settings within the CR framework. In this article, the CR framework is then used to systematically investigate three fundamental questions concerning distributional similarity. First, is the relationship of lexical similarity necessarily symmetric, or are there advantages to be gained from considering it as an asymmetric relationship? Second, are some co-occurrences inherently more salient than others in the calculation of distributional similarity? Third, is it necessary to consider the difference in the extent to which each word occurs in each co-occurrence type? Two application-based tasks are used for evaluation: automatic thesaurus generation and pseudo-disambiguation. It is possible to achieve significantly better results on both these tasks by varying the parameters within the CR framework rather than using other existing distributional similarity measures; it will also be shown that any single unparameterized measure is unlikely to be able to do better on both tasks. This is due to an inherent asymmetry in lexical substitutability and therefore also in lexical distributional similarity.

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5

Duchi, John C., Peter W. Glynn, and Hongseok Namkoong. "Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach." Mathematics of Operations Research 46, no. 3 (2021): 946–69. http://dx.doi.org/10.1287/moor.2020.1085.

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We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a generalized empirical likelihood framework—based on distributional uncertainty sets constructed from nonparametric f-divergence balls—for Hadamard differentiable functionals, and in particular, stochastic optimization problems. As consequences of this theory, we provide a principled method for choosing the size of distributional uncertainty regions to provide one- and two-sided confidence intervals that achieve exact coverage. We also give an asymptotic expansion for our distributionally robust formulation, showing how robustification regularizes problems by their variance. Finally, we show that optimizers of the distributionally robust formulations we study enjoy (essentially) the same consistency properties as those in classical sample average approximations. Our general approach applies to quickly mixing stationary sequences, including geometrically ergodic Harris recurrent Markov chains.

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6

Beare, Brendan K. "Distributional Replication." Entropy 23, no. 8 (2021): 1063. http://dx.doi.org/10.3390/e23081063.

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A function which transforms a continuous random variable such that it has a specified distribution is called a replicating function. We suppose that functions may be assigned a price, and study an optimization problem in which the cheapest approximation to a replicating function is sought. Under suitable regularity conditions, including a bound on the entropy of the set of candidate approximations, we show that the optimal approximation comes close to achieving distributional replication, and close to achieving the minimum cost among replicating functions. We discuss the relevance of our results to the financial literature on hedge fund replication; in this case, the optimal approximation corresponds to the cheapest portfolio of market index options which delivers the hedge fund return distribution.

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7

Kroese, A. H., E. A. Meulen, K. Poortema, and W. Schaafsma. "Distributional inference." Statistica Neerlandica 49, no. 1 (1995): 63–82. http://dx.doi.org/10.1111/j.1467-9574.1995.tb01455.x.

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8

Bonilla, Antonio, and Marko Kostić. "Reiterative Distributional Chaos on Banach Spaces." International Journal of Bifurcation and Chaos 29, no. 14 (2019): 1950201. http://dx.doi.org/10.1142/s0218127419502018.

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If we change the upper and lower densities in the definition of distributional chaos of a continuous linear operator on a Banach space [Formula: see text] by the Banach upper and Banach lower densities, respectively, we obtain Li–Yorke chaos. Motivated by this, we introduce the notions of reiterative distributional chaos of types [Formula: see text], [Formula: see text] and [Formula: see text] for continuous linear operators on Banach spaces, which are characterized in terms of the existence of an irregular vector with additional properties. Moreover, we study its relations with other dynamical properties and present the conditions for the existence of a vector subspace [Formula: see text] of [Formula: see text], such that every nonzero vector in [Formula: see text] is both irregular for [Formula: see text] and distributionally near zero for [Formula: see text].

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9

DE BOLLA, PETER, EWAN JONES, PAUL NULTY, GABRIEL RECCHIA, and JOHN REGAN. "Distributional Concept Analysis." Contributions to the History of Concepts 14, no. 1 (2019): 66–92. http://dx.doi.org/10.3167/choc.2019.140104.

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This article proposes a novel computational method for discerning the structure and history of concepts. Based on the analysis of co-occurrence data in large data sets, the method creates a measure of “binding” that enables the construction of verbal constellations that comprise the larger units, “concepts,” that change over time. In contrast to investigation into semantic networks, our method seeks to uncover structures of conceptual operation that are not simply semantic. These larger units of lexical operation that are visualized as interconnected networks may have underlying rules of formation and operation that have as yet unexamined—perhaps tangential—connection to meaning as such. The article is thus exploratory and intended to open the history of concepts to some new avenues of investigation.

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10

Bruni, E., N. K. Tran, and M. Baroni. "Multimodal Distributional Semantics." Journal of Artificial Intelligence Research 49 (January 23, 2014): 1–47. http://dx.doi.org/10.1613/jair.4135.

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Distributional semantic models derive computational representations of word meaning from the patterns of co-occurrence of words in text. Such models have been a success story of computational linguistics, being able to provide reliable estimates of semantic relatedness for the many semantic tasks requiring them. However, distributional models extract meaning information exclusively from text, which is an extremely impoverished basis compared to the rich perceptual sources that ground human semantic knowledge. We address the lack of perceptual grounding of distributional models by exploiting computer vision techniques that automatically identify discrete visual words in images, so that the distributional representation of a word can be extended to also encompass its co-occurrence with the visual words of images it is associated with. We propose a flexible architecture to integrate text- and image-based distributional information, and we show in a set of empirical tests that our integrated model is superior to the purely text-based approach, and it provides somewhat complementary semantic information with respect to the latter.

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11

Jensen, Martin Kaae. "Distributional Comparative Statics." Review of Economic Studies 85, no. 1 (2017): 581–610. http://dx.doi.org/10.1093/restud/rdx021.

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12

Oprocha, Piotr. "Distributional chaos revisited." Transactions of the American Mathematical Society 361, no. 09 (2009): 4901–25. http://dx.doi.org/10.1090/s0002-9947-09-04810-7.

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13

Anastassiou, George A. "Distributional Taylor formula." Nonlinear Analysis: Theory, Methods & Applications 70, no. 9 (2009): 3195–202. http://dx.doi.org/10.1016/j.na.2008.04.022.

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14

Allaire, Douglas L., and Karen E. Willcox. "Distributional sensitivity analysis." Procedia - Social and Behavioral Sciences 2, no. 6 (2010): 7595–96. http://dx.doi.org/10.1016/j.sbspro.2010.05.134.

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15

Hirth, Kenneth G. "The Distributional Approach." Current Anthropology 39, no. 4 (1998): 451–76. http://dx.doi.org/10.1086/204759.

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16

Roemer, John E. "Eclectic distributional ethics." Politics, Philosophy & Economics 3, no. 3 (2004): 267–81. http://dx.doi.org/10.1177/1470594x04046238.

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17

Pathak, R. S., and Abhishek Singh. "Distributional Wavelet Transform." Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 86, no. 2 (2016): 273–77. http://dx.doi.org/10.1007/s40010-015-0225-1.

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18

Li, Risong, Tianxiu Lu, Jingmin Pi, and Waseem Anwar. "Three Types of Distributional Chaos for a Sequence of Uniformly Convergent Continuous Maps." Advances in Mathematical Physics 2022 (June 18, 2022): 1–7. http://dx.doi.org/10.1155/2022/5481666.

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Let h s s = 1 ∞ be a sequence of continuous maps on a compact metric space W which converges uniformly to a continuous map h on W . In this paper, some equivalence conditions or necessary conditions for the limit map h to be distributional chaotic are obtained (where distributional chaoticity includes distributional chaotic in a sequence, distributional chaos of type 1 (DC1), distributional chaos of type 2 (DC2), and distributional chaos of type 3 (DC3)).

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19

Huyghe, Richard, and Marine Wauquier. "Distributional semantics insights on agentive suffix rivalry in French." Word Structure 14, no. 3 (2021): 354–91. http://dx.doi.org/10.3366/word.2021.0194.

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The formation of French agent nouns (ANs) involves a large variety of morphological constructions, and particularly of suffixes. In this study, we focus on the semantic counterpart of agentive suffix diversity and investigate whether the morphological variety of ANs correlates with different agentive subtypes. We adopt a distributional semantics approach and combine manual, computational and statistical analyses applied to French ANs ending in -aire, -ant, -eur, -ien, -ier and -iste. Our methodology allows for a large-scale study of ANs and involves both top-down and bottom-up procedures. We first characterize agentive suffixes with respect to their morphosemantic and distributional properties, outlining their specificities and similarities. Then we automatically cluster ANs into distributionally relevant subsets and examine their properties. Based on quantitative analysis, our study provides a new perspective on agentive suffix rivalry in French that both confirms existing claims and sheds light on previously unseen phenomena.

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20

Aitchison, John, Gloria Mateu-Figueras, and Kai W. Ng. "Characterization of Distributional Forms for Compositional Data and Associated Distributional Tests." Mathematical Geology 35, no. 6 (2003): 667–80. http://dx.doi.org/10.1023/b:matg.0000002983.12476.89.

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21

Marshall, C. Tara, and Kenneth T. Frank. "Geographic Responses of Groundfish to Variation in Abundance: Methods of Detection and Their Interpretation." Canadian Journal of Fisheries and Aquatic Sciences 51, no. 4 (1994): 808–16. http://dx.doi.org/10.1139/f94-079.

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Recent published studies have used data from bottom trawl surveys of groundfish populations to test whether distributional area and abundance are correlated. Two studies that used different indices to represent the distributional area of Georges Bank haddock (Melanogrammus aeglefinus) yielded conflicting results. To determine whether this is an example of different distributional indices measuring different things, both indices were regressed against estimates of abundance of haddock from a different but neighbouring location on the southwestern Scotian Shelf. Positive correlations were observed for immature age-classes using both indices whereas only one of the two indices resulted in positive correlations for mature age-classes. The following factors contributed to the lack of agreement among distributional indices: (1) age-aggregated indices potentially obscure correlations between distributional area and abundance for individual age-classes; (2) distributional indices that depend on the magnitude of catch rates confound variation in the large-scale horizontal distribution of stocks with diurnal variation in the three-dimensional distribution of schools; (3) distributional indices that scale positively with abundance generate spurious correlations. The results suggest that the outcome of any test of whether distributional area and abundance are correlated depends on the index chosen to represent distributional area.

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22

Lyle, Clare, Marc G. Bellemare, and Pablo Samuel Castro. "A Comparative Analysis of Expected and Distributional Reinforcement Learning." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 4504–11. http://dx.doi.org/10.1609/aaai.v33i01.33014504.

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Since their introduction a year ago, distributional approaches to reinforcement learning (distributional RL) have produced strong results relative to the standard approach which models expected values (expected RL). However, aside from convergence guarantees, there have been few theoretical results investigating the reasons behind the improvements distributional RL provides. In this paper we begin the investigation into this fundamental question by analyzing the differences in the tabular, linear approximation, and non-linear approximation settings. We prove that in many realizations of the tabular and linear approximation settings, distributional RL behaves exactly the same as expected RL. In cases where the two methods behave differently, distributional RL can in fact hurt performance when it does not induce identical behaviour. We then continue with an empirical analysis comparing distributional and expected RL methods in control settings with non-linear approximators to tease apart where the improvements from distributional RL methods are coming from.

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23

BATTAGLINI, MARCO, ERNEST K. LAI, WOOYOUNG LIM, and JOSEPH TAO-YI WANG. "The Informational Theory of Legislative Committees: An Experimental Analysis." American Political Science Review 113, no. 1 (2018): 55–76. http://dx.doi.org/10.1017/s000305541800059x.

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We experimentally investigate the informational theory of legislative committees (Gilligan and Krehbiel 1989). Two committee members provide policy-relevant information to a legislature under alternative legislative rules. Under the open rule, the legislature is free to make any decision; under the closed rule, the legislature chooses between a member’s proposal and a status quo. We find that even in the presence of biases, the committee members improve the legislature’s decision by providing useful information. We obtain evidence for two additional predictions: the outlier principle, according to which more extreme biases reduce the extent of information transmission; and the distributional principle, according to which the open rule is more distributionally efficient than the closed rule. When biases are less extreme, we find that the distributional principle dominates the restrictive-rule principle, according to which the closed rule is more informationally efficient. Overall, our findings provide experimental support for Gilligan and Krehbiel’s informational theory.

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24

Li, Luchen, and A. Aldo Faisal. "Bayesian Distributional Policy Gradients." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 10 (2021): 8429–37. http://dx.doi.org/10.1609/aaai.v35i10.17024.

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Distributional Reinforcement Learning (RL) maintains the entire probability distribution of the reward-to-go, i.e. the return, providing more learning signals that account for the uncertainty associated with policy performance, which may be beneficial for trading off exploration and exploitation and policy learning in general. Previous works in distributional RL focused mainly on computing the state-action-return distributions, here we model the state-return distributions. This enables us to translate successful conventional RL algorithms that are based on state values into distributional RL. We formulate the distributional Bellman operation as an inference-based auto-encoding process that minimises Wasserstein metrics between target/model return distributions. The proposed algorithm, BDPG (Bayesian Distributional Policy Gradients), uses adversarial training in joint-contrastive learning to estimate a variational posterior from the returns. Moreover, we can now interpret the return prediction uncertainty as an information gain, which allows to obtain a new curiosity measure that helps BDPG steer exploration actively and efficiently. We demonstrate in a suite of Atari 2600 games and MuJoCo tasks, including well known hard-exploration challenges, how BDPG learns generally faster and with higher asymptotic performance than reference distributional RL algorithms.

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25

Roth, Zuzana. "Distributional Chaos and Dendrites." International Journal of Bifurcation and Chaos 28, no. 14 (2018): 1850178. http://dx.doi.org/10.1142/s021812741850178x.

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Many definitions of chaos have appeared in the last decades and there is a concerned question if they are equivalent in some more specific spaces. Our focus will be on distributional chaos, first defined in 1994 and later subdivided into three major types (and even more subtypes). These versions of chaos are equivalent on a closed interval, but distinct in more complicated spaces. Since dendrites have much in common with the interval, we explore whether or not we can distinguish these kinds of chaos already on dendrites. At the end of the paper we will also briefly look at their correlation with other types of chaos.

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26

Peltonen, S., P. Kuosmanen, and J. Astola. "Output distributional influence function." IEEE Transactions on Signal Processing 49, no. 9 (2001): 1953–60. http://dx.doi.org/10.1109/78.942624.

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27

Liu, Youming. "A Distributional Sampling Theorem." SIAM Journal on Mathematical Analysis 27, no. 4 (1996): 1153–57. http://dx.doi.org/10.1137/s0036141094266930.

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28

Kameda, Keigo, and Miho Sato. "Distributional preference in Japan." Japanese Economic Review 68, no. 3 (2016): 394–408. http://dx.doi.org/10.1111/jere.12112.

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29

Baroni, Marco. "Composition in Distributional Semantics." Language and Linguistics Compass 7, no. 10 (2013): 511–22. http://dx.doi.org/10.1111/lnc3.12050.

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30

Oprocha, Piotr, and Paweł Wilczyński. "Distributional chaos via semiconjugacy." Nonlinearity 20, no. 11 (2007): 2661–79. http://dx.doi.org/10.1088/0951-7715/20/11/010.

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31

Doleželová-Hantáková, Jana. "Distributional chaos and factors." Journal of Difference Equations and Applications 22, no. 1 (2015): 99–106. http://dx.doi.org/10.1080/10236198.2015.1077814.

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32

Jacobsen, Brian J. "Forecasting with distributional scaling." Applied Financial Economics 20, no. 24 (2010): 1891–92. http://dx.doi.org/10.1080/09603107.2010.528364.

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33

Garfinkle, David. "Metrics with distributional curvature." Classical and Quantum Gravity 16, no. 12 (1999): 4101–9. http://dx.doi.org/10.1088/0264-9381/16/12/324.

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34

Smith, Michael E. "On Hirth's “Distributional Approach”." Current Anthropology 40, no. 4 (1999): 528–30. http://dx.doi.org/10.1086/200049.

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35

G�tze, F., and M. Bloznelis. "applications to distributional asymptotics." Annals of Statistics 29, no. 3 (2001): 899–917. http://dx.doi.org/10.1214/aos/1009210694.

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36

Inderst, Roman, Holger M. Müller, and Karl Wärneryd. "Distributional conflict in organizations." European Economic Review 51, no. 2 (2007): 385–402. http://dx.doi.org/10.1016/j.euroecorev.2006.01.003.

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37

Hencl, Stanislav, Zhuomin Liu, and Jan Malý. "Distributional Jacobian equal toH1measure." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 31, no. 5 (2014): 947–55. http://dx.doi.org/10.1016/j.anihpc.2013.08.002.

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38

Griffin, Lewis D., M. Husni Wahab, and Andrew J. Newell. "Distributional Learning of Appearance." PLoS ONE 8, no. 2 (2013): e58074. http://dx.doi.org/10.1371/journal.pone.0058074.

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39

Arce M, Daniel G. "Distributional Conflict and Inflation." Comparative Economic Studies 40, no. 2 (1998): 112–13. http://dx.doi.org/10.1057/ces.1998.15.

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40

Ahmadabadi, Zahra Nili, and Fatemah Ayatollah Zadeh Shirazi. "Distributional Chaotic Generalized Shifts." Journal of Dynamical Systems and Geometric Theories 18, no. 1 (2020): 53–70. http://dx.doi.org/10.1080/1726037x.2020.1774156.

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41

TAN, Feng, and Heman FU. "On distributional n-chaos." Acta Mathematica Scientia 34, no. 5 (2014): 1473–80. http://dx.doi.org/10.1016/s0252-9602(14)60097-7.

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42

Piketty, Thomas, Emmanuel Saez, and Gabriel Zucman. "Simplified Distributional National Accounts." AEA Papers and Proceedings 109 (May 1, 2019): 289–95. http://dx.doi.org/10.1257/pandp.20191035.

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This paper develops a simplified methodology to distribute total national income across income groups that reproduces closely the sophisticated methodology of Piketty, Saez, and Zucman (2018). It starts from top income share series based on fiscal income of Piketty and Saez (2003) and makes two basic assumptions on how national income components not included in fiscal income are distributed: (1) nontaxable labor income and capital income from pension funds are distributed like taxable labor income; (2) other nontaxable capital income is distributed like taxable capital income. This methodology could be applied to countries with less data.

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43

Esping-Andersen, Gosta. "Power and Distributional Regimes." Politics & Society 14, no. 2 (1985): 223–56. http://dx.doi.org/10.1177/003232928501400204.

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Erik Talvila. "The Distributional Denjoy Integral." Real Analysis Exchange 33, no. 1 (2008): 51. http://dx.doi.org/10.14321/realanalexch.33.1.0051.

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Asaria, Miqdad, Susan Griffin, and Richard Cookson. "Distributional Cost-Effectiveness Analysis." Medical Decision Making 36, no. 1 (2015): 8–19. http://dx.doi.org/10.1177/0272989x15583266.

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46

Estrada, Ricardo. "Distributional radius of curvature." Mathematical Methods in the Applied Sciences 29, no. 4 (2006): 427–44. http://dx.doi.org/10.1002/mma.692.

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47

Betancor, J. J., J. D. Betancor, and J. M. R. Méndez. "Distributional Chébli–Trimèche transforms." Journal of Mathematical Analysis and Applications 313, no. 2 (2006): 537–50. http://dx.doi.org/10.1016/j.jmaa.2005.04.079.

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48

Zhou, Yunhua. "Distributional chaos for flows." Czechoslovak Mathematical Journal 63, no. 2 (2013): 475–80. http://dx.doi.org/10.1007/s10587-013-0031-3.

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Loonker, Deshna, and P. K. Banerji. "On the Solution of Distributional Abel Integral Equation by Distributional Sumudu Transform." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–8. http://dx.doi.org/10.1155/2011/480528.

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Moeng, Emily. "Distributional learning on Mechanical Turk and effects of attentional shifts." Proceedings of the Linguistic Society of America 2 (June 14, 2017): 48. http://dx.doi.org/10.3765/plsa.v2i0.4105.

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This study seeks to determine whether distributional learning can be replicated on an online platform like Mechanical Turk. In doing so, factors that may affect distributional learning, such as level of attention, participant age, and stimuli, are explored. It is found that even distributional learning, which requires making fine phonetic distinctions, can be replicated on Mechanical Turk, and that attention may nullify the effect of distributional learning.

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