Deterministic and Stochastic Dynamics for Language Learning and Change

语言学习和变化的确定性和随机动力学

• 批准号: 0734783
• 负责人: William Mitchener
• 金额: $ 7.33万
• 依托单位: College of Charleston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0734783&HistoricalAwards=false
• 关键词: Deterministic; Stochastic; Dynamics; Language; Learning

Mitchener proposes to study stochastic processes and dynamical systems that model language learning and change, supported by statisticalanalysis of manuscript and corpus data. The proposed models aredesigned to account for variability in speech in ways that mostexisting models do not. Some of the proposed models aredeterministic, and represent the distribution of speech patterns in apopulation as probability density functions governed byBanach-space-valued differential equations. Other proposed models arestochastic, based on discrete Markov chains and stochasticdifferential equations. The Markov chain models are the mostdetailed, including simulated learning algorithms based on Bayesianstatistics. The PI plans to develop perfect sampling algorithms todetermine the mixing behavior of these Markov chains, which shouldgive some insight into linguistic questions of how typical the set ofexisting human languages is with respect to the set of all possiblehuman languages. The stochastic differential equation modelsrepresent the simplification of the Markov chain simulations to aninfinite population and continuous time. For all of these models, thePI plans to run computer simulations and prove theorems about theirbehavior using tools from dynamical systems theory, functionalanalysis, and probability. The research will first address the simplecase of unstructured, well mixed populations, then add socialstructure, and then delay dynamics as a model of literacy. The PIplans to find hypotheses under which the delay dynamics give rise towell posed problems. The PI is collaborating with linguist MishaBecker at the University of North Carolina at Chapel Hill to developrealistic models of human language learning and to test these modelsagainst linguistic data.Mitchener proposes to study mathematical models of language learningand change. Most existing models assume an idealized form of speech.For example, each person might have just one way of stating a givenmeaning. In contrast, true speech is variable. The same person canconvey the same meaning by using a variety of word orders, forexample: John gave Fred a book. John gave a book to Fred. Fred wasgiven a book by John. As an improvement upon models that assumeidealized speech, the proposed models account for language variabilityin two ways. Some of them represent each speaker's utterances with alist of random choices among the alternatives. The others are notexplicitly random, but instead keep track of how often a speakerprefers the possible options for expressing a meaning. In a modelwith idealized speech, learning takes place when a speaker chooses onealternative from a list. Under a variable speech model, learning ismuch more complicated because each speaker must learn which of many

Mitchener提议研究随机过程和动态系统，这些过程对语言和语料库数据的统计分析进行了支持，以模拟语言学习和变化。 提出的模型以最多可见的模型没有的方式来解释语音的可变性。 某些提出的模型属于决定性的模型，并表示语音模式的分布是由BABANACH空间值的微分方程控制的概率密度函数。 基于离散的马尔可夫链和随机分化方程的其他提议的模型杂志。 马尔可夫链模型是最多的，包括基于贝叶斯阶层的模拟学习算法。 PI计划开发完美的抽样算法，以确定这些马尔可夫连锁店的混合行为，这应该使人们对语言问题有一些洞察力，即对所有可能的人类语言集的典型性存在典型性。 随机微分方程将马尔可夫链模拟的简化为Aninfinite群体和连续时间。 对于所有这些模型，ThePI计划使用动态系统理论，函数分析和概率中的工具运行计算机模拟并证明其行为的定理。 该研究将首先解决非结构化，混合良好的人群的简单酶，然后添加社会结构，然后延迟动态作为识字模型。 Piplans发现延迟动力学的假设带来了问题。 PI正在与北卡罗来纳大学教堂山分校的语言学家Mishabecker合作，以开发人类语言学习的真实性模型，并测试这些模型的语言数据。Mitchener提议研究语言学习和变化的数学模型。 大多数现有模型都采用理想的语音形式。例如，每个人可能只有一种说明给定的方式。 相反，真实的语音是可变的。 同一个人通过使用各种单词订单来具有相同的含义，例如：约翰给了弗雷德一本书。 约翰把书写给了弗雷德。 弗雷德（Fred）写了约翰的书。 作为对假设语音的模型的改进，提出的模型在两种方式中说明了语言可变性。 他们中的一些人在替代方案中以随机选择的方式代表了每个说话者的话语。 其他人并不是随机的，而是跟踪扬声器的频率来表达含义的可能选择。 在Modelwith理想的演讲中，学习是在说话者从列表中选择Onealternative时进行的。 在可变的语音模型下，学习更加复杂，因为每个说话者都必须学习许多