DOCSLIB.ORG

Linguistic Theory in Statistical Language Learning

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Linguistic Theory in Statistical Language Learning II Linguistic Theory in Statistical Language Learning i Christer Samuelsson Bell Laboratories, Lucent Technologies Hi 600 Mountain Ave, Room 2D-339, Murray Hill, NJ 07974, USA HI christer@research, bell-labs, tom m Abstract into most linguistictheories and, for the very same reason, be used in models that striveto model lan- i This article attempts to determine what ele- guage successfully. ments of linguistic theory are used in statisti- cal language learning, and why the extracted So what do the linguistictheories underlying vari- language models look like they do. The study ous statisticallanguage models look like? And why? m indicates that some linguistic elements, such as It may be useful to distinguishbetween those aspects the notion of a word, are simply too useful to of linguistictheory that are incidentallyin the lan- be ignored. The second most important factor seems to be features inherited from the origi- guage model, and those that are there intentionally. i nal task for which the technique was used, for We will start our tour of statisticallanguage learn- example using hidden Markov models for part- ing by inspecting language models with "very little" of-speech tagging, rather than speech recogni- linguistic content, and then proceed to analyse in- tion. The two remaining important factors are creasingly more linguisticmodels, until we end with m properties of the runtime processing scheme employing the extracted language model, and models that are entirely linguistic,in the sense that the properties of the available corpus resources they are pure grammars, associated with no statis- to which the statistical learning techniques are tical parameters. ill applied. Deliberate attempts to include lin- guistic theory seem to end up in a fifth place. 2 Word N-gr_~m Models IH Let us return to the simple bigram word model, 1 Introduction where the probability of each next word is deter- What role does linguistics play in statistical lan- mined from the current one. We already noted that i guage learning? "None at all!" might be the answer, this model relies on the notion of a word, the notion if we ask hard-core speech-recognition professionals. of an utterance, and the notion that an utterance is But even the most nonlinguistic language model, for a sequence of words. IH example a statistic word bigram model, actually re- The way this model is best visualized, and as it lies on key concepts integral to virtually all linguistic happens, best implemented, is as a finite-state au- theories. Words, for example, and the notion that tomaton (FSA), with arcs and states both labelled IH sequences of words form utterances. with words, and transition probabilities associated Statistical language learning is applied to some set with each arc. For example, there will be one state of data to extract a language model of some kind. labelled The with one arc to each other state, for This language model can serve a purely decorative example to the state Cat, and this arc will be la- HI purpose, but is more often than not used to pro- belled cat. The reason for labelling both arcs and cess data in some way, for example to aid speech states with words is that the states constitute the recognition. Anyone working under the pressure of only memory device available to an FSA. To re- I producing better results, and who employs language member that the most recent word was "cat", all models to this purpose, such a researchers in the arcs labelled cat must fall into the same state Cat. field of speech recognition, will have a high incen- The transitionprobability from the state The along I tive of incorporating useful aspects of language into the unique arc labelled cat to the state Cat will be his or her language models. Now, the most useful, the probabilityof the word "cat" following the word and thus least controversial ways of describing lan- "the", P(cat l the). I guage will, due to their usefulness, find their way More generally, we enumerate the words I Samuelsson 83 Linguistic Theory i Christer Samuelsson, Bell Laboratories (1998) Linguistic Theory in Statistical Language Learning. In D.M.W. Powers (ed.) NeMLaP3/CoNLL98: New Methods in Language Processing and Computational Natural Language Learning, ACL, pp 83-89. I II {Wa,...,wlv} and associate a state Si with finite-state automata results in simplistic models of each word wl. Now the automaton has the states interword dependencies. II {$1,..., SN} and from each state Si there is an arc General word N-gram models, of which word bi- labelled wj to state Sj with transition probability gram models are a special case with "N" equal to P(wj I wi), the word bigram probability. To two, can be accommodated in very much the same II establish the probabilities of each word starting or way by introducing states that remember not only finishing off the utterance, we introduce the special the previous word, but the N-1 previous words. This state So and special word w0 that marks the end generalization is purely technical and adds little or II of the utterance, and associate the arc from So to no linguistic fuel to the model from a theoretical Si with the probability of wi starting an utterance, point of view. From a practical point of view, the and the arc from Si to So with the probability of gain in predictive power using more conditioning in an utterance ending with word wl. the probability distributions is very quickly over- II If we want to calculate the probability of a word come by the difficulty in estimating these probabil- sequence wil ... wi,,, we simply multiply the bigram ity distributions accurately from available training probabilities: data; the perennial sparse-data problem. II So why does this model look like it does? We P(wi~ . ..wi,~) = conjecture the following explanations: Firstly, it is = P(wi, I WO)" P(wi2 I wi,)..... P(wo I Wi.) directly applicable to the representation used by an II acoustic speech recognizer, and this can be done ef- We now recall something from formal language ficiently as it essentially involves intersecting two theory about the equivalence between finite-state finite-state automata. Secondly, the model parame- II automata and regular languages. What does the ters -- the word bigram probabilities -- Can be es- equivalent regular language look like? Let's just first timated directly from electronically readable texts, rename So S and, by stretching it just a little, let the and there is a lot of that a~ilable. II end-of-utterance marker wo be ~, the empty string. 3 Tag N-gram Models S ~ wiSi P(wi [ e) S~ ~ wjSj P(wj [wi) Let us now move on to a somewhat more linguisti- II Si -* e P(~ [ wi) cally sophisticated language model, the tag N-gram model. Here, the interaction between words is me- Does this give us any new insight? Yes, it does! Let's diated by part-of-speech (PoS) tags, which consti- define a string rewrite in the usual way: cA7 =~ a~7 tute linguistically motivated labels that we assign to if the rule A -+ fl is in the grammar. We can then each word in an utterance. For example, we might derive the string Wil ... wl, from the top symbol S look at the basic word classes adjectives, adverbs, II in n+l steps: articles, conjunctions, nouns, numbers, prepositions, pronouns and verbs, essentially introduced already S ::~ WilSil ~ WilWi2Si2 :=~ ... by the ancient Greek Dionysius Thrax. We imme- Wi 1 • . Wi n diately realise that this gives us the opportunity to include a vast amount of linguistic knowledge into Now comes the clever bit: if we define the deriva- our model by selecting the set of PoS tags appro- tion probability as the product of the rewrite proba- priately; consequently, this is a much debated and bilities, and identify the rewrite and the rule proba- controversial issue. bilities, we realize that the string probability is sim- Such a representation can be used for disambigua- ply the derivation probability. This illustrates one tion, as in the case of the well-known, highly ambigu- of the most central aspects of probabilistic parsing: ous example sentence "Time flies like an arrow". We String probabilities are defined in terms o] can for example prescribe that "Time" is a noun, derivation probabilities. "flies" is a verb, "like" is a preposition (or adverb, II according to your taste), "an" is an article, and that So the simple word bigram model not only em- "arrow" is a noun. In effect, a label, i.e., a part- ploys highly useful notions from linguistic theory, of-speech tag, has been assigned to each word. We II it implicitly employs the machinery of rewrite rules realise that words may be assigned different labels and derivations from formal language theory, and it in different context, or in different readings; for ex- also assigns string probabilities in terms of deriva- ample, if we instead prescribe that '2]ies" is a noun II tion probabilities, just like most probabilistic pars- and "like" is a verb, we get another reading of the ing schemes around. However, the heritage from sentence. II Samuelsson 84 Linguistic Theory II II II What does this language model look like in more The interpretation of this is that we start off in the detail? We can actually recast it in virtually the initial state S, select a PoS tag Tia at random, ac- II same terms as the word bigram model, the only dif- cording to the probability distribution in state S, ference being that we interpret each state Si as a then generate the word wkl at random according PoS tag (in the bigram case, and as a tag sequence to the lexical distribution associated with tag Til, II in the general N-gram case): then draw a next PoS tag Ti2 at random according to the transition probabilitiesassociated with state S -+ wkSi P(Si ~ wk [S) Si~, hop to the corresponding state Si2,generate the II S~ -+ ~kSj P(Sj ~ wk I S~) word wk2 at random according to the lexical distri- S~ -+ e P(e I &) bution associated with tag Ti2, etcetera.
Load more

Recommended publications
  • Computer Vision Stochastic Grammars for Scene Parsing
    Computer Vision Stochastic Grammars for Scene Parsing Song-Chun Zhu Ying Nian Wu August 18, 2020 Contents 0.1 This Book in the Series . ix Part I Stochastic Grammars in Vision 1 Introduction 3 1.1 Vision as Joint Parsing of Objects, Scenes, and Events . .3 1.2 Unified Representation for Models, Algorithms, and Attributes . .6 1.2.1 Three Families of Probabilistic Models . .6 1.2.2 Dynamics of Three Inferential Channels . .7 1.2.3 Three Attributes associated with each Node . .7 1.3 Missing Themes in Popular Data-Driven Approaches . .8 1.3.1 Top-Down Inference in Space and Time . .8 1.3.2 Vision is to be a Continuous Computational Process . .9 1.3.3 Resolving Ambiguities and Preserving Distinct Solutions . 11 1.3.4 Vision is Driven by a Large Number of Tasks . 12 1.4 Scope of Book: Compositional Patterns in the Middle Entropy Regime . 13 1.4.1 Information Scaling and Three Entropy Regimes . 14 1.4.2 Organization of Book . 14 2 Overview of Stochastic Grammar 17 2.1 Grammar as a Universal Representation of Intelligence . 17 2.2 An Empiricist’s View of Grammars . 18 2.3 The Formalism of Grammars . 20 2.4 The Mathematical Structure of Grammars . 21 2.5 Stochastic Grammar . 23 2.6 Ambiguity and Overlapping Reusable Parts . 24 2.7 Stochastic Grammar with Context . 26 3 Spatial And-Or Graph 29 3.1 Three New Issues in Image Grammars in Contrast to Language . 29 3.2 Visual Vocabulary . 31 3.2.1 The Hierarchical Visual Vocabulary – the "Lego Land" .
    [Show full text]
  • UNIVERSITY of CALIFORNIA Los Angeles Human Activity
    UNIVERSITY OF CALIFORNIA Los Angeles Human Activity Understanding and Prediction with Stochastic Grammar A thesis submitted in partial satisfaction of the requirements for the degree Master of Science in Computer Science by Baoxiong Jia 2019 c Copyright by Baoxiong Jia 2019 ABSTRACT OF THE THESIS Human Activity Understanding and Prediction with Stochastic Grammar by Baoxiong Jia Master of Science in Computer Science University of California, Los Angeles, 2019 Professor Song-Chun Zhu, Chair Video understanding is a booming research problem in computer vision. With its innate fea- ture where spatial and temporal information entangles with each other, video understand- ing has been challenging mainly because of the difficulty for having a unified framework where these two aspects can be modeled jointly. Among the tasks in video understand- ing, human activity understanding and prediction serve as a good starting point where the spatial-temporal reasoning capability of learning modules can be tested. Most of the current approaches towards solving the human activity understanding and prediction problems use deep neural networks for spatial-temporal reasoning. However, this type of approach lacks the ability to reason beyond the local frames and conduct long-term temporal reasoning. On the other hand, stochastic grammar models are used to model observed sequences on a symbolic level with all history information considered, but they perform poorly on handling noisy input sequences. Given these insights and problems of current approaches, we propose the generalized Earley parser for bridging the gap between sequence inputs and symbolic grammars. By combining the advantages of these two types of methods, we show that the proposed model achieves a better performance on both human activity recognition and future prediction.
    [Show full text]
  • Using an Annotated Corpus As a Stochastic Grammar
    Using an Annotated Corpus as a Stochastic Grammar Rens Bod Department of Computational Linguistics University of Amsterdam Spuistraat 134 NL-1012 VB Amsterdam [email protected] Abstract plausible parse(s) of an input string from the implausible ones. In stochastic language processing, it In Data Oriented Parsing (DOP), an annotated is assumed that the most plausible parse of an input corpus is used as a stochastic grammar. An string is its most probable parse. Most instantiations input string is parsed by combining subtrees of this idea estimate the probability of a parse by from the corpus. As a consequence, one parse assigning application probabilities to context free tree can usually be generated by several rewrite roles (Jelinek, 1990), or by assigning derivations that involve different subtrces. This combination probabilities to elementary structures leads to a statistics where the probability of a (Resnik, 1992; Schabes, 1992). parse is equal to the sum of the probabilities of all its derivations. In (Scha, 1990) an informal There is some agreement now that context free rewrite introduction to DOP is given, while (Bed, rules are not adequate for estimating the probability of 1992a) provides a formalization of the theory. a parse, since they cannot capture syntactie/lexical In this paper we compare DOP with other context, and hence cannot describe how the probability stochastic grammars in the context of Formal of syntactic structures or lexical items depends on that Language Theory. It it proved that it is not context. In stochastic tree-adjoining grammar possible to create for every DOP-model a (Schabes, 1992), this lack of context-sensitivity is strongly equivalent stochastic CFG which also overcome by assigning probabilities to larger assigns the same probabilities to the parses.
    [Show full text]
  • GRAMMAR IS GRAMMAR and USAGE IS USAGE Frederick J
    GRAMMAR IS GRAMMAR AND USAGE IS USAGE Frederick J. Newmeyer Department of Linguistics University of Washington Seattle, WA 98195-4340 [email protected] January 2003 1. Usage-based models of grammar The late 1960s was an exciting time to enter field of linguistics for someone like me, whose interests tended to syntax and semantics.1 My first year as a graduate student witnessed the birth of the approach called ‘generative semantics’. Generative semantics promised to totally revolutionize the field of transformational generative grammar, which itself was barely a decade old at the time. With each passing year, generative semanticists declared that some seemingly well-established boundary was nothing but an illusion. It all began in 1967 when George Lakoff and Haj Ross challenged the existence of the level of Deep Structure, and with it the boundary between syntax and semantics (Lakoff and Ross 1967/1976). The following year Jim McCawley argued that syntactic and lexical structures were formal objects of the same sort (McCawley 1968). Then in quick succession, the dividing line between semantics and pragmatics (Lakoff 1970/1972), grammaticality and ungrammaticality (Lakoff 1973), category membership and non-membership (Ross 1973a; b), and, finally, grammar and usage (Lakoff 1974) were all cast into doubt. At the same time, many sociolinguists were proposing models in which statistical facts about the speech community were incorporated into grammatical rules (Labov 1969; 1972). But by the late 1970s, generative semantics, for reasons I have discussed elsewhere (Newmeyer 1986), had all but disappeared. Most syntacticians had re- embraced the boundaries whose demise had been heralded only a few years earlier.
    [Show full text]
  • Application of Stochastic Grammars to Understanding Action
    Application of sto chastic grammars to understanding action by Yuri A Ivanov MS Computer Science State AcademyofAir and Space Instrumentation St Petersburg Russia February Submitted to the Program in Media Arts and Sciences Scho ol of Architecture and Planning in partial fulllmentofthe requirements for the degree of MASTER OF SCIENCE IN MEDIA ARTS AND SCIENCES at the Massachusetts Institute of Technology February c Massachusetts Institute of Technology All Rights Reserved Signature of Author Program in Media Arts and Sciences January Certied by Aaron F Bobick LG Electronics Inc Career Development AssistantProfessor of Computational Vision Program in Media Arts and Sciences Thesis Sup ervisor Accepted by Stephen A Benton Chairp erson Departmental Committee on Graduate Students Program in Media Arts and Sciences Application of sto chastic grammars to understanding action by Yuri A Ivanov Submitted to the Program in Media Arts and Sciences Scho ol of Architecture and Planning on January in partial fulllmentofthe requirements for the degree of Master of Science in Media Arts and Sciences Abstract This thesis addresses the problem of using probabilistic formal languages to describ e and understand actions with explicit structure The thesis explores several mechanisms of pars ing the uncertain input string aided byastochastic contextfree grammar This metho d originating in sp eechrecognition lets us combine a statistical recognition approach with a syntactical one in a unied syntacticsemantic framework for action recognition The basic
    [Show full text]
  • W. G. M., a Stochastic Model of Language Change Through Social
    A STOCHASTIC MODEL OF LANGUAGE CHANGE THROUGH SOCIAL STRUCTURE AND PREDICTION-DRIVEN INSTABILITY W. GARRETT MITCHENER ABSTRACT. We develop a new stochastic model of language learning and change that incorporates variable speech and age structure. Children detect correlations between age and speech, predict how the language is changing, and speak according to that prediction. Although the popu- lation tends to be dominated by one idealized grammar or another, the learning process amplifies chance correlation between age and speech, generating prediction-driven instability and spontaneous language change. The model is formulated as a Markov chain, and a stochastic differential equation. It exhibits the abrupt monotonic shifts among equilibria char- acteristic of language changes. Fundamental results are proved. 1. THE PARADOX OF LANGUAGE CHANGE One of the primary tools in the field of linguistics is the idealized gram- mar, that is, a formalism that identifies correct utterances (1, 2). Much of the research on how children acquire their native language focuses on how they might choose an idealized grammar from many innate possibilities on the basis of example sentences from the surrounding society (3–5). From the perspective of idealized grammar, language change is paradoxical: Children acquire their native language accurately and communicate with adults from preceding generations, yet over time, the language can change drastically. Some changes may be attributed to an external event, such as political up- heaval, but not every instance of language change seems to have an external cause. Despite their variability, languages do maintain considerable short- term stability, consistently accepting and rejecting large classes of sentences Key words and phrases.
    [Show full text]
  • The Plasticity of Grammar
    The Plasticity of Grammar JOAN BRESNAN Stanford University & CSLI, The Center for the Study of Language and Information The plasticity of grammar A simplifying assumption of linguistic theory: knowledge of language is characterized by a static, categorical system of grammar. The plasticity of grammar A simplifying assumption of linguistic theory: knowledge of language is characterized by a static, categorical system of grammar. —A fruitful idealization, but it ultimately underestimates human language capacities. The plasticity of grammar A simplifying assumption of linguistic theory: knowledge of language is characterized by a static, categorical system of grammar. —A fruitful idealization, but it ultimately underestimates human language capacities. Language users can match the probabilities of linguistic features of the environment and they have powerful predictive capabilities that enable them to anticipate the variable linguistic choices of others. The plasticity of grammar A simplifying assumption of linguistic theory: knowledge of language is characterized by a static, categorical system of grammar. —A fruitful idealization, but it ultimately underestimates human language capacities. Language users can match the probabilities of linguistic features of the environment and they have powerful predictive capabilities that enable them to anticipate the variable linguistic choices of others. Therefore, a strongly contrasting hypothesis: grammar itself is inherently variable and stochastic in nature, rather than categorical and algebraic. Implicit knowledge of variability Low-level continuous phonetic variation is sensitive to high-level construction probabilities in speech production (Gahl & Garnsey 2004, Tily et al. 2009, Kuperman & Bresnan 2012) Construction probability is not merely a summary statistic for determinative individual factors affecting pronunciation, but has a direct effect in itself (Kuperman & Bresnan 2012) Illustrations from Victor Kuperman & Joan Bresnan (2012).
    [Show full text]
  • Calibrating Generative Models: the Probabilistic Chomsky-Schutzenberger¨ Hierarchy∗
    Calibrating Generative Models: The Probabilistic Chomsky-Schutzenberger¨ Hierarchy∗ Thomas F. Icard Stanford University [email protected] December 14, 2019 1 Introduction and Motivation Probabilistic computation enjoys a central place in psychological modeling and theory, ranging in application from perception (Knill and Pouget, 2004; Orban´ et al., 2016), at- tention (Vul et al., 2009), and decision making (Busemeyer and Diederich, 2002; Wilson et al., 2014) to the analysis of memory (Ratcliff, 1978; Abbott et al., 2015), categorization (Nosofsky and Palmeri, 1997; Sanborn et al., 2010), causal inference (Denison et al., 2013), and various aspects of language processing (Chater and Manning, 2006). Indeed, much of cognition and behavior is usefully modeled as stochastic, whether this is ultimately due to indeterminacy at the neural level or at some higher level (see, e.g., Glimcher 2005). Ran- dom behavior may even enhance an agent’s cognitive efficiency (see, e.g., Icard 2019). A probabilistic process can be described in two ways. On one hand we can specify a stochastic procedure, which may only implicitly define a distribution on possible out- puts of the process. Familiar examples include well known classes of generative mod- els such as finite Markov processes and probabilistic automata (Miller, 1952; Paz, 1971), Boltzmann machines (Hinton and Sejnowski, 1983), Bayesian networks (Pearl, 1988), topic models (Griffiths et al., 2007), and probabilistic programming languages (Tenenbaum et al., 2011; Goodman and Tenenbaum, 2016). On the other hand we can specify an analytical ex- pression explicitly describing the distribution over outputs. Both styles of description are commonly employed, and it is natural to ask about the relationship between them.
    [Show full text]
  • Stochastic Definite Clause Grammars
    Stochastic Definite Clause Grammars Christian Theil Have Research group PLIS: Programming, Logic and Intelligent Systems Department of Communication, Business and Information Technologies Roskilde University, P.O.Box 260, DK-4000 Roskilde, Denmark [email protected] Abstract where corpus annotations dictate the derivations, can This paper introduces Stochastic Definite Clause be done by counting expansions used in the annota- Grammars, a stochastic variant of the well- tions. Estimation with incomplete data can be ac- known Definite Clause Grammars. The grammar complished using the Expectation-Maximization (EM) formalism supports parameter learning from an- algorithm [8]. notated or unannotated corpora and provides a In stochastic unification grammars, the choice of mechanism for parse selection by means of sta- rules to expand is stochastic and the values assigned tistical inference. Unlike probabilistic context- free grammars, it is a context-sensitive gram- to unification variables are determined implicitly by mar formalism and it has the ability to model rule selection. This means that in some derivations, cross-serial dependencies in natural language. instances of the same logic variable may get different SDCG also provides some syntax extensions values and unification will fail as result. which makes it possible to write more compact Some of the first attempts to define stochastic uni- grammars and makes it straight-forward to add fication grammars did not address the issue of how lexicalization schemes to a grammar. they should be trained. Brew [2] and Eisele [9] tries to address this problem using EM, but their methods have problems handling cases where variables fails to 1 Introduction and background unify.
    [Show full text]
  • Stochastic Attribute-Value Grammars
    Stochastic Attribute-Value Grammars Steven P. Abney* AT&T Laboratories Probabilistic analogues of regular and context-free grammars are well known in computational linguistics, and currently the subject of intensive research. To date, however, no satisfactory probabilistic analogue of attribute-value grammars has been proposed: previous attempts have failed to define an adequate parameter-estimation algorithm. In the present paper, I define stochastic attribute-value grammars and give an algorithm for computing the maximum-likelihood estimate of their parameters. The estimation algorithm is adapted from Della Pietra, Della Pietra, and Lafferty (1995). To estimate model parameters, it is necessary to compute the expectations of certain functions under random fields. In the appli- cation discussed by Della Pietra, Della Pietra, and Lafferty (representing English orthographic constraints), Gibbs sampling can be used to estimate the needed expectations. The fact that attribute-value grammars generate constrained languages makes Gibbs sampling inapplicable, but I show that sampling can be done using the more general Metropolis-Hastings algorithm. 1. Introduction Stochastic versions of regular grammars and context-free grammars have received a great deal of attention in computational linguistics for the last several years, and ba- sic techniques of stochastic parsing and parameter estimation have been known for decades. However, regular and context-free grammars are widely deemed linguisti- cally inadequate; standard grammars in computational linguistics are attribute-value (AV) grammars of some variety. Before the advent of statistical methods, regular and context-free grammars were considered too inexpressive for serious consideration, and even now the reliance on stochastic versions of the less-expressive grammars is often seen as an expedient necessitated by the lack of an adequate stochastic version of attribute-value grammars.
    [Show full text]
  • Unsupervised Language Acquisition: Theory and Practice
    Unsupervised Language Acquisition: Theory and Practice Alexander Simon Clark Submitted for the degree of D.Phil. University of Sussex September, 2001 Declaration I hereby declare that this thesis has not been submitted, either in the same or different form, to this or any other university for a degree. Signature: Acknowledgements First, I would like to thank Bill Keller, for his supervision over the past three years. I would like to thank my colleagues at ISSCO for making me welcome and especially Susan Armstrong for giving me the job in the first place, and various people for helpful comments and discussions including Chris Manning, Dan Klein, Eric Gaussier, Nicola Cancedda, Franck Thollard, Andrei Popescu-Beilis, Menno van Zaanen and numerous other people including Sonia Halimi for check- ing my Arabic. I would also like to thank Gerald Gazdar and Geoffrey Sampson for their helpful comments as part of my thesis committee. I would also like to thank all of the people that have worked on the various software packages and operating systems that I have used, such as LaTeX, Gnu/Linux, and the gcc compiler, as well as the people who have worked on the preparation of the various corpora I have used: in particular I am grateful to John McCarthy and Ramin Nakisa for allowing me to use their painstakingly collected data sets for Arabic. Finally I would like to thank my wife, Dr Clare Hornsby, for her unfailing support and encouragement (in spite of her complete lack of understanding of the subject) and my children, Lily and Francis, for putting up with my absences both physical and mental, and showing me how language acquisition is really done – over-regularisation of past tense verbs included.
    [Show full text]
  • A Stochastic Grammar of Images
    A Stochastic Grammar of Images The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Zhu, Song Chun, and David Bryant Mumford. 2006. A stochastic grammar of images. Foundations and Trends in Computer Graphics and Vision 2(4): 259-362. Published Version doi:10.1561/0600000018 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:3637153 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Foundations and TrendsR in Computer Graphics and Vision Vol. 2, No. 4 (2006) 259–362 c 2007 S.-C. Zhu and D. Mumford DOI: 10.1561/0600000018 A Stochastic Grammar of Images Song-Chun Zhu1,∗ and David Mumford2 1 University of California, Los Angeles, USA, [email protected] 2 Brown University, USA, David [email protected] Abstract This exploratory paper quests for a stochastic and context sensitive grammar of images. The grammar should achieve the following four objectives and thus serves as a unified framework of representation, learning, and recognition for a large number of object categories. (i) The grammar represents both the hierarchical decompositions from scenes, to objects, parts, primitives and pixels by terminal and non-terminal nodes and the contexts for spatial and functional relations by horizon- tal links between the nodes. It formulates each object category as the set of all possible valid configurations produced by the grammar.
    [Show full text]