Sparse Convex Optimization Methods for Machine Learning
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Sparse Convex Optimization Methods for Machine Learning

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  • dissertation
Diss. ETH No. 20013 Sparse Convex Optimization Methods for Machine Learning A dissertation submitted to ETH Zurich for the degree of Doctor of Sciences presented by Martin Jaggi Dipl. Math. ETH born Mai 23, 1982 citizen of Lenk BE, Switzerland accepted on the recommendation of Prof. Dr. Emo Welzl, examiner Dr. Bernd Gartner, co-examiner Dr. Elad Hazan, co-examiner Prof. Dr. Joachim Giesen, co-examiner Prof.
  • poor man
  • entire path
  • low rank approximation
  • die gleichen grenzen
  • regularisierte konvexe
  • gute von
  • bewegen wir
  • convex optimization
  • norm
  • optimization

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THE COMPREHENSION OF RELATIVE CLAUSES ANDWH QUESTIONS INHEBREW AND PALESTINIANARABIC HEARING IMPAIRMENT
NAAMAFRIEDMANN, RONITSZTERMAN,ANDMANAR HADDADHANNA
1. Introduction
The lack of exposure to language input during the sensitive period for language acquisition can have farreaching consequences for the syntax of individuals with hearing impairment (de Villiers, de Villiers, & Hoban, 1994; Delage & Tuller, 2007; Friedmann & Szterman, 2006; Haddad Hanna & Friedmann, 2009). In this study we explored the way the lack of exposure affects syntax, and specifically, the comprehension of sentences derived by Whmovement. We tested the comprehension of subject and objectrelatives and ofwhichandwhosubject and objectWhquestions in Hebrewand Palestinian Arabicspeaking orally trained schoolaged children with hearing impairment.
2. Participants
2.1. Hebrew-speaking participants The Hebrewspeaking participants were 18 children with hearing impairment from birth. They were 13 girls and 5 boys, aged 9;112;3 years (M = 10;2, SD = 1;0). They had moderate to severe binaural hearing loss and were trained orally. At the time of testing, they were studying in primary schools in hearing classes with inclusive schooling using oral education, with additional classes of teachers of the deaf. All the participants constantly wore hearing aids: 13 children used binaural hearing aids, and 5 used a cochlear implant. Subject files included no other disabilities, and in all cases neither parent was deaf, and they all came from families that spoke only Hebrew. The control groups included hearing children with typical language development, no neurological or developmental difficulties, and no socio
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Relative clauses and Wh question comprehension in hearing impairment
emotional behavior problems. They were studying in public schools serving a middle class population, similarly to the participants with hearing impairment. The hearing control group in the relative clause comprehension test consisted 14 fourth graders, aged 8;109;6 years (M = 9;4). The hearing control group of the question comprehension test consisted 12 children, aged 7;59;0 (M = 8;3). We selected hearing children who were on average 2 years younger than the hearing impairment group, and at a chronological age at which children have already (just) acquired relative clause and Wh question comprehension according to previous research (Friedmann, Belletti, & Rizzi, 2009; Friedmann and Novogrodsky, 2004). 2.2 Palestinian Arabic-speaking participants The PalestinianArabicspeaking participants were 21 children and adolescents with hearing impairment aged 9;621;0 years (M = 14;6), 16 girls and 5 boys. All of them had binaural hearing loss, all of them except one were reported to have congenital hearing loss, and one lost her hearing at the age of 3 months. All the participants were trained orally, and all but one studied in regular schools (8 of them vocational schools), in hearing classes with inclusive schooling using oral education, with an individualized educational plan, and with additional classes by teachers for the deaf. One participant studied in a special education class. In all cases, neither of the parents was deaf.Nineteen of The participantslived in the Galilee, in the north of Israel, and were minimally exposed to Hebrew, and two lived in a city in central Israel, where they spoke Hebrew in addition to Arabic. Fifteen used binaural hearing aids routinely, 2 used a cochlear implant, and 4 preferred not to use any type of hearing device, although medically they needed one.The control groups included Palestinian Arabicspeaking children and adolescents with normal hearing and normal language development whose age average was approximately 2.5 years younger than that of the children with the hearing impairment. The control group for the relative clause task included 13 participants, 8 boys and 5 girls. Their age range was 9;017;9 (M = 12;7). The control group for the Wh questions task included 10 children with normal hearing, 5 boys and 5 girls, aged 7;1017;9 (M = 11;10). None of the children in the control groups had any report of neurological developmental difficulties or socioemotional problems.
3. The comprehension of relative clauses3.1. Relative clauses: Hebrew 3.1.1. Method
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We assessed the participants’ comprehension of relative clauses using a sentencepicture matching task (see Friedmann & Szterman, 2006). The participant heard a semantically reversible sentence read by a native speaker of Hebrew, and saw 2 pictures on the same page, one above the other; In one picture the roles matched the sentence; in the other picture the roles were reversed. The participant was asked to point to the picture that correctly described the sentence. 3.1.2. Material The Hebrew test included a total of 40 sentences: 20 subject relatives and 20 object relatives (examples (1) and (2), respectively, which appeared with the Figure below). All verbs were agentive transitive. All the sentences were semantically reversible so that the comprehension of the meaning of the words alone cannot assist in the interpretation of the sentences. The figures in every picture were always of the same gender and number (a girl and a female giraffe, a little boy and a grandfather, etc.), to preclude an agreement cue on the verb (as verbs in Hebrew agree with the subject in gender, number, and person). Every picture pair was presented twice: once with a subject relative and once with an object relative. Sentences were randomly ordered so that there was no sequence of more than two sentences of the same type, the correct picture in each pair was randomized too: the correct pictu top picture, and sometimes the bottom picture. (1)Subject relative tare li et hapil shemartiv et haarye. Show meACCtheelephant thatwetsACCthelion Show me the elephant that wets down the lion. (2)Object relatives tare li et hapil shehaarye martiv. Show meACCtheelephant thatthelion wets. Show me the elephant that the lion wets down.
3.1.3. Results The mean score of the control group in the comprehension of object relatives was 94% correct. Eleven of the hearing impaired participants performed below this score. These participants comprehended object relatives significantly poorer than the control group (U = 12,p =.0004). As shown in Figure 1, these 11 participants did not show any difficulty in the comprehension of subject relatives – they performed well on subject relatives, and not differently from the control group, U = 67,p =.44. They understood subject relatives significantly better than object relatives, T = 0,p= .002.
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Relative clauses and Wh question comprehension in hearing impairment
Figure 1. Comprehension of relative clauses: Hebrew-speaking hearing impaired and the control group.
When the individual performance was tested, the comparison of each hearing impaired individual to the control group showed that 7 of the 11 participants performed significantly poorer on object relatives than the control group (p <.05, using Crawford and Howell's, 1998 ttest). In the subject relatives, only one participant performed significantly poorer than the control group. Seven of the 11 participants performed significantly better in subject relatives than in object relatives. Seven of the hearing impaired participants performed at chance on object relatives, indicating a guessing pattern. All the participants performed significantly above chance level on subject relatives. 3.2.Relative clauses:Palestinian Arabic 3.2.1. Method The method and pictures were identical to those used in the Hebrew task. 3.2.2. Material Because in Palestinian Arabic both subjectverb order and verbsubject orders are possible, we included in this task object relatives of these two orders. The test included 60 sentences, 20 subject relatives, 20 object relatives in SV order, and 20 object relatives in VS order (examples 35). (3)Subject relative: fargini elfil elliamberasheq elasad showme theelephant that presentwets thelion Show me the elephant that is wetting down the lion.’(4)Object relative SV: fargini elfil elli elasadamberashqo showme theelephant that thelion presentwetshim Show me the elephant that the lion is wetting down.’ (5)Object relative VS: fargini elfil elliamberashqo elasad showme theelephant that preswetshim thelion Show me the elephant that the lion is wettingdown.’
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3.2.3. Results The results indicate that, similarly to the results in Hebrew, Palestinian Arabicspeaking children with hearing impairment have severe difficulty in the comprehension of object relatives. As seen in Figure 2, The comprehension of both types of object relatives was very poor, and significantly poorer than the control group, both for the SV object relatives, t(32) = 3.37,p= .002, and for the VS object relatives,t(32) = 5.56,p< .0001. They performed relatively well on the subject relatives, though they performed marginally poorer than the control group on this structure as well,t(32) = 2.01,p= .05.
Figure 2. Comprehension of relative clauses: Palestinian Arabic-speaking hearing impaired and the control group.
The performance of the participants with hearing impairment on object relatives was significantly poorer than on subject relatives, both for SV object relatives,t(20) = 3.48,p= .002, and for VS object relatives,t(20) = 6.13,p< .0001. Although both types of object relatives were comprehended poorly, the performance on VS object relatives was even significantly poorer than on the SV object relatives,t(20)= 4.96, p< .0001. The analysis of the performance of each hearing impaired participant indicates that 7 of the 21 participants performed significantly poorer than the control group on subject relatives; 14 performed significantly below the controls on the SV object relatives, and 18 performed significantly below the controls on the VS object relatives (using Crawford & Howell’s ttest, 1998). The comparison to chance level indicates that whereas all but one participant performed significantly above chance on the subject relatives, 8 of the 21 participants performed at chance in the comprehension of SV object relatives, and 11 performed at chance on the VS object relatives, indicating a guessing pattern. All the participants in the control group performed above chance level on all sentence types.
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Relative clauses and Wh question comprehension in hearing impairment
4.The comprehension of Wh questions
The impaired comprehension of object relatives can be ascribed to either the involvement of Whmovement, or to embedding. If Whmovement is the source of the difficulty, Wh questions are also expected to be difficult to understand, at least the ones that include the crossing of one argument over another one. If, however, embedding is the source of the difficulty, Wh questions are not expected to be difficult. We now turn to test whether Wh questions are impaired. In Hebrew, we comparedwhich andwho questions, because in many populations that have difficulty with Whmovement,which questions reflect the difficulty in comprehension, whereas the performance onwhoquestions is relatively good (de Vincenzi et al., 1999, and Avrutin, 2000, for Italian and Englishspeaking children; Friedmann, Belletti, & Rizzi, 2009 for normal acquisition of Hebrew, Friedmann & Novogrodsky, in press, and Levy & Friedmann, 2009 for syntactic SLI in Hebrew; Hickok & Avrutin, 1996 for agrammatic aphasia). 4.1. Wh questions: Hebrew 4.1.1. Method Wh question comprehension was tested using a picture selection task. The experimenter asked a question while the participant was looking at a picture. The participant was then requested to point at the figure that answered the question, selecting one of three figures. 4.1.2. Material Twenty pictures were presented, each picture included three figures: two of the same type, which differed in at least one feature (a blue and a purple elephant; a blond and a redhead girl) and a third figure of a different kind. In the picture, the first figure was performing an action on the second, and the second figure was performing the same action on the third figure, which was of the same type of the first one (see below the figure presented with sentences 69). In each picture, the figures were of the same gender, to preclude an agreement cue on the verb. The pictures were randomly ordered, so that there were no 3 consecutive pictures in which the agent was on the same side of the picture, and no 3 consecutive pictures in which the correct answer was in the same position. Each picture was presented four times, every time with a different type of question. The questions were randomly ordered, so that no more than two questions of the same type appeared in a row. The Hebrew test included 80 questions of four types: 20 subjectwhich
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questions (6), 20 objectwhichquestions (7), 20 subjectwhoquestions (8), and 20 objectwhoquestions (9). (6)Subjectwhichquestion Eyze pil martiv et hayeled? Which elephant wetsACCtheboy Which elephant wets the boy? (7)Objectwhichquestion et eyze pil hayeled martiv? ACCwhich elephant theboy wets Which elephant does the boy wet? (8)Subjectwhoquestion mi martiv et hayeled?Who wetsACCtheboy Who wetsthe boy? (9)Objectwhoquestion et mi hayeled martiv?ACCwho theboy wets? Whom does boy wet? 4.1.3. Results The eleven Hebrewspeaking hearing impaired children who showed impaired comprehension of object relatives demonstrated impaired comprehension of another structure that involves the Wh movement of the object across the subject: objectwhich questions. Most of the children performed well on subject questions (bothwhoandwhich) and on object whoquestions, as shown in Figure 3. The 7 children who performed well on object relatives also performed well on Wh questions. Whereas the performance of the hearing impaired children in the comprehension ofwhoand object questions was high (95% and subject 96%, respectively), their performance in subject and objectwhichquestions was poorer: they performed 89% correct on subjectwhichquestions and only 69% on the objectwhichquestions. Within the subject questions, subjectwho questions were significantly better than subject whichT = 0, questions, p= .02; within object questions, objectwhoquestions were significantly better than objectwhich questions, T = 0,p= .002. No difference was found betweenwhoand object subject question (almost all the participants showed the same performance in the two types of questions), but there was a significant difference between the subject and objectwhichobject questions: whichwere questions significantly poorer than subjectwhichquestions T = 0,p< .0001. The performance of the hearing impaired participants in the comprehension of subjectwhichwas poorer than that of the questions control group, U = 18,p= .002, and so was their performance in the object
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Relative clauses and Wh question comprehension in hearing impairment
whichU = 1, questions, p< .0001. The performance on thewho subject and object questions did not differ from that of the control group.
Figure 3. Comprehension ofwhich andwhoquestions: Hebrew-speaking hearing impaired and the control group.
Each of the 11 hearing impaired participants performed significantly poorer than the control group in the comprehension of objectwhichquestions. Five of the 11 hearing impaired participants performed at chance level in the comprehension of objectwhichquestions, 2 performed at chance in the comprehension of subjectwhichand only 1 questions, participant performed at chance in the comprehension of subjectwhoquestions. All the participants performed significantly above chance level on the objectwhoquestions.
4.2.Wh questions:Palestinian Arabic 4.2.1. Method The method and pictures was identical to those used in the Hebrew task. 4.2.2. Material Sixty questions were tested in Palestinian Arabic, allwhichquestions. These questions included 20 subject questions, 20 object questions in SV order, and 20 object questions in VS order (examples 10 12). (10)Subject question Aya filamberasheq elwalad? which elephant preswets theboyWhich elephant is wettingdown the boy?(11)Object question SV Aya fil elwaladamberashqo? which elephant theboy preswetshim Which elephant is the boy wettingdown?
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(12)Object question VS Aya filamberashqo elwalad? which elephant preswetshim theboy Which elephant is the boy wettingdown? 4.2.3. Results Similarly to the findings from Hebrew, the Palestinian Arabicspeaking children with hearing impairment had considerable difficulty understandingwhich object questions, both in SV and VS order. Their performance in the comprehension ofwhichquestions was object significantly poorer than that of the controls, both for SV object questions, t(22) = 2.12,p= .005, and for VS object questions,t(22) = 6.21,p< .0001, as shown in Figure 4. Responses to the subject questions differed between the groups in three respects.Firstly, whereas the hearing participants tended to interpret these questions as subject questions, and in 199 of their 200 responses pointed to the agent figure when they heard these questions, 11 of the 14 participants with hearing impairment responded to some of the subject questions as object questions. This yielded a significant difference in subject question interpretation,t(22) = 2.21,p= .03. Another important difference between the participants with hearing impairment and the hearing group was that the participants with hearing impairment, and only them, sometimes pointed to the middle figure. That is, when they heard a question like “Which elephant did the boy wet?”, they sometimes pointed to the boy. This occurred in 4.7% of the subject questions, 8.4% of the SV object questions, and 6.6% of the VS object questions.
Figure 4. Comprehension ofwhichquestions: Palestinian Arabic-speaking hearing impaired and the control group.
Performance on subject questions (when subject interpretation was considered the correct answer) was significantly better than on object questions both for SV and for VS object relatives,t(13) = 2.72, p= .009, t(13) = 5.10,p= .0001, respectively. Although both VS and SV object questions yielded very poor comprehension, the VS object questions were significantly poorer than the SV object questions,t(13) = 2.58,p= .01.
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Relative clauses and Wh question comprehension in hearing impairment
In the comparison of the performance of each individual participant with hearing impairment in each question type to the control group, 10 of the 14 participants performed significantly poorer than controls on the SV object questions, and 13 of the 14 were significantly poorer than the control group on the VS object questions.of the 14 hearing Twelve impaired participants performed significantly above chance level on the subject questions, but only 8 and 3 of the 14 performed above chance level on the SV and VS object questions respectively, indicating a guessing pattern. All the participants in the control group performed above chance level on all question types.
4. Discussion This study assessed the comprehension of two structures derived by Wh movement: relative clauses and Wh questions in orallytrained hearing impaired children speaking two Semitic languages: Hebrew and Palestinian Arabic. The main results indicated that hearing impaired children speaking Hebrew or Palestinian Arabic have a significant difficulty in the comprehension of object relatives and object (which) questions. The finding that not only object relatives but also object questions caused difficulty indicates that it is the Whmovement, rather than the embedding in relative clauses that is the source of the deficit in comprehension. This is consistent with our previous findings that showed that object topicalized sentences, which include Whmovement but no embedding, were also difficult for Hebrewspeaking and Palestinian Arabic speaking children with hearing impairment (Friedmann & Szterman, 2006; HaddadHanna & Friedmann, 2009). It is also consistent with our previous studies indicating intact embedding in hearing impairment. Nave, Szterman, and Friedmann (2009) reported good repetition of sentences with sentential embedding (such asThe boy said that the girl jumped) for the same children who could not repeat object relatives, Wh questions, and topicalization sentences, and Friedmann and Szterman (2006, and Friedmann et al., 2008) found good production of subject relatives, and no omissions of embedding markers.Given the prominence of relative clauses and Wh questions in everyday discourse as well as in academic texts, it is essential to assess the ability of the children with hearing impairment in these domains. This study further emphasizes the fruitful interaction between linguistics and the study of language impairments: linguistics serves as a toolbox for the identification of impaired structures and for generalizations on the deficit, whereas data from language impairment, in this case, the one that is
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caused by limited input during the sensitive period for syntax acquisition, contribute in determining natural classes of syntactic structures (for example, the ones that are impaired together), and provide evidence for the psychological reality of linguistic constructs, in this case—Whmovement.
Acknowledgement
This research was supported by the Israel Science Foundation (grant no. 1296/06, Friedmann), and by the Lieselotte Adler Laboratory for Research on Child Development. References Crawford, J. R., & Howell, D. C. (1998). Regression equations in clinical neuropsychology: An evaluation of statistical methods for comparing predicted and observed scores.Journal of Clinical and Experimental Neuropsychology,20, 755762. De Villiers, J., de Villiers P., & Hoban, E. (1994). The central problem of functional categories in English syntax of oral deaf children. In H. Tager Flusberg (Ed.), Constraints on language acquisition:Studies of atypical children(pp. 947). Hillsdale, NJ: Erlbaum.De Vincenzi, M., Arduino, L.S., Ciccarelli, L., & Job, R. (1999). Parsing strategies in children comprehension of interrogative sentences. In: Bagnara, S. (Ed.), Proceedings of the European Conference on Cognitive Science. Rome: Istituto di Psicologia del CNR, pp. 301308. Delage, H., & Tuller, L. (2007). Language development and mildtomoderate hearing loss: Does language normalize with age?Journal of Speech, Language, and Hearing Research, 50, 13001313 Friedmann, N., Belletti, A., & Rizzi, L. (2009). Relativized relatives: Types of intervention in the acquisition of Abar dependencies.Lingua,119, 6788. Friedmann, N., & Novogrodsky, R. (2004). The acquisition of relative clause comprehension in Hebrew: A study of SLI and normal development.Journal of Child Language,31, 661681. Friedmann, N., & Novogrodsky, R. (in press). Which questions are most difficult to understand? The comprehension of Wh questions in three subtypes of SLI. Lingua.Friedmann, N., and Szterman, R. (2006). Syntactic movement in orallytrained children with hearing impairment.Journal of Deaf Studies and Deaf Education, 11, 5675. HaddadHanna, M., & Friedmann, N. (2009). The comprehension of syntactic structures by Palestinian Arabicspeaking individuals with hearing impairment. Language and Brain, 9, 79104. (in Arabic) Nave, M., Szterman, R., & Friedmann N. (2009). Comprehension and production of Wh questions by Hebrewspeaking children with hearing impairment: another evidence for the difficulty in syntactic movement.Language and Brain, 9, 129.