The learnability of tones from the speech signal Kristine M. Yu Department of Linguistics University of Maryland College Park University of Massachusetts Amherst Macquarie University November 30, 2011 Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 1
Defining tonal maps The learnability of tonal maps Overview 1 What is the target of learning in learning phonological categories? 2 What are inductive biases for learning phonological categories? Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 2
Defining tonal maps The learnability of tonal maps Overview 1 What is the target of learning in learning phonological categories? 2 What are inductive biases for learning phonological categories? Model system: lexical tones in tonal languages Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 2
Defining tonal maps The learnability of tonal maps Overview 1 What is the target of learning in learning phonological categories? 2 What are inductive biases for learning phonological categories? Model system: lexical tones in tonal languages Methods: 0 Theoretical inquiry 1 Cross linguistic fieldwork 2 Psychological experiments 3 Computational modeling Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 2
Defining tonal maps The learnability of tonal maps Phonological categories must be learned . . .categories, defined as relations between a discrete level and a parametric phonetic level, cannot be universal. That is, the picture of human phonetic resources as pegs in an IPA-like phonetic pegboard cannot be sustained. (Pierrehumbert 2003: 127) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 3
Defining tonal maps The learnability of tonal maps Phonological categories must be learned . . .categories, defined as relations between a discrete level and a parametric phonetic level, cannot be universal. That is, the picture of human phonetic resources as pegs in an IPA-like phonetic pegboard cannot be sustained. (Pierrehumbert 2003: 127) The “same” categories have different phonetic realizations in different languages (Cho and Ladefoged 1999, i.a.) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 3
Defining tonal maps The learnability of tonal maps Phonological categories must be learned . . .categories, defined as relations between a discrete level and a parametric phonetic level, cannot be universal. That is, the picture of human phonetic resources as pegs in an IPA-like phonetic pegboard cannot be sustained. (Pierrehumbert 2003: 127) Infants begin as “universal citizens” in being able to discriminate (almost) any speech sound contrast but develop language-specific sensitivity to contrasts in the first year of life (tones: Mattock et al. 2008) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 3
Defining tonal maps The learnability of tonal maps The target of learning: what are tones? What does it mean to learn the lexical tones in a tonal lan- guage, e.g. in Mandarin? (Xu 1997) Tone 1 (high level): Ă £ma (55) ‘mother’ Tone 2 (rise): Ę£ma (35) ‘hemp’ Tone 3 (fall-rise): ŁŘ£ma (214) ‘horse’ Tone 4 (fall): Ď£ma (51) ‘scold’ Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 4
Defining tonal maps The learnability of tonal maps Interlude: A vowel map in 2-D formant space Figure: Peterson and Barney (1952): An English vowel map in F1SS , F2SS space Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 5
Defining tonal maps The learnability of tonal maps Interlude: A vowel map in 2-D formant space Figure: Peterson and Barney (1952): An English vowel map in F1SS , F2SS space F1SS , F2SS Vowel 240, 2280 {/i/} Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 5
Defining tonal maps The learnability of tonal maps Interlude: A vowel map in 2-D formant space Figure: Peterson and Barney (1952): An English vowel map in F1SS , F2SS space F1SS , F2SS Vowel 240, 2280 {/i/} 460, 1330 {/Ç/} Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 5
Defining tonal maps The learnability of tonal maps Interlude: A vowel map in 2-D formant space Figure: Peterson and Barney (1952): An English vowel map in F1SS , F2SS space F1SS , F2SS Vowel 240, 2280 {/i/} 460, 1330 {/Ç/} 475, 1220 {/U/} Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 5
Defining tonal maps The learnability of tonal maps Interlude: A vowel map in 2-D formant space Figure: Peterson and Barney (1952): An English vowel map in F1SS , F2SS space F1SS , F2SS Vowel 240, 2280 {/i/} 460, 1330 {/Ç/} 475, 1220 {/U/} 686, 1028 {/A, O/} Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 5
Defining tonal maps The learnability of tonal maps Interlude: A vowel map in 2-D formant space Figure: Peterson and Barney (1952): An English vowel map in F1SS , F2SS space F1SS , F2SS Vowel 240, 2280 {/i/} 460, 1330 {/Ç/} 475, 1220 {/U/} 686, 1028 {/A, O/} 400, 3500 {/i/} Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 5
Defining tonal maps The learnability of tonal maps Interlude: A vowel map in 2-D formant space Figure: Peterson and Barney (1952): An English vowel map in F1SS , F2SS space F1SS , F2SS Vowel 240, 2280 {/i/} 460, 1330 {/Ç/} 475, 1220 {/U/} 686, 1028 {/A, O/} 400, 3500 {/i/} : : Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 5
Defining tonal maps The learnability of tonal maps The target of learning: what are tones? {Data} Learner − − − − → {Phonological maps} Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 6
Defining tonal maps The learnability of tonal maps The target of learning: what are tones? {Phonetic data} Learner − − − − → {Tonal maps} Restriction for this project: “pure speech” situation—refer only to acoustic information (methodological abstraction) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 6
Defining tonal maps The learnability of tonal maps Defining phonological maps Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 7
Defining tonal maps The learnability of tonal maps Defining phonological maps Morphosyntactic maps: {sequences of morphemes} → {sets of meanings} Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 7
Defining tonal maps The learnability of tonal maps Defining phonological maps Morphosyntactic maps: {sequences of morphemes} → {sets of meanings} Phonological maps: {sequences of phonetic parameter values} → {sets of phonological categories} Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 7
Defining tonal maps The learnability of tonal maps A vowel map in 2-D formant space Figure: Peterson and Barney (1952): An English vowel map in F1SS , F2SS space F1SS , F2SS Vowel 240, 2280 {/i/} 460, 1330 {/Ç/} 475, 1220 {/U/} 686, 1028 {/A, O/} 400, 3500 {/i/} : : Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 8
Defining tonal maps The learnability of tonal maps Defining phonological maps Parallels with morphosyntax Generalization from finite sample to infinite set in learning Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 9
Defining tonal maps The learnability of tonal maps Defining phonological maps Parallels with morphosyntax Generalization from finite sample to infinite set in learning Abstraction away from unbounded context to focus on primary evidence: speech signal Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 9
Defining tonal maps The learnability of tonal maps Defining phonological maps Parallels with morphosyntax Generalization from finite sample to infinite set in learning Abstraction away from unbounded context to focus on primary evidence: speech signal Ambiguity ⇒ probabilistic distribution of phonological categories over phonetic spaces (Pierrehumbert 2003) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 9
Defining tonal maps The learnability of tonal maps Defining phonological maps Parallels with morphosyntax Generalization from finite sample to infinite set in learning Abstraction away from unbounded context to focus on primary evidence: speech signal Ambiguity ⇒ probabilistic distribution of phonological categories over phonetic spaces (Pierrehumbert 2003) F1SS = 686, F2SS = 1028 → {/A, O/} Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 9
Defining tonal maps The learnability of tonal maps Defining phonological maps Parallels with morphosyntax Generalization from finite sample to infinite set in learning Abstraction away from unbounded context to focus on primary evidence: speech signal Ambiguity ⇒ probabilistic distribution of phonological categories over phonetic spaces (Pierrehumbert 2003) F1SS = 686, F2SS = 1028 → {p(/A/) = 0.45, p(/O/) = 0.55} Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 9
Defining tonal maps The learnability of tonal maps Characterizing phonological maps Key questions: Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 10
Defining tonal maps The learnability of tonal maps Characterizing phonological maps Key questions: 1 What kinds of phonological categories are to be represented in the range of the map? (Here: phonemes, by stipulation) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 10
Defining tonal maps The learnability of tonal maps Characterizing phonological maps Key questions: 1 What kinds of phonological categories are to be represented in the range of the map? (Here: phonemes, by stipulation) 2 What is the phonetic parameter space—the space of phonetic parameters—for the phonological categories? Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 10
Defining tonal maps The learnability of tonal maps Characterizing phonological maps Key questions: 1 What kinds of phonological categories are to be represented in the range of the map? (Here: phonemes, by stipulation) 2 What is the phonetic parameter space—the space of phonetic parameters—for the phonological categories? 3 What are properties of the distribution of the phonological categories over the phonetic parameter space? Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 10
Defining tonal maps The learnability of tonal maps Methodological abstraction: which parameters? Reality: Probabilistic distribution of phonological categories over phonetic spaces Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 11
Defining tonal maps The learnability of tonal maps Methodological abstraction: which parameters? Reality: Probabilistic distribution of phonological categories over phonetic spaces Model: partition of set of phonological categories over phonetic spaces Tonal identification (humans), hard classification algorithms (machines) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 11
Defining tonal maps The learnability of tonal maps Methodological abstraction: which parameters? Reality: Probabilistic distribution of phonological categories over phonetic spaces Model: partition of set of phonological categories over phonetic spaces Tonal identification (humans), hard classification algorithms (machines) Example: A two tone tonal inventory, e.g. {H, L} Duda, Hart and Stork (2001) Probability distribution p(x|ω) over x, x = mean fundamental frequency (f0) Two classes: ω1 = L, ω2 = H Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 11
Defining tonal maps The learnability of tonal maps Language input begins in the womb Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 12
Defining tonal maps The learnability of tonal maps Language input begins in the womb Mic introduced at beginning of labor, after amniotic sac rupture Audio file courtesy of Christine Moon, recorded by Denis Querleu, see methods in Querleu et al. (1988). Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 12
Defining tonal maps The learnability of tonal maps Language input begins in the womb Pitch information is available in the womb. Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 12
Defining tonal maps The learnability of tonal maps 2-D tonal spaces: f0init , f0fin Figure: Cantonese citation tones in f0init , f0fin space (Barry and Blamey 2004) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 13
Defining tonal maps The learnability of tonal maps 2-D tonal spaces: f0init , f0fin Figure: Cantonese citation tones in f0init , f0fin space (Barry and Blamey 2004) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 13
Defining tonal maps The learnability of tonal maps Can we characterize tonal maps as being feasibly learnable? Figure: Map in a 2-D parameter space In phonetic space: each parameter defines a dimension and can take a real value Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 14
Defining tonal maps The learnability of tonal maps Can we characterize tonal maps as being feasibly learnable? Figure: Map in a 3-D parameter space In phonetic space: each parameter defines a dimension and can take a real value Potentially an infinite number of parameters, each with a potentially infinite range of possible values Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 14
Defining tonal maps The learnability of tonal maps Phonological maps are non recursively-enumerable Phonological maps are defined over real-valued parameters Reg CF Fin non!RE RE CS MG Figure: The Chomsky hierarchy of formal languages Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 15
Defining tonal maps The learnability of tonal maps Structure permits feasible learning even in infinite spaces But comfort from the finiteness of the space of possible grammars is tenuous indeed. For a grammatical theory with an infinite number of possible grammars might be well structured, permitting informed search that converges quickly to the correct grammar—even though uninformed, exhaustive search is infeasible. And it is of little value that exhaustive search is guaranteed to terminate eventually when the space of possible grammars is finite, if the number of grammars is astronomical. In fact, a well-structured theory admitting an infinity of grammars could well be feasibly learnable, while a poorly structured theory admitting a finite, but very large, number of possible grammars might not. (Tesar and Smolensky 2000: 3) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 16
Defining tonal maps The learnability of tonal maps Structure permits feasible learning even in infinite spaces This talk: don’t panic! Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 16
Defining tonal maps The learnability of tonal maps Can we characterize tonal maps as being feasibly learnable? Figure: Map in a 3-D parameter space In phonetic space: each parameter defines a dimension and can take a real value Potentially an infinite number of parameters, each with a potentially infinite range of possible values Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 17
Defining tonal maps The learnability of tonal maps Can we characterize tonal maps as being feasibly learnable? Figure: Scary map in a 2-D parameter space (Miller 1989) In phonetic space: each parameter defines a dimension and can take a real value Potentially an infinite number of parameters, each with a potentially infinite range of possible values Complex shapes/distributions can make maps in even 2-D spaces not feasibly learnable Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 17
Defining tonal maps The learnability of tonal maps Can we characterize tonal maps as being feasibly learnable? Figure: Scary map in a 2-D parameter space (Miller 1989) In phonetic space: each parameter defines a dimension and can take a real value Potentially an infinite number of parameters, each with a potentially infinite range of possible values Complex shapes/distributions can make maps in even 2-D spaces not feasibly learnable Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 17
Defining tonal maps The learnability of tonal maps Can we characterize tonal maps as being feasibly learnable? Figure: Scary map in a 2-D parameter space (Miller 1989) In phonetic space: each parameter defines a dimension and can take a real value Potentially an infinite number of parameters, each with a potentially infinite range of possible values Complex shapes/distributions can make maps in even 2-D spaces not feasibly learnable ⇒ there must exist inductive biases to constrain the hypothesis space Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 17
Defining tonal maps The learnability of tonal maps Inductive biases for learning phonological categories The modeler (and learner?) must start with a finite set of parameters for parameterizing the speech signal Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 18
Defining tonal maps The learnability of tonal maps Inductive biases for learning phonological categories The modeler (and learner?) must start with a finite set of parameters for parameterizing the speech signal Any results on learning and observations about shapes/distributions are conditioned on that parameterization Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 18
Defining tonal maps The learnability of tonal maps Inductive biases for learning phonological categories The modeler (and learner?) must start with a finite set of parameters for parameterizing the speech signal Any results on learning and observations about shapes/distributions are conditioned on that parameterization How to decide on parameters? Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 18
Defining tonal maps The learnability of tonal maps Inductive biases for learning phonological categories The modeler (and learner?) must start with a finite set of parameters for parameterizing the speech signal Any results on learning and observations about shapes/distributions are conditioned on that parameterization How to decide on parameters? A lower bound: parameters that yield well-separated tonal categories in acoustic and perceptual spaces in any tonal language ⇒ Need for cross-linguistic language sample Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 18
Defining tonal maps The learnability of tonal maps Inductive biases for learning phonological categories The modeler (and learner?) must start with a finite set of parameters for parameterizing the speech signal Any results on learning and observations about shapes/distributions are conditioned on that parameterization How to decide on parameters? A lower bound: parameters that yield well-separated tonal categories in acoustic and perceptual spaces in any tonal language ⇒ Need for cross-linguistic language sample Can only guess based on computational modeling (category separability) and psychological experimentation (human perception) ⇒ Need for interplay of computational modeling and psychological experimentation Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 18
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Cross-linguistic tonal language sample Language Area Tonal inventory Bole Nigeria Ă £, Ă£ (H,L) Mandarin Beijing Ă £, Ę£, ŁŘ£, Ď£ Cantonese Hong Kong Ă £, Ă £, Ă£, Ą£, Ę£, Ę£ Hmong Laos/Thailand Ă £, Ă£, Ă£, Č£, Ć£, Ą£, Ę£ Languages chosen for diversity in level/contour distinctions and voice quality contrasts Multiple speakers (6M/6F for all but Bole (3M/2F)) All legal bitone combinations recorded sentence-medially Data collection from additional languages always in progress Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 19
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Cross-linguistic tonal language sample Language Area Tonal inventory Bole Nigeria Ă £, Ă£ (H,L) Mandarin Beijing Ă £, Ę£, ŁŘ£, Ď£ Cantonese Hong Kong Ă £, Ă £, Ă£, Ą£, Ę£, Ę£ Hmong Laos/Thailand Ă £, Ă£, Ă£, Č£, Ć£, Ą£, Ę£ Languages chosen for diversity in level/contour distinctions and voice quality contrasts Multiple speakers (6M/6F for all but Bole (3M/2F)) All legal bitone combinations recorded sentence-medially Data collection from additional languages always in progress Perception experiments done in Cantonese Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 19
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Inductive biases for learning tonal categories Is onset and offset f0 sufficient for defining tonal spaces? 1 The role of (phonetic) context 2 A lack of simple f0 universal invariants 3 Voice quality parameters beyond f0 Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 20
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Inductive biases for learning tonal categories Is onset and offset f0 sufficient for defining tonal spaces? 1 The role of (phonetic) context 2 A lack of simple f0 universal invariants 3 Voice quality parameters beyond f0 Structure in the hypothesis space 1 Coarse-grained temporal resolution 2 Initial thoughts on category shapes/distributions Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 20
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space f0 is not a single dimension . . .tones typically involve a single primary acoustic dimension, namely, f0. This contrasts with the multiple acoustic dimensions such as formants or spectral peaks required for characterizing vowels and consonants. The variability problem with tones is therefore at least limited to a single dimension. . . (Gauthier et al. 2007) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 21
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space f0 is not a single dimension . . .tones typically involve a single primary acoustic dimension, namely, f0. This contrasts with the multiple acoustic dimensions such as formants or spectral peaks required for characterizing vowels and consonants. The variability problem with tones is therefore at least limited to a single dimension. . . (Gauthier et al. 2007) Assertion: f0 is a set of acoustic dimensions Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 21
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space f0 is not a single dimension . . .tones typically involve a single primary acoustic dimension, namely, f0. This contrasts with the multiple acoustic dimensions such as formants or spectral peaks required for characterizing vowels and consonants. The variability problem with tones is therefore at least limited to a single dimension. . . (Gauthier et al. 2007) Assertion: f0 is a set of acoustic dimensions Temporal domain: how much context? Parameterization: f0, f0 velocity, polynomial coefficients, . . . Temporal resolution: how many samples of a parameter? Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 21
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Temporal domain: how much phonetic context? Modeling phonological learning: just the associated syllable Gauthier et al. (2007) for Mandarin tones and all other phonological learning studies (de Boer and Kuhl 2003, Vallabha et al. 2007, i.a.) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 22
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Temporal domain: how much phonetic context? Context beyond syllable Speech perception: mostly work on effect of preceding context in vowels (Ladefoged and Broadbent (1980), for level tones (Wong and Diehl 2003) contour tones (Huang and Holt 2009), minimal work on following context Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 22
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Temporal domain: how much phonetic context? Context beyond syllable Speech perception: mostly work on effect of preceding context in vowels (Ladefoged and Broadbent (1980), for level tones (Wong and Diehl 2003) contour tones (Huang and Holt 2009), minimal work on following context Peak delay (Silverman & Pierrehumbert 1990, Myers 1999) suggests role for following context in tonal perception Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 22
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Temporal domain: how much phonetic context? Context beyond syllable Speech perception: mostly work on effect of preceding context in vowels (Ladefoged and Broadbent (1980), for level tones (Wong and Diehl 2003) contour tones (Huang and Holt 2009), minimal work on following context Automatic tonal recognition Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 22
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Temporal domain: how much phonetic context? Context beyond syllable Speech perception: mostly work on effect of preceding context in vowels (Ladefoged and Broadbent (1980), for level tones (Wong and Diehl 2003) contour tones (Huang and Holt 2009), minimal work on following context Automatic tonal recognition Acoustic parameters from preceding and following syllables: Qian et al. (2007), Levow (2006), Zhang et al. (2005) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 22
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Temporal domain: how much phonetic context? Context beyond syllable Speech perception: mostly work on effect of preceding context in vowels (Ladefoged and Broadbent (1980), for level tones (Wong and Diehl 2003) contour tones (Huang and Holt 2009), minimal work on following context Automatic tonal recognition Acoustic parameters from preceding and following syllables: Qian et al. (2007), Levow (2006), Zhang et al. (2005) Hypothesis: Following context can be important for good tonal category separability. Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 22
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Human perception experiments: stimuli Cantonese tritones: nonce 3-syllable phrases built from syllables in the lexicon First and third syllables held fixed: < waiĂ£, {wai Ă £, Ę£, Ă £, Ą£, Ę£, Ă£}, matĂ£ > Tritone Gloss < waiĂ£, wai Ă £, matĂ£ > fear power clean < waiĂ£, waiĘ£, matĂ£ > fear appoint clean < waiĂ£, wai Ă £, matĂ£ > fear fear clean < waiĂ£, waiĄ£, matĂ£ > fear surround clean < waiĂ£, waiĘ£, matĂ£ > fear great clean < waiĂ£, waiĂ£, matĂ£ > fear stomach clean Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 23
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Human perception experiments: stimuli Cantonese tritones: nonce 3-syllable phrases built from syllables in the lexicon First and third syllables held fixed: < waiĂ£, {wai Ă £, Ę£, Ă £, Ą£, Ę£, Ă£}, matĂ£ > Tritone Gloss < waiĂ£, wai Ă £, matĂ£ > fear power clean < waiĂ£, waiĘ£, matĂ£ > fear appoint clean < waiĂ£, wai Ă £, matĂ£ > fear fear clean < waiĂ£, waiĄ£, matĂ£ > fear surround clean < waiĂ£, waiĘ£, matĂ£ > fear great clean < waiĂ£, waiĂ£, matĂ£ > fear stomach clean Syllables identified with orthographic characters Some characters may be more frequent than others: Ę£ > Ą£ > Ă £ >> Ę£ > Ă £, Ă£ (based on corpus count of Mandarin cognates, Da (2004) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 23
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Human perception experiment: contextual information Stimuli: Cantonese citation tones and parts of tritones, < waiĂ£, {wai Ă £, Ę£, Ă £, Ą£, Ę£, Ă£}, matĂ£ > from 5 speakers (3M, 2F) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 24
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Human perception experiment: contextual information Stimuli: Cantonese citation tones and parts of tritones, < waiĂ£, {wai Ă £, Ę£, Ă £, Ą£, Ę£, Ă£}, matĂ£ > from 5 speakers (3M, 2F) Methodological inspiration: Perceptual normalization studies (Ladefoged and Broadbent (1957), Wong and Diehl (2003)); Manipulated variable: context (mono, pre, post, tri, isolation) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 24
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Human perception experiment: contextual information Stimuli: Cantonese citation tones and parts of tritones, < waiĂ£, {wai Ă £, Ę£, Ă £, Ą£, Ę£, Ă£}, matĂ£ > from 5 speakers (3M, 2F) Methodological inspiration: Perceptual normalization studies (Ladefoged and Broadbent (1957), Wong and Diehl (2003)); Manipulated variable: context (mono, pre, post, tri, isolation) Task: 6-alternative forced choice orthographic identification of target tone Participants: 36 native Cantonese speakers, tested in Hong Kong and Los Angeles Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 24
Is onset/offset f0 sufficient for defining tonal spaces? 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TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI TRI 0.2 0.4 0.6 Speaker q q q f4 f3 m6 m1 m5 Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 25
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Human perception: following context helps separate rise Time (s) log f0/[Hz] 4.8 4.9 5.0 5.1 5.2 5.3 5.4 PRE−TARGET TARGET TRITONE POST−TARGET ISOLATION 0.1 0.2 0.3 0.4 0.5 0.6 Tone 25 23 Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 26
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Human perception: following context helps separate rise Tone Percent of correct responses 0 20 40 60 80 55 25 33 21 23 22 Context mono pre post tri iso Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 26
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Human perception: following context helps separate rise Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 26
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Computational modeling for insight into experiment What were listeners listening to? Effects of particular task/stimuli? Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 27
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Computational modeling for insight into experiment What were listeners listening to? Effects of particular task/stimuli? Computational modeling allows explicit and tradeable assumptions. Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 27
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Computational modeling for insight into experiment What were listeners listening to? Effects of particular task/stimuli? Computational modeling allows explicit and tradeable assumptions. Assume: mean f0 values extracted from each sample, for 2-7 samples per syllable Extracted using implementation of RAPT pitch tracker (Talkin 1995) Assume: no lexical bias Uniform prior (all tonal categories equally likely) Ask: How accurate is tonal identification by machine? Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 27
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Computational modeling: support vector machines Bennett and Bredensteiner (2000), Vapnik (1995) 1 Given labeled training data, e.g. << 200, 210, 224 >, Ă £ > Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 29
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Computational modeling: support vector machines Bennett and Bredensteiner (2000), Vapnik (1995) 1 Given labeled training data, e.g. << 200, 210, 224 >, Ă £ > 2 Draw convex hull around data from a given category 3 Find separating hyperplane maximizing margin between convex hulls Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 29
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Computational modeling: support vector machines Bennett and Bredensteiner (2000), Vapnik (1995) 1 Given labeled training data, e.g. << 200, 210, 224 >, Ă £ > 2 Draw convex hull around data from a given category 3 Find separating hyperplane maximizing margin between convex hulls 4 Use separating hyperplane to classify test data (unseen data): train on 4 speakers, test on 5th, average results Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 29
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Computational modeling: higher weight to post-target syllable f0 values for separating rises Hyperplane influenced more by post than pre-target f0 Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 30
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Local summary: temporal domain Cantonese listeners benefit from having preceding and following context available in tonal identification Following context is especially informative for separating out the Tone 25 rise, as shown in listener performance and by computational modeling Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 31
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Local summary: temporal domain Cantonese listeners benefit from having preceding and following context available in tonal identification Following context is especially informative for separating out the Tone 25 rise, as shown in listener performance and by computational modeling Temporal domain may extend beyond associated syllable in both directions Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 31
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Parameterization: f0 and f0 velocity (I) Gauthier et al. (2007): Computational simulations on learning Mandarin tones: better categorization performance with f0 velocity alone than f0 height alone Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 32
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Parameterization: f0 and f0 velocity (I) Gauthier et al. (2007): Computational simulations on learning Mandarin tones: better categorization performance with f0 velocity alone than f0 height alone Strong hypothesis: f0 velocity is a sufficient acoustic cue for good category separability of lexical tones for all tone languages Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 32
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Parameterization: f0 and f0 velocity (I) Gauthier et al. (2007): Computational simulations on learning Mandarin tones: better categorization performance with f0 velocity alone than f0 height alone Strong hypothesis: f0 velocity is a sufficient acoustic cue for good category separability of lexical tones for all tone languages ⇒ To test: Cross-linguistic tonal production data Natural test case: languages with level tonal contrasts Methods: very difficult to test using psychological experimentation ⇒ rely on computational modeling Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 32
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Parameterization: f0 and f0 velocity (II) Level and rise Rise and fall Two rises Two levels Time f0 Time f0 velocity Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 33
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Parameterization: f0 and f0 velocity (II) Level and rise Rise and fall Two rises Two levels Time f0 Time f0 Time f0 velocity Time f0 velocity Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 33
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Parameterization: f0 and f0 velocity (II) Level and rise Rise and fall Two rises Two levels Time f0 Time f0 Time f0 Time f0 velocity Time f0 velocity Time f0 velocity Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 33
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Parameterization: f0 and f0 velocity (II) Level and rise Rise and fall Two rises Two levels Time f0 Time f0 Time f0 Time f0 Time f0 velocity Time f0 velocity Time f0 velocity Time f0 velocity Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 33
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Level tone languages have contours too (Bole) ` an` ın LL n´ em` a HL m´ eng` o HL ‘The owners of prosperity came back’ Time (s) 0 1.003 Pitch (Hz) 50 150 L L H L H L Time (s) 0 1.003 Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 34
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Linear discriminant analysis for dimensionality reduction Don’t project there! Project here! (Hastie, Tibshirani, and Friedman 2009) Project onto axis to maximize ratio of between-class to within-class scatter Between-class scatter: roughly, distance between class means Within-class scatter: class variances Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 35
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Better separability of H/L in Bole with f0 velocity than f0 for syllable averages log mean f0 Density 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 110 120 130 140 150 160 170 tone H L Bole: mean log f0 f0 change between 2 uniform f0 samples Density 0.00 0.01 0.02 0.03 0.04 0.05 0.06 −40 −20 0 20 40 tone H L Bole: mean f0 change Possible to have separability better with f0 velocity alone than f0 alone in Bole if 1 real value Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 36
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space But f0 velocity alone can’t separate level tone contrasts in Cantonese, Hmong Hmong: log f0, 10 values Hmong: f0 change, 10 values Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 37
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Summary: beyond 2-D tonal spaces What have we learned about the learner’s predicament so far? Temporal domain beyond associated syllable is a source of some dimensionality Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 38
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Summary: beyond 2-D tonal spaces What have we learned about the learner’s predicament so far? Temporal domain beyond associated syllable is a source of some dimensionality No simple invariant f0 parameter set: just f0 or just f0 velocity Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 38
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Parameterization: voice quality parameters beyond f0 f0-related parameters are a subset of voice quality parameters Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 39
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Parameterization: voice quality parameters beyond f0 f0-related parameters are a subset of voice quality parameters Existence of languages with tonal contrasts cued by phonation contrasts (e.g. Hmong, Vietnamese) ⇒ tonal space must include voice quality parameters beyond f0 Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 39
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Parameterization: voice quality parameters beyond f0 f0-related parameters are a subset of voice quality parameters Existence of languages with tonal contrasts cued by phonation contrasts (e.g. Hmong, Vietnamese) ⇒ tonal space must include voice quality parameters beyond f0 What about tonal languages without contrastive phonation? Cantonese tonal perception: listeners are sensitive to presence of creak and creak can increase tonal identification accuracy (Lam and Yu 2010, Yu and Lam 2011) Result: Even in tonal languages without contrastive phonation, tonal space must include voice quality parameters beyond f0 values. Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 39
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Summary: beyond 2-D tonal spaces What have we learned about the learner’s predicament so far? Temporal domain beyond associated syllable is a source of some dimensionality No simple invariant f0 parameter set: just f0 or just f0 velocity Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 40
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Summary: beyond 2-D tonal spaces What have we learned about the learner’s predicament so far? Temporal domain beyond associated syllable is a source of some dimensionality No simple invariant f0 parameter set: just f0 or just f0 velocity Learner must consider other voice quality parameters than just idealized f0 values in a wide range of tone languages Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 40
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Temporal resolution: how many samples? (I) Dense sampling Coarse sampling Time f0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q Time f0 q q q q Each sampled point could contribute to complexity in tonal map! Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 41
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Temporal resolution: how many samples? (II) Dense sampling Gauthier et al. (2007): 30 samples/syllable (1 sample/6 ms) Automatic speech recognition: 1 sample/10 ms Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 42
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Temporal resolution: how many samples? (II) Dense sampling Gauthier et al. (2007): 30 samples/syllable (1 sample/6 ms) Automatic speech recognition: 1 sample/10 ms Coarse sampling Linguistics: Chao (1933, 1968), International Phonetic Alphabet Ă £,Ę£,ŁŘ£,Ď£, 3 samples/tone Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 42
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Temporal resolution: how many samples? (II) Dense sampling Gauthier et al. (2007): 30 samples/syllable (1 sample/6 ms) Automatic speech recognition: 1 sample/10 ms Coarse sampling Linguistics: Chao (1933, 1968), International Phonetic Alphabet Ă £,Ę£,ŁŘ£,Ď£, 3 samples/tone Automatic speech recognition 3 - 5 samples/tone: Qian et al. (2007): Cantonese; Wang and Levow (2008), Zhou et al. (2008): Mandarin Tian et al. (2004): Higher tonal ID accuracy with 4 samples/tone than 1 sample/10 ms (Mandarin) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 42
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Temporal resolution: how many samples? (II) Dense sampling Gauthier et al. (2007): 30 samples/syllable (1 sample/6 ms) Automatic speech recognition: 1 sample/10 ms Coarse sampling Linguistics: Chao (1933, 1968), International Phonetic Alphabet Ă £,Ę£,ŁŘ£,Ď£, 3 samples/tone Automatic speech recognition 3 - 5 samples/tone: Qian et al. (2007): Cantonese; Wang and Levow (2008), Zhou et al. (2008): Mandarin Tian et al. (2004): Higher tonal ID accuracy with 4 samples/tone than 1 sample/10 ms (Mandarin) Hypothesis: Good tonal category separability can be maintained under coarse temporal sampling of phonetic parameters. Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 42
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Human perception experiment Stimuli: Cantonese tritones, < waiĂ£, {wai Ă £, Ę£, Ă £, Ą£, Ę£, Ă£}, matĂ£ > from 5 speakers (3M, 2F) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 43
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Human perception experiment Stimuli: Cantonese tritones, < waiĂ£, {wai Ă £, Ę£, Ă £, Ą£, Ę£, Ă£}, matĂ£ > from 5 speakers (3M, 2F) Methodological inspiration: Multiple phoneme restoration in interrupted speech (Warren 1970) Manipulated variable: sampling resolution (2, 3, 5, 7 samples/syllable, intact) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 43
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Human perception experiment Stimuli: Cantonese tritones, < waiĂ£, {wai Ă £, Ę£, Ă £, Ą£, Ę£, Ă£}, matĂ£ > from 5 speakers (3M, 2F) Methodological inspiration: Multiple phoneme restoration in interrupted speech (Warren 1970) Manipulated variable: sampling resolution (2, 3, 5, 7 samples/syllable, intact) Task: 6-alternative forced choice orthographic identification of second tone in tritone Participants: 39 native Cantonese speakers, tested in Hong Kong and Los Angeles Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 43
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Stimuli example: waveform/spectrogram [Intact tritone] Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 44
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Stimuli example: waveform/spectrogram [7 samples per syllable] Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 45
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Stimuli example: waveform/spectrogram [5 samples per syllable] Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 46
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Stimuli example: waveform/spectrogram [3 samples per syllable] Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 47
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Stimuli example: waveform/spectrogram [2 samples per syllable] Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 48
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Tonal ID accuracy maintained with coarse resolution Tonal ID accuracy well above chance even down to 2 samples/syllable! Resolution Percent of correct responses 0 10 20 30 40 50 60 70 samp2 samp3 samp5 samp7 intact Resolution Percent correct samp2 52.54 (2.41) samp3 60.51 (2.76) samp5 64.13 (2.83) samp7 66.38 (2.91) intact 67.46 (2.90) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 49
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Tonal ID accuracy maintained with coarse resolution Tonal ID accuracy well above chance even down to 2 samples/syllable! Resolution Percent of correct responses 0 10 20 30 40 50 60 70 samp2 samp3 samp5 samp7 intact Resolution Percent correct samp2 52.54 (2.41) samp3 60.51 (2.76) samp5 64.13 (2.83) samp7 66.38 (2.91) intact 67.46 (2.90) SVM classification accuracy ≈75% for all conditions Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 49
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Tonal ID accuracy maintained with coarse resolution Tonal ID accuracy well above chance even down to 2 samples/syllable! Resolution Percent of correct responses 0 10 20 30 40 50 60 70 samp2 samp3 samp5 samp7 intact Resolution Percent correct samp2 52.54 (2.41) samp3 60.51 (2.76) samp5 64.13 (2.83) samp7 66.38 (2.91) intact 67.46 (2.90) SVM classification accuracy ≈75% for all conditions Accuracy with as few as 6 real values not statistically different from accuracy with 69 Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 49
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Cross-linguistic computational modeling for sampling resolution example: Bole, log f0 values Linear discriminant 1, 2 f0 samples Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 −2 0 2 4 tone H L 2 log f0 values Linear discriminant 1, 3 f0 samples Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 −2 0 2 4 tone H L 3 log f0 values Linear discriminant 1, 10 f0 samples Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 −2 0 2 4 tone H L 10 log f0 values Little difference in overlap between H/L from 2 to 10 f0 samples Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 50
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Local summary: temporal resolution Cantonese listeners maintain tonal ID accuracy under low temporal resolution Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 51
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Local summary: temporal resolution Cantonese listeners maintain tonal ID accuracy under low temporal resolution Computational modeling shows that this result can be understood given only a minimal acoustic parameterization of the speech signal Result also holds for computational modeling in other languages studied Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 51
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Local summary: temporal resolution Cantonese listeners maintain tonal ID accuracy under low temporal resolution Computational modeling shows that this result can be understood given only a minimal acoustic parameterization of the speech signal Result also holds for computational modeling in other languages studied What about vowels and consonants? Vowels similar situation to tones (Strange et al. 1983, Nearey and Assmann 1986, Liberman p.c.); “landmarks” for consonants (Stevens 2002) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 51
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Local summary: temporal resolution Cantonese listeners maintain tonal ID accuracy under low temporal resolution Computational modeling shows that this result can be understood given only a minimal acoustic parameterization of the speech signal Result also holds for computational modeling in other languages studied What about vowels and consonants? Vowels similar situation to tones (Strange et al. 1983, Nearey and Assmann 1986, Liberman p.c.); “landmarks” for consonants (Stevens 2002) Hypothesis: there is structure in the class of phonological maps in natural language Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 51
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Local summary What have we learned about the learner’s predicament so far? Temporal domain beyond associated syllable is a source of some dimensionality No simple invariant f0 parameter set: just f0 or just f0 velocity Learner must consider both information from the speech signal and top down information Learner must consider other voice quality parameters than just idealized f0 values in a wide range of tone languages Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 52
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Local summary What have we learned about the learner’s predicament so far? Temporal domain beyond associated syllable is a source of some dimensionality No simple invariant f0 parameter set: just f0 or just f0 velocity Learner must consider both information from the speech signal and top down information Learner must consider other voice quality parameters than just idealized f0 values in a wide range of tone languages Sufficiency of coarse temporal resolution hints at structure in tonal maps Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 52
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Local summary What have we learned about the learner’s predicament so far? Temporal domain beyond associated syllable is a source of some dimensionality No simple invariant f0 parameter set: just f0 or just f0 velocity Learner must consider both information from the speech signal and top down information Learner must consider other voice quality parameters than just idealized f0 values in a wide range of tone languages Sufficiency of coarse temporal resolution hints at structure in tonal maps Learner must consider both information from the speech signal and top down information (Lin 2005, Feldman et al. 2009, Yeung and Werker 2009) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 52
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Studying learnability to inform studying learning {Phonetic data} Learner − − − − → {Tonal maps} Understanding how the hypothesis space is structured helps us understand how the learner might proceed Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 53
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Computational simulations of learning: distributional learning Studies of phonological category learning use Gaussian mixture models Figure: Demonstration of distributional learning in infants (Maye et al. 2002) Figure: Some mixtures of two Gaussians (Kalai et al. 2010) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 54
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Computational simulation of learning: example −3 −2 −1 0 1 2 3 4 −3 −2 −1 0 1 2 3 LD1 LD1 Classification Figure: The target: Bole H and L tones from a single speaker in f0 and f0 velocity space Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 55
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Computational simulation of learning: example −3 −2 −1 0 1 2 3 4 −3 −2 −1 0 1 2 3 LD1 LD1 Classification Figure: The target: Bole H and L tones from a single speaker in f0 and f0 velocity space −3 −2 −1 0 1 2 3 4 −3 −2 −1 0 1 2 3 LD1 LD1 Classification Figure: Gaussian mixture clustering solution: WRONG! Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 55
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Computational simulation of learning: what went wrong? What can we learn from the failure of the learner? Is that space a cognitively motivated space? Are we missing relevant dimensions? Is the learning algorithm exploiting structure in the hypothesis space? Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 56
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Conclusions Assertions: There is structure in the potentially high-dimensional definition of phonological maps Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 57
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Conclusions Assertions: There is structure in the potentially high-dimensional definition of phonological maps To study phonological category learning, we need to understand how the hypothesis space is structured The structure provides inductive biases for the learner Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 57
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Conclusions Assertions: There is structure in the potentially high-dimensional definition of phonological maps To study phonological category learning, we need to understand how the hypothesis space is structured The structure provides inductive biases for the learner To characterize structure in the hypothesis space, we need to understand what phonetic parameters are involved Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 57
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Conclusions What have we learned so far about tonal maps? Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 57
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Conclusions What have we learned so far about tonal maps? Temporal window for phonetic parameters larger than associated syllable Both f0 and f0 change values may contribute in parameterization of f0-based information Phonetic space includes voice quality parameters beyond f0 values Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 57
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Conclusions What have we learned so far about tonal maps? Temporal window for phonetic parameters larger than associated syllable Both f0 and f0 change values may contribute in parameterization of f0-based information Phonetic space includes voice quality parameters beyond f0 values Sufficiency of coarse temporal resolution is consistent with structure in tonal maps Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 57
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Conclusions What have we learned so far about tonal maps? Temporal window for phonetic parameters larger than associated syllable Both f0 and f0 change values may contribute in parameterization of f0-based information Phonetic space includes voice quality parameters beyond f0 values Sufficiency of coarse temporal resolution is consistent with structure in tonal maps Studied tonal maps appear to have nearly linearly separable concepts Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 57
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Conclusions The future: structure in the hypothesis space Separability: how well separated? linearly separable? Shapes: connected? convex? ellipses? Distributions: simple Gaussian mixtures? With an understanding of structure in the hypothesis space, we can build a cognitively motivated model of phonological category acquisition Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 57
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Acknowledgments For help with recordings, linguistic consultation: Alhaji Maina Gimba and Russell Schuh (Bole) Jianjing Kuang (Beijing Mandarin) Cindy Chan, Vincie Ho, Hiu Wai Lam, Shing Yin Li, Cedric Loke (Cantonese) Chou Khang and Phong Yang, CSU Fresno Department of Linguistics (Hmong) For help with perception experiments, data processing: Hiu Wai Lam, Prairie Lam; Cindy Chan, Samantha Chan, Chris Fung, Shing Yin Li, Cedric Loke, Antonio Sou, Grace Tsai, Joanna Wang For invaluable discussion: Edward Stabler and Megha Sundara; Abeer Alwan, Robert Daland, Bruce Hayes, Sun-Ah Jun, Patricia Keating, John Kingston, Jody Kreiman, Mark Liberman, Russell Schuh, Colin Wilson, and Kie Zuraw; U. Maryland PFNA group This work was supported by a NSF graduate fellowship, NSF grant BCS-0720304, and a UCLA Linguistics Department Ladefoged scholarship and Summer Graduate Research Fellowship Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 58
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Creaky voice in Cantonese tonal perception Experiment 1 (Lam and Yu 2010) Stimuli: Minimal tone set on monosyllable, extracted from connected speech (4M/4F) Manipulated variable: presence of creak in Ą£ (T4) Task: 6-alternative forced choice orthographic lexical identification Participants: 16 native Cantonese speakers, tested in Los Angeles Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 59
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Creaky voice in Cantonese tonal perception Experiment 1 (Lam and Yu 2010) Stimuli: Minimal tone set on monosyllable, extracted from connected speech (4M/4F) Manipulated variable: presence of creak in Ą£ (T4) Task: 6-alternative forced choice orthographic lexical identification Participants: 16 native Cantonese speakers, tested in Los Angeles Experiment 2 (Yu and Lam 2011) Stimuli: Mono/bisyllables, extracted from connected speech: minimal pair (in Ą£ (T4), Ă£), (1M/1F) Methodological inspiration: Contextual normalization of f0 (Wong and Diehl 2002) Manipulated variable: presence of creak, f0 shift (8 steps on first syllable in bisyllable) Task: 2-alternative forced choice orthographic lexical identification Participants: 20 native Cantonese speakers, tested in Hong Kong Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 59
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Experimental results: the role of creaky voice in Cantonese tonal perception Presence of creak Percent of correct responses for T4 0 20 40 60 80 100 83.11 (2.25) 58.98 (3.57) creak no Exp 1: Increase in ID accuracy of T4 f0 shift (semitones) Proportion of T4 responses 0.2 0.4 0.6 0.8 q q q q q q q q q q q q q q q q −1 0 1 2 Voice quality q modal q creaky Exp 2: Bias for T4 Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 60
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Difficult to abstract away from phonation in studying tone Since we knew we would have to exclude any Tone 3 productions which had creaky voice, we obtained twice as many Tone 3 syllables as the others. (Whalen and Xu 1992) Creaky voice is prevalent in Mandarin , Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 61
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Difficult to abstract away from phonation in studying tone Since we knew we would have to exclude any Tone 3 productions which had creaky voice, we obtained twice as many Tone 3 syllables as the others. (Whalen and Xu 1992) Creaky voice is prevalent in Mandarin , Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 61
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Confusion matrix for temporal resolution experiment (human perception) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 62
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Confusion matrix for phonetic context experiment (human perception) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 63
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Vapnik-Chervonenkis dimension: definition by example — rays in R rθ x θ rθ = {x ∈ R|θ ≤ x} rθ = 1 if θ ≤ x 0 otherwise r∞ = {} ∀x ∈ R (empty ray) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 64
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Vapnik-Chervonenkis dimension: definition by example — rays in R Given sample S ⊆ R, class of tonal maps T if {S ∩ T|T ∈ T } = ℘(S), then S is shattered by T Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 64
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Vapnik-Chervonenkis dimension: definition by example — rays in R Given sample S ⊆ R, class of tonal maps T if {S ∩ T|T ∈ T } = ℘(S), then S is shattered by T rθ x Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 64
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Vapnik-Chervonenkis dimension: definition by example — rays in R Given sample S ⊆ R, class of tonal maps T if {S ∩ T|T ∈ T } = ℘(S), then S is shattered by T x −4 −3 −2 −1 0 1 2 3 4 S |S| ℘(S) T for T ∩ S Shattered? {} 0 {} r∞ Yes Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 64
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Vapnik-Chervonenkis dimension: definition by example — rays in R Given sample S ⊆ R, class of tonal maps T if {S ∩ T|T ∈ T } = ℘(S), then S is shattered by T x −4 −3 −2 −1 0 1 2 3 4 S |S| ℘(S) T for T ∩ S Shattered? {} 0 {} r∞ Yes {1} 1 {}, {1} r∞, rθ≤1 Yes Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 64
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Vapnik-Chervonenkis dimension: definition by example — rays in R Given sample S ⊆ R, class of tonal maps T if {S ∩ T|T ∈ T } = ℘(S), then S is shattered by T r1 x −4 −3 −2 −1 0 1 2 3 4 S |S| ℘(S) T for T ∩ S Shattered? {} 0 {} r∞ Yes {1} 1 {}, {1} r∞, rθ≤1 Yes Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 64
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Vapnik-Chervonenkis dimension: definition by example — rays in R Given sample S ⊆ R, class of tonal maps T if {S ∩ T|T ∈ T } = ℘(S), then S is shattered by T r1 x −4 −3 −2 −1 0 1 2 3 4 S |S| ℘(S) T for T ∩ S Shattered? {} 0 {} r∞ Yes {1} 1 {}, {1} r∞, rθ≤1 Yes {0, 1} 2 {}, {1} r∞, rθ≤1 Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 64
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Vapnik-Chervonenkis dimension: definition by example — rays in R Given sample S ⊆ R, class of tonal maps T if {S ∩ T|T ∈ T } = ℘(S), then S is shattered by T r0 x −4 −3 −2 −1 0 1 2 3 4 S |S| ℘(S) T for T ∩ S Shattered? {} 0 {} r∞ Yes {1} 1 {}, {1} r∞, rθ≤1 Yes {0, 1} 2 {}, {1} r∞, rθ≤1 {0, 1} rθ≤0 Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 64
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Vapnik-Chervonenkis dimension: definition by example — rays in R Given sample S ⊆ R, class of tonal maps T if {S ∩ T|T ∈ T } = ℘(S), then S is shattered by T r1 x −4 −3 −2 −1 0 1 2 3 4 S |S| ℘(S) T for T ∩ S Shattered? {} 0 {} r∞ Yes {1} 1 {}, {1} r∞, rθ≤1 Yes {0, 1} 2 {}, {1} r∞, rθ≤1 {0, 1} rθ≤0 {0} ?? No! Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 64
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Vapnik-Chervonenkis dimension: definition by example — rays in R Given sample S ⊆ R, class of tonal maps T if {S ∩ T|T ∈ T } = ℘(S), then S is shattered by T r0 x −4 −3 −2 −1 0 1 2 3 4 S |S| ℘(S) T for T ∩ S Shattered? {} 0 {} r∞ Yes {1} 1 {}, {1} r∞, rθ≤1 Yes {0, 1} 2 {}, {1} r∞, rθ≤1 {0, 1} rθ≤0 {0} ?? No! Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 64
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Vapnik-Chervonenkis dimension: definition by example — rays in R Given sample S ⊆ R, class of tonal maps T if {S ∩ T|T ∈ T } = ℘(S), then S is shattered by T V C(T ) = max{|S| : S is shattered by T } = 1 Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 64
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space Vapnik-Chervonenkis dimension: definition by example — rays in R Given sample S ⊆ R, class of tonal maps T if {S ∩ T|T ∈ T } = ℘(S), then S is shattered by T What if T consisted of the union of a finite number of intervals on R? [0,1] [-4,-1] x −4 −3 −2 −1 0 1 2 3 4 V C(T ) = max{|S| : S is shattered by T } infinite Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 64
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space VC dimension and feasible learnability Finite VC dimension is a criterion for feasible learnability Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 65
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space VC dimension and feasible learnability Finite VC dimension is a criterion for feasible learnability VC dim of ellipsoids in Rd : (d2 + 3d)/2 (Akama et al. 2011) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 65
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space VC dimension and feasible learnability Finite VC dimension is a criterion for feasible learnability VC dim of ellipsoids in Rd : (d2 + 3d)/2 (Akama et al. 2011) VC dim of arbitrary convex polygons in Rd ∀d is infinite (Blumer et al. 1989) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 65
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space VC dimension and feasible learnability Finite VC dimension is a criterion for feasible learnability VC dim of ellipsoids in Rd : (d2 + 3d)/2 (Akama et al. 2011) VC dim of arbitrary convex polygons in Rd ∀d is infinite (Blumer et al. 1989) VC dimension is applicable to real and discrete spaces Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 65
Is onset/offset f0 sufficient for defining tonal spaces? Structure in the hypothesis space VC dimension and feasible learnability Finite VC dimension is a criterion for feasible learnability VC dim of ellipsoids in Rd : (d2 + 3d)/2 (Akama et al. 2011) VC dim of arbitrary convex polygons in Rd ∀d is infinite (Blumer et al. 1989) VC dimension is applicable to real and discrete spaces VC dimension of constraint ranking/weighting hypothesis spaces for OT and HG is finite (Riggle 2009, Bane et al. 2010) Kristine M. Yu UMD College Park, UMASS Amherst Learnability of tones from the speech signal 65
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