Learning Phonetic Categories by Learning a Lexicon¶

語彙の学習による音声学的カテゴリの学習

Naomi H. Feldman (naomi feldman@brown.edu)
- Department of Cognitive and Linguistic Sciences, Brown University, Providence, RI 02912 USA
Thomas L. Griffiths (tom griffiths@berkeley.edu)
- Department of Psychology, University of California at Berkeley, Berkeley, CA 94720 USA
James L. Morgan (james morgan@brown.edu)
- Department of Cognitive and Linguistic Sciences, Brown University, Providence, RI 02912 USA

注釈

この文章は菊池ゼミ院生ミーティング用に表題の論文を翻訳したものです.

この研究は私の研究と同じような参考文献を使用しており,かつ,方法論が似ていて, 音素の獲得に,ある程度,語彙的なものを導入するとhappyであるということを主張しています.

この論文の具体的なテーマと私のテーマの相違点は, 私の研究テーマが持続時間的な音素対立を扱っている点(ただし,この点に関しては表題の論文でもVOIを使用しているので,一部かぶります)と, 出現頻度の差による学習の困難さを問題意識にしている点です. この2つに関しては表題の論文では直接問題にはしていません.

音素の獲得という大枠で見た場合の,この論文の私の研究に対する優位点は,学習モデルとしてノンパラメトリックなモデルを使用している点です.

一方,この論文では,上位知識として単語(より精確に言えば,ある単語がどの音素を含んているのかの情報)を使用しており, この実装上,ある言語において音素がいくつであるのかを限定的にしている点があります. 私のモデルの場合,クラスタ数の推定を目的としており,具体的にどの音素を発話したか(弁別の問題ですね)より,基礎的な学習を行えているはずです.

そのため.基本的にはこの論文の優位点を私の研究にも応用できればよい(新規性が生まれる)わけで,私としての問題意識は,具体的にどのようなアルゴリズムのモデルであるのかを理解すること,その際のモデルの解釈方法を参考に(できれば)することの二点です.

それとメタ的な話として,同じ畑の参考文献を引いているので,私の研究の背景を英語で書く場合,どのように書けばよいのかの参考にしたいと思います.

Abstract¶

乳児は母国語の音声学的なカテゴリを学習するのと同時期に,流暢な発話から単語のセグメントを学習している. しかし,音声学的なカテゴリの獲得の説明は典型的に音声の中に現れる単語についての情報を無視してきた. 我々は,ベイジアンモデルを使用して,単語のセグメントから,どの程度のフィードバックが音声学的なカテゴリ学習に制約を加え, 学習者が音声学的カテゴリのオーバーラップを明確にするを手助けするのかを例に示す. シミュレーションは人工的なレキシコン由来の情報は英語の母音カテゴリを上手に明確にすることが可能であることを示し, 分布の情報のみの場合と比べ,より頑健なカテゴリ学習を行った.

Infants learn to segment words from fluent speech during the same period as they learn native language phonetic categories, yet accounts of phonetic category acquisition typically ignore information about the words in which speech sounds appear. We use a Bayesian model to illustrate how feedback from segmented words might constrain phonetic category learning, helping a learner disambiguate overlapping phonetic categories. Simulations show that information from an artificial lexicon can successfully disambiguate English vowel categories, leading to more robust category learning than distributional information alone.

注釈

Keywords: language acquisition; Bayesian inference phonetic categories;

Introduction¶

彼らの母国語を学んでいる乳児は,様々なレベルで,知覚空間における音声学的カテゴリの位置や,流暢な発話から彼らは小分けにする単語の同定を含む構造体を抽出する必要がある. 乳児は最初に彼らの言語の音声学的なカテゴリを学習し,ついで,これらのカテゴリを単語のトークンを語彙的なアイテムにマッピングをするヒントに使うという,これらのステップが連続的に生じることは,しばしば暗黙的に当然のこととされている. しかし,乳児は流暢な発話から単語の区分けを,6ヶ月程度から始める(Jusczyk & Aslin, 1995; Jusczyk, Houston, & Newsome, 1999). 非母語発話の弁別は対照的に同じくらいの時期,6-12ヶ月にかけて減衰する(Werker & Tees, 1984). このことは,乳児が言語音と単語の両方をカテゴライズすることを同時に学習している場合における,従来とは異なり,潜在的に2つの学習のプロセスが相互作用する可能性のあるような学習の道筋を示唆している.

Infants learning their native language need to extract several levels of structure, including the locations of phonetic categories in perceptual space and the identities of words they segment from fluent speech. It is often implicitly assumed that these steps occur sequentially, with infants first learning about the phonetic categories in their language and subsequently using those categories to help them map word tokens onto lexical items. However, infants begin to segment words from fluent speech as early as 6 months (Bortfeld, Morgan, Golinkoff, & Rathbun, 2005) and this skill continues to develop over the next several months (Jusczyk & Aslin, 1995; Jusczyk, Houston, & Newsome, 1999). Discrimination of non-native speech sound contrasts declines during the same time period, between 6 and 12 months (Werker & Tees, 1984). This suggests an alternative learning trajectory in which infants simultaneously learn to categorize both speech sounds and words, potentially allowing the two learning processes to interact.

本稿では,我々は乳児が流暢な発話から切り分けるを単語は音声的なカテゴリの獲得のための役立つ情報源を提供することができるという仮説を検討した. 我々は,区切られた単語からの情報をフィードバックしたり音声学的的なカテゴリ学習を抑制したりできる相互作用的なシステムにおける音声学的カテゴリの学習の問題の本質を調査するためにベイジアンアプローチを使用した. 我々の相互作用的モデルは基礎的な語彙と音声学的なすべてのリストを同時に学習し,区切られたトークンの音響的な表現が同じか,違うのか(例えば, bed vs bad)を決定し,語彙的なアイテムは同じ母音を含んでいるのかいないのかを判断する(例えば,send vs act).

In this paper we explore the hypothesis that the words infants segment from fluent speech can provide a useful source of information for phonetic category acquisition. We use a Bayesian approach to explore the nature of the phonetic category learning problem in an interactive system, where information from segmented words can feed back and constrain phonetic category learning. Our interactive model learns a rudimentary lexicon and a phoneme inventory[1] simultaneously, deciding whether acoustic representations of segmented tokens correspond to the same or different lexical items (e.g. bed vs. bad) and whether lexical items contain the same or different vowels (e.g. send vs. act).

注釈

[1] We make the simplifying assumption that phonemes are equivalent to phonetic categories, and use the terms interchangeably.

[1] 我々は音素は音声的なカテゴリと同等であり,同じ意味の用語を使用するという単純化した仮説をおいています.

シミュレーションでは,セグメントされた単語からの情報を音声学的なカテゴリの獲得を制限するために使用することは,より眼瞼なカテゴリ学習を少ないデータ数からでも可能にし,特に,ある単語が特定の発話音声を含んでいるという情報を使う相互作用的な能力はオーバラップをしたカテゴリの曖昧性をなくすということを実証した.

Simulations demonstrate that using information from segmented words to constrain phonetic category acquisition allows more robust category learning from fewer data points, due to the interactive learner’s ability to use information about which words contain particular speech sounds to disambiguate overlapping categories.

本稿は次のように構成されている. 我々は,我々のモデルのための数学的なフレームワークに関する導入を行う.その後,その定性的な性質を示すためにおもちゃのシミュレーションを示す. 続いてシミュレーションは人工的な語彙からの情報は英語の母音カテゴリを関係する母音のフォルマントをはっきりさせることができることを示す. 最後に,言語獲得のための潜在的な影響について議論し,モデルの解釈を再検討し,後の研究のための方向性を示唆する.

The paper is organized as follows. We begin with an introduction to the mathematical framework for our model, then present toy simulations to demonstrate its qualitative properties. Next, simulations show that information from an artificial lexicon can disambiguate formant values associated with English vowel categories. The last section discusses potential implications for language acquisition, revisits the model’s assumptions, and suggests directions for future research.

Bayesian Model of Phonetic Category Learning¶

音声学的カテゴリの学習を扱っている最近の研究は,頻度学習の重要性に着目してきた. Maye, Werker, and Gerken (2002)は,発話に沿った音声の特別な頻度分布(バイモーダルかユニモーダルか)が, 乳児の連続体の終了点 [1] (多分,特徴量自体は連続して変化するわけだけど,そのカテゴリを知覚するための境界のこと) の弁別に影響することを発見した. つまり,乳児はバイモーダルの分布に親しんだ [2] とき, 境界の弁別がうまく行くことを示したのだ. この業績はガウス混合分布を使用した機械学習にインスパイアされたものであり,音声学的なカテゴリは音声のガウシアン分布,要は正規分布である,として,表現されていることを仮定しており, 学習者は彼らが聞いた音声の分布を最もよく再現できるガウス分布のカテゴリを発見すると仮定している. Boer and Kuhl (2003)はEMアルゴリズム(Dempster, Laird, & Rubin, 1977)をフォルマントデータから木構造の位置の学習を行うために使用している. McMurray, Aslin, and Toscano (2009) EMアルゴリズムに似た最急降下法 [3] を有声子音の閉鎖子音の学習に導入し,このアルゴリズムは母音と子音両方のデータ用に多次元に拡張された(Toscano & McMurray, 2008; Vallabha, McClelland, Pons, Werker, & Amano, 2007).

Recent research on phonetic category acquisition has focused on the importance of distributional learning. Maye, Werker, and Gerken (2002) found that the specific frequency distribution (bimodal or unimodal) of speech sounds along a continuum could affect infants’ discrimination of the continuum endpoints, with infants showing better discrimination of the endpoints when familiarized with the bimodal distribution. This work has inspired computational models that use a Mixture of Gaussians approach, assuming that phonetic categories are represented as Gaussian, or normal, distributions of speech sounds and that learners find the set of Gaussian categories that best represents the distribution of speech sounds they hear. Boer and Kuhl (2003) used the Expectation Maximization (EM) algorithm (Dempster, Laird, & Rubin, 1977) to learn the locations of three such vowel categories from formant data. McMurray, Aslin, and Toscano (2009) introduced a gradient descent algorithm similar to EM to learn a stop consonant voicing contrast, and this algorithm has been extended to multiple dimensions for both consonant and vowel data (Toscano & McMurray, 2008; Vallabha, McClelland, Pons, Werker, & Amano, 2007).

我々のモデルはガウス混合アプローチを上記の先行モデルを採用したが,ノンパラメトリックなベイジアンのフレームワークを使用した. このフレームワークはモデルを単語レベルまで拡張し,構造体の複数のレベルを操作する際に,学習結果を調査することを可能にする. 先行モデルのように,我々のモデルにおける発話音声は安定状態のフォルマントやVOTなどの音声学的次元を使って再現された. 単語は音声学的な値 [4] の連続体で,そこは,それぞれの音素の音声学的な値の一つの非連続体のセット(例えば第一,第二フォルマント)と一致する場所である. Toy corpusの一つのフラグメント [5] を図1に示す. 発話音声を使用した音声学的な一覧 [6] は4つのカテゴリを持っており,A,B,C,Dというラベルが振られている. つまり,5つの単語が示されており,それぞれ,ADA,AB,D,AB,DCという語彙的な要素を表現している. 学習は,発話音声を使用したものと,相互作用的学習者の場合は,単語において,他の音のどれが現れるのかについての情報を含んでおり,コーパスを発生させた音声学的カテゴリを復元することが目的である.

Our model adopts the Mixture of Gaussians approach from these previous models but uses a non-parametric Bayesian framework that allows extension of the model to the word level, making it possible to investigate the learning outcome when multiple levels of structure interact. As in previous models, speech sounds in our model are represented using phonetic dimensions such as steady-state formant values or voice onset time. Words are sequences of these phonetic values, where each phoneme corresponds to a single discrete set (e.g. first and second formant) of phonetic values. A sample fragment of a toy corpus is shown in Figure 1. The phoneme inventory has four categories, labeled A, B, C, and D; five words are shown, representing lexical items ADA, AB, D, AB, and DC, respectively. Learning involves using the speech sounds and, in the case of an interactive learner, information about which other sounds appear with them in words, to recover the phonetic categories that generated the corpus.

注釈

図1の説明

アスタリスクは発話音声を表しており,ラインは単語の境界を示している. モデルはどのカテゴリが発話音声を発生させたのかは知らなく,データからA,B,C,Dのカテゴリを復元する必要がある.

Asterisks represent speech sounds, and lines represent word boundaries. The model does not know which categories generated the speech sounds, and needs to recover categories A, B, C, and D from the data.

シミュレーションでは2つのモデルを比較した. これらは,学習者に割り当てる仮説空間が異なる. 分布モデルでは,学習者の仮説空間は音素一覧に含まれており,そこは,音声学的空間における発話音声のガウス分布が音素と一致する. 語彙-分布モデルでは,学習者は上記と同じ音素一覧を考えるが,それらの音素一覧は音素の連続体からなる語彙的な要素を含む目録とのみ結合すると考える. そのため,語彙-分布モデル学習者は,音声学的カテゴリのセットの復元に音声学的情報のみでなく,それらの音を含む単語についての情報も使用できる.

Simulations compare two models that differ in the hypothesis space they assign to the learner. In the distributional model, the learner’s hypothesis space contains phoneme inventories, where phonemes correspond to Gaussian distributions of speech sounds in phonetic space. In the lexical-distributional model, the learner considers these same phoneme inventories, but considers them only in conjunction with lexicons that contain lexical items composed of sequences of phonemes. This allows the lexical-distributional learner to use not only phonetic information, but also information about the words that contain those sounds, in recovering a set of phonetic categories.

訳者注

[1]	多分,特徴量自体は連続して変化するわけだけど,そのカテゴリを知覚するための境界のこと

[2]	訓練されたくらいかな

[3]	でいいと思う.wikipediaには”For the analytical method called “steepest descent”, see Method of steepest descent”って書いてあるし

[4]	多分,特徴量自身のことじゃないかな.

[5]	一つの発話区間のことかと.

[6]	獲得したい音素の目録のことだと思う.

Distributional Model¶

分布モデルにおいては,学習者は我々が,音素イベントCと呼ぶ音韻のセットをコーパスの音声から復元する必要がある [7] . このモデルは単語,単語境界に関するすべての情報を無視し,音韻空間の発話音声の分布からのみ学習を行う. 発話音声は音韻イベントリから音素カテゴリ $C$ を選択することによって生成されると仮定し, そのカテゴリに関連するガウシアン分布から,音韻の値 [#f42]_ を抽出している. カテゴリは,それらのデータの平均値 $\mu_c$ ではなく, 共分散行列 $\Sigma_c$ であり,発生頻度である. 以下の先行研究,形態論の先行研究(Goldwater, Griffiths, & Johnson, 2006),単語のセグメント(Goldwater, Griffiths, & Johnson, in press),そして文法の学習(Johnson, Griffiths, & Goldwater, 2007)では, 学習者の音素のイベントに関する事前知識はDirichlet process(Ferguson, 1973)と呼ばれるノンパラメトリックなベイズモデルを使用して実装されている. この分布は音素一覧のカテゴリ数に対するバイアス [#f43]_ と,これらのカテゴリの音響的パラメータに対するバイアスをエンコードしたものである. 音韻的カテゴリの数についての事前知識は, 学習者が潜在的に莫大な数のカテゴリ数を考慮することを可能にするが, 少ない数のカテゴリへと向かわせるバイアスを提供する.バイアスの強さについてはパラメータ $\alpha$ により制御されている. これは先行モデル(McMurray et al., 2009; Vallabha et al., 2007)で使用された, カテゴリの割り当てにおける”勝者総取りバイアス”に置き換えることができ, データを表現するのに必要なカテゴリの数の明示的な推定を可能にする.

In the distributional model, a learner is responsible for recovering a set of phonetic categories, which we refer to as a phoneme inventory $C$, from a corpus of speech sounds. The model ignores all information about words and word boundaries, and learns only from the distribution of speech sounds in phonetic space. Speech sounds are assumed to be produced by selecting a phonetic category $c$ from the phoneme inventory and then sampling a phonetic value from the Gaussian associated with that category. Categories differ in their means $\mu_c$ , covariance matrices $\Sigma_c$ , and frequencies of occurrence. Following previous work in morphology (Goldwater, Griffiths, & Johnson, 2006), word segmentation (Goldwater, Griffiths, & Johnson, in press), and grammar learning (Johnson, Griffiths, & Goldwater, 2007), learners’ prior beliefs about the phoneme inventory are encoded using a nonparametric Bayesian model called the Dirichlet process (Ferguson, 1973), $C∼DP(\alpha, G_C)$. This distribution encodes biases over the number of categories in the phoneme inventory, as well as over phonetic parameters for those categories. Prior beliefs about the number of phonetic categories allow the learner to consider a potentially infinite number of categories, but produce a bias toward fewer categories, with the strength of the bias controlled by the parameter $\alpha$.[2] This replaces the winner-take-all bias in category assignments that has been used in previous models (McMurray et al., 2009; Vallabha et al., 2007) and allows explicit inference of the number of categories needed to represent the data.

訳者注

[7]	音素イベントC : 要はある言語のある音素のこと

[8]	Phonetic value : 調べると音価(音楽においての音の長さのこと)って出てくんのよね

[9]	biases over A : A にかかってるバイアス

注釈

筆者注2

[2] This bias is needed to induce any grouping at all; the maximum likelihood solution assigns each speech sound to its own category.

このバイアスはすべてからいくつかのグループに減らすために必要なものである. 最大尤度法はそれぞれの発話音声を自身のカテゴリに割り当てる

音韻パラメータの事前分布は $G_C$ によって定義され,このモデルにおいては,カテゴリの分散 $\Sigma_c∼IW(\nu_0,\Sigma_0 )$ に対する逆ウィシャート事前分布とカテゴリの平均値 $\mu_c \mid \Sigma_c ∼ N(\mu_0 , {\Sigma_c \over \nu_0} )$ に対するガウシアン事前分布を含んでいる,ガウシアンな音韻カテゴリに対するものである. これらの分布のパラメータは擬似データの $\mu_0$ , $\Sigma_0$ , $\nu_0$ が平均,共分散及び学習者がすでに新しいカテゴリに割り当てられたと想像する音声の数をどこでエンコードするのかを考えることが可能です. この音韻パラメータに対する事前分布は論理モデルの中心ではなく,計算を簡単にするための処理である.擬似データにおける発話音声の数は可能な限り少なくしている[3]ため,事前バイアスはリアルデータによって書き換えられることになる. 音響的な値の連続値を提示することで,学習者はこれらの音響的な値から発生するガウシアンのカテゴリセットを復元することが必要である. マルコフ連鎖モンテカルロ法の形で,ギブズサンプリング (Geman & Geman, 1984) は理想的な学習者がコーパスを生成した可能性が高いと考えている音素の目録の例を復元するために使用された. 発話音声ははじめはランダムな割り当てで与えら得ており,各sweepの間で,コーパスを通じて,順番にすべての現在の割り当てに基づいた新しいカテゴリの割り当てが与えられる.

The prior distribution over phonetic parameters is defined by $G_C$ , which in this model is a distribution over Gaussian phonetic categories that includes an Inverse-Wishart prior over category variances, $\Sigma_c∼IW(\nu_0,\Sigma_0 )$, and a Gaussian prior over category means, $\mu_c \mid \Sigma_c ∼ N(\mu_0 , {\Sigma_c \over \nu_0} )$. The parameters of these distributions can be thought of as pseudo data, where $\mu_0$ , $\Sigma_0$ , and $\nu_0$ encode the mean, covariance, and number of speech sounds that the learner imagines having already assigned to any new category. This prior distribution over phonetic parameters is not central to the theoretical model, but rather is included for ease of computation; the number of speech sounds in the pseudodata is made as small as possible[3] so that the prior biases are overshadowed by real data. Presented with a sequence of acoustic values, the learner needs to recover the set of Gaussian categories that generated those acoustic values. Gibbs sampling (Geman & Geman, 1984), a form of Markov chain Monte Carlo, is used to recover examples of phoneme inventories that an ideal learner believes are likely to have generated the corpus. Speech sounds are initially given random category assignments, and in each sweep through the corpus, each speech sound in turn is given a new category assignment based on all the other current assignments. The probability of assignment to category $c$ is given by Bayes’ rule,

\[p(c \mid w_{ij} ) \propto p(w_{ij} \mid c) p(c)\]

where wi j denotes the phonetic parameters of the speech sound in position j of word i. The prior p(c) is given by the Dirichlet process and is

\[\begin{split}\cases{\frac{n_c}{\sum_c N_c + \alpha}&$for existing categories$\cr \frac{\alpha}{\sum_c N_c + \alpha}&for a new category\cr}\end{split}\]

making it proportional to the number of speech sounds $n_c$ already assigned to that category, with some probability $\alpha$ of assignment to a new category. The likelihood $p(w_{ij} \mid c)$ is obtained by integrating over all possible means and covariance matrices for category $c$ , $\int\int p(w_{ij} \mid \mu_c , \sum_c)p(\mu_c \mid\sum_c )p(\sum_c )d\mu_c d\sum_c$ , where the probability distributions $p(\mu_c \mid\sum_c)$ and $p(\sum_c)$ are modified to take into account the speech sounds already assigned to that category.

注釈

[3] To form a proper distribution, nu 0 needs to be greater than d − 1, where d is the number of phonetic dimensions.

This likelihood function has the form of a multivariate tdistribution and is discussed in more detail in Gelman, Carlin, Stern, and Rubin (1995). Using this procedure, category assignments converge to the posterior distribution on phoneme inventories, revealing an ideal learner’s beliefs about which categories generated the corpus.

Lexical-Distributional Model¶

This non-parametric Bayesian framework has the advantage that it is straightforward to extend to hierarchical structures (Teh, Jordan, Beal, & Blei, 2006), allowing us to explore the influence of words on phonetic category acquisition. In the lexical-distributional model, the learner recovers not only the same phoneme inventory C as in the distributional model, but also a lexicon L with lexical items composed of sequences of phonemes. This creates an extra step in the generative process: instead of assuming that the phoneme inventory generates a corpus directly, as in the distributional model, this model assumes that the phoneme inventory generates the lexicon and that the lexicon generates the corpus. The corpus is generated by selecting a lexical item to produce and then sampling an acoustic value from each of the phonetic categories contained in that lexical item.

The prior probability distribution over possible lexicons is a second Dirichlet process, L ∼ DP(β, GL ) where GL defines a prior distribution over lexical items. This prior favors shorter lexical items, assuming word lengths to be generated from a geometric distribution, and assumes that a category for each phoneme slot has been sampled from the phoneme inventory C. Thus, the prior probability distribution over words is defined according to the phoneme inventory, and the learner needs to optimize the phoneme inventory so that it generates the lexicon. Parallel to the bias toward fewer phonetic categories, the model encodes a bias toward fewer lexical items but allows a potentially infinite number of lexical items.

Presented with a corpus consisting of isolated word tokens, each of which consists of a sequence of acoustic values, the language learner needs to recover the lexicon and phoneme inventory of the language that generated the corpus. Learning is again performed through Gibbs sampling. Each iteration now includes two sweeps: one through the corpus, assigning each word to the lexical item that generated it, and one through the lexicon, assigning each position of each lexical item to its corresponding phoneme from the phoneme inventory. In the first sweep we use Bayes’ rule to calculate the probability that word wi corresponds to lexical item k,

p(k|wi ) proptop(wi midk)p(k) (3)

Parallel to Equation 2, the prior is

nk / ∑ k_n_k +β for existing categories

p(k) = (4): β / ∑ k_n_k +β for a new category

where nk is the number of word tokens already assigned to lexical item k. A word is therefore assigned to a lexical item with a probability proportional to the number of times that lexical item has already been seen, with some probability β reserved for the possibility of seeing a new lexical item. The likelihood is a product of the likelihoods of each speech sound having been generated from its respective category,

p(wi midk) = ∏ p(wi j midck j ) (5): j

where j indexes a particular position in the word and ck j is the phonetic category that corresponds to position j of lexical item k. Any lexical item with a different length from the word wi is given a likelihood of zero, and samples from the prior distribution on lexical items are used to estimate the likelihood of a new lexical item (Neal, 1998). The second sweep uses Bayes’ rule

p(cmidw{k} j ) proptop(w{k} j midc)p(c) (6)

to assign a phonetic category to position j of lexical item k, where w{k} j is the set of phonetic values at position j in all of the words in the corpus that have been assigned to lexical item k. The prior p(c) is the same prior over category assignments as was used in the distributional model, and is given by Equation 2. The likelihood p(w{k} j midc) is again computed by integrating over all possible means and covariance maRR trices, FF ∏ wi ∈ k p(wi j midmuc , Sigma c )p(muc midSigma c )p(Sigma c )dmuc dSigma c , this time taking into account phonetic values from all the words assigned to lexical item k. The sampling procedure converges on samples from the joint posterior distribution on lexicons and phoneme inventories, allowing learners to recover both levels of structure simultaneously.

Qualitative Behavior of an Interactive Learner¶

このセクションでは,Toy simulation [10] がどの語彙が提供するのか

In this section, toy simulations demonstrate how a lexicon can provide disambiguating information about overlapping categories that would be interpreted as a single category by a purely distributional learner. We show that it is not the simple presence of a lexicon, but rather specific disambiguating information within the lexicon, that increases the robustness of category learning in the lexical-distributional learner. Corpora were constructed for these simulations using four categories labeled A, B, C, and D, whose means are located at -5, -1, 1, and 5 along an arbitrary phonetic dimension (Figure 2 (a)). All four categories have a variance of 1. Because the means of categories B and C are so close together, being separated by only two standard deviations, the overall distribution of tokens in these two categories is unimodal. To test the distributional learner, 1200 acoustic values were sampled from these categories, with 400 acoustic values sampled from each of Categories A and D and 200 acoustic values sampled from each of Categories B and C. Results indicate that these distributional data are not strong enough to disambiguate categories B and C, leading the learner to interpret them as a single category (Figure 2 (b)).[4] While this may be due in part to the distributional learner’s prior bias toward fewer categories, simulations in the next section will show that the gradient descent learner from Vallabha et al. (2007), which has no such explicit bias, shows similar behavior.

訳者注

[10]	Toy simulation : 多分,この文章でいうtoyはダミーということじゃないかな.

[11]	Phonetic value : 調べると音価(音楽においての音の長さのこと)って出てくんのよね

[12]	biases over A : A にかかってるバイアス

注釈

[4] Simulations in this section used parameters alpha = β = 1, mu = 0, 0 Sigma 0 = 1, and nu 0 = 0.001; each simulation was run for 500 iterations.

注釈

Figure 2: Toy data with two overlapping categories as (a) generated, (b) learned by the distributional model, (c) learned by the lexical-distributional model from a minimal pair corpus, and (d) learned by the lexical-distributional model from a corpus without minimal pairs.

Two toy corpora were constructed for the lexicaldistributional model from the 1200 phonetic values sampled above. The corpora differed from each other only in the distribution of these values across lexical items. The lexicon of the first corpus contained no disambiguating information about speech sounds B and C. It was generated from six lexical items, with identities AB, AC, DB, DC, ADA, and D. Each lexical item was repeated 100 times in the corpus for a total of 600 word tokens. In this corpus, Categories B and C appeared only in minimal pair contexts, since both AB and AC, as well as both DB and DC, were words. As shown in Figure 2 (c), the lexical-distributional learner merged categories B and C when trained on this corpus. Merging the two categories allowed the learner to condense AB and AC into a single lexical item, and the same happened for DB and DC. Because the distribution of these speech sounds in lexical items was identical, lexical information could not help disambiguate the categories.

The second corpus contained disambiguating information about categories B and C. This corpus was identical to the first except that the acoustic values representing the phonemes B and C of words AC and DB were swapped, converting these words into AB and DC, respectively. Thus, the second corpus contained only four lexical items, AB, DC, ADA, and D, and there were now 200 tokens of words AB and DC. Categories B and C did not appear in minimal pair contexts, as there was a word AB but no word AC, and there was a word DC but no word DB. The lexical-distributional learner was able to use the information contained in the lexicon in the second corpus to successfully disambiguate categories B and C (Figure 2 (d)). This occurred because the learner could categorize words AB and DC as two different lexical items simply by recognizing the difference between categories A and D, and could use those lexical classifications to notice small phonetic differences between the second phonemes in these lexical items.

In this model it is non-minimal pairs, rather than minimal pairs, that help the lexical-distributional learner disambiguate phonetic categories. While minimal pairs may be useful when a learner knows that two similar sounding tokens have different referents, they pose a problem in this model because the learner hypothesizes that similar sounding tokens represent the same word. Thiessen (2007) has made a similar observation with 15-month-olds in a word learning task, showing that infants may fail to notice a difference between similarsounding object labels, but are better at discriminating these words when familiarized with non-minimal pairs that contain the same sounds.

Learning English Vowels¶

自然言語におけるカテゴリのオーバーラップの典型例は母音のカテゴリである. 例えば,Hillenbrand, Getty, Clark, and Wheeler (1995)らは英語の母音に関して図4(a)を示している. したがって我々は英語の母音カテゴリを語彙的な分布学習者の実際の音韻カテゴリパラメータを基本にしたオーヴァラップをカテゴリの曖昧さをなくす能力をテストするために英語の母音を使用した.

The prototypical examples of overlapping categories in natural language are vowel categories, such as the English vowel categories from Hillenbrand, Getty, Clark, and Wheeler (1995) shown in Figure 4 (a).[5] We therefore use English vowel categories to test the lexical-distributional learner’s ability to disambiguate overlapping categories that are based on actual phonetic category parameters.

Hillenbrand et al. (1995)の母音フォルマントデータを基本にした音韻カテゴリを使用して2つのコーパスを作成した. 最初のコーパスのカテゴリは男性によって発話された母音をベースにしており,適度なオーバーラップしかない(図3 (a)). 2つ目のコーパスのカテゴリは男性,女性,子供によって発話された母音をベースにしており,オーバーラップの程度が大きい(図4 (a)). どちらのケースでも,12音素のカテゴリの平均と共分散行列は対応する母音トークンから算出した. それぞれのコーパスのために発生モデルを使用して,母音のみからなる語彙項目の仮想的な集合を作成し,トークンをガウスカテゴリパラメータの適当なセットから,この語彙をベースに5000語のトークンを作成した.

Two corpora were constructed using phonetic categories based on the Hillenbrand et al. (1995) vowel formant data. Categories in the first corpus were based on vowels spoken by men, and had only moderate overlap (Figure 3 (a)); categories in the second corpus were based on vowels spoken by men, women, and children, and had a much higher degree of overlap (Figure 4 (a)). In each case, means and covariance matrices for the twelve phonetic categories were computed from corresponding vowel tokens. Using the generative model, a hypothetical set of lexical items consisting only of vowels was generated for each corpus, and 5,000 word tokens were generated based on this lexicon from the appropriate set of Gaussian category parameters.

これらのコーパスは以下の3つのモデルにテストデータとして与えられた.

語彙-分布モデル
分布モデル
Vallabha et al.(2007)で使用された多次元勾配降下アルゴリズム[6]

男性発話をベースにしたコーパスを使用した結果を図3に示す. また,すべての話者の発話をベースにしたコーパスへの結果は図4である. それぞれの場合で,語彙-分布モデルは母音カテゴリのセットの復元に成功し,曖昧な近隣との境界推定に成功した. 一方,語彙がかけたモデルでは近隣の母音カテゴリのペアをいくつか誤ってマージしてしまった. そのため,語彙を仮定することは,語彙に含まれる音韻フォームが明示的に学習者に与えなくとも,学習者の母音カテゴリの重複の曖昧さをなくすことを助けることを示す証拠になる.

These corpora were given as training data to three models: the lexical-distributional model, the distributional model, and the multidimensional gradient descent algorithm used by Vallabha et al. (2007).[6] Results for the corpus based on men’s productions are shown in Figure 3, and results from the corpus based on all speakers’ productions are shown in Figure 4. In each case, the lexical-distributional learner recovered the correct set of vowel categories and successfully disambiguated neighboring categories. In contrast, the models lacking a lexicon mistakenly merged several pairs of neigh boring vowel categories. Positing the presence of a lexicon therefore showed evidence of helping the ideal learner disambiguate overlapping vowel categories, even though the phonological forms contained in the lexicon were not given explicitly to the learner.

ペアごとの正確性と完全性の対策は、モデルの性能（表1）の定量的尺度として、各学習者に対して計算された. これらの尺度では,正しく同じカテゴリーに入れた母音のトークンのペアを、ヒットとしてカウントし,同じカテゴリにされているべきときに、誤って別のカテゴリに割り当てられたトークンのペアはミスとしてカウントした. また異なるカテゴリにされているべきときに、誤って同じカテゴリに割り当てられたトークンのペアは、誤警報としてカウントした.

Pairwise accuracy and completeness measures were computed for each learner as a quantitative measure of model performance (Table 1). For these measures, pairs of vowel tokens that were correctly placed into the same category were counted as a hit; pairs of tokens that were incorrectly assigned to different categories when they should have been in the same category were counted as a miss; and pairs of tokens that were incorrectly assigned to the same category when they should have been in different categories were counted as a false alarm.

注釈

[5] These vowel data were obtained through download from http://homepages.wmich.edu/˜hillenbr/.

注釈

[6] Parameters for the Bayesian models were alpha = β = 1,

500 1 0

mu =[ ], Sigma_0 =[ ], and nu 0 = 1.001,and each simulation was run for 600 iterations.: 1500 0 1

No attempt was made to optimize these parameters, and they were actually different from the parameters used to generate the data, as alpha = β = 10 was used to help produce a corpus that contained all twelve vowel categories. Using the generating parameters during inference did not qualitatively affect the results. Parameters for the gradient descent algorithm were identical to those used by Vallabha et al. (2007); optimizing the learning rate parameter produced little qualitative change in the learning outcome.

注釈

Figure 3: Ellipses delimit the area corresponding to 90% of vowel tokens for Gaussian categories (a) computed from men’s vowel productions from Hillenbrand et al. (1995) and learned by the (b) lexical-distributional model, (c) distributional model, and (d) gradient descent algorithm.

注釈

Figure 4: Ellipses delimit the area corresponding to 90% of vowel tokens for Gaussian categories (a) computed from all speakers’ vowel productions from Hillenbrand et al. (1995) and learned by the (b) lexical-distributional model, (c) distributional model, and (d) gradient descent algorithm.

accuracyの得点は”hits/ hits + false alarms”で計算し,completenessは”hits/hits+misses”として計算した. 両方の基準で語彙-分布モデルは高い点数を出したが,誤って複数の重複するカテゴリを合併しているという事実を反映して、accuracyの得点は実質的に純粋に分布だけから学習した場合よりも低かった.

The accuracy score was computed a hits/ hits + false alarms and the completeness score as hits/hits+misses . Both measures were high for the lexical-distributional learner, but accuracy scores were substantially lower for the purely distributional learners, reflecting the fact that these models mistakenly merged several overlapping categories.

この結果は,予測されるように,音韻のカテゴリに加えて、単語のカテゴリを学習に使用するモデルは、音素のカテゴリを学習したモデルよりも優れた表音カテゴリの学習結果が得られることを示している. 分布のモデルの学習者は、ちょうど最初の2フォルマントを超え次元を与えたりしている場合(Vallabha et al., 2007)や、学習中に、より多くのデータ·ポイントを与えられている場合は,より良い性能を示す可能性があることに注目してほしい. これら2つのソリューションは確かに,お互いに対して機能する.つまり,デモンストレーションを加えるごとに,おなじ学習結果を維持するのに必要なデータ数が増えていく. しかし,我々は純粋な分布の学習モデルは音韻のカテゴリを取得できないことを示唆する気はない. ここで紹介したシミュレーションは音韻カテゴリに実質的にオーバーラップのある言語において,学習者が特定の言語音を含む単語情報を使用できるインタラクティブなシステムは,表音カテゴリ学習の頑健さを高めることができることを実証するものである.

Results suggest that as predicted, a model that uses the input to learn word categories in addition to phonetic categories produces better phonetic category learning results than a model that only learns phonetic categories. Note that the distributional learners are likely to show better performance if they are given dimensions beyond just the first two formants (Vallabha et al., 2007) or if they are given more data points during learning. These two solutions actually work against each other: as dimensions are added, more data are necessary to maintain the same learning outcome. Nevertheless, we do not wish to suggest that a purely distributional learner cannot acquire phonetic categories. The simulations presented here are instead meant to demonstrate that in a language where phonetic categories have substantial overlap, an interactive system, where learners can use information from words that contain particular speech sounds, can increase the robustness of phonetic category learning.

Discussion¶

This paper has presented a model of phonetic category acquisition that allows interaction between speech sound and word categorization. The model was not given a lexicon a priori, but was allowed to begin learning a lexicon from the data at the same time that it was learning to categorize individual speech sounds, allowing it to take into account the distribution of speech sounds in words. This lexical-distributional learner outperformed a purely distributional learner on a corpus whose categories were based on English vowel categories, showing better disambiguation of overlapping categories from the same number of data points.

Infants learn to segment words from fluent speech around the same time that they begin to show signs of acquiring native language phonetic categories, and they are able to map these segmented words onto tokens heard in isolation (Jusczyk & Aslin, 1995), suggesting that they are performing some sort of rudimentary categorization on the words they hear. Infants may therefore have access to information from words that can help them disambiguate overlapping categories. If information from words can feed back to constrain phonetic category learning, the large degree of overlap be tween phonetic categories may not be such a challenge as is often supposed.

Table1¶
LexicalDistrib.	Distrib.	Gradient	Descent
Accuracy	0.97	0.63	0.56
Completeness	0.98	0.93	0.94
Accuracy	0.99	0.54	0.40
Completeness	0.99	0.85	0.95

注釈

Table 1: Accuracy and completeness scores for learning vowel categories based on productions by (a) men and (b) all speakers. For the Bayesian learners, these were computed at the annealed solutions; for the gradient descent learner, they were based on maximum likelihood category assignments.

In generalizing these results to more realistic learning situations, however, it is important to take note of two simplifying assumptions that were present in our model. The first key assumption is that speech sounds in phonetic categories follow the same Gaussian distribution regardless of phonetic or lexical context. In actual speech data, acoustic characteristics of sounds change in a context-dependent manner due to coarticulation with neighboring sounds (e.g. Hillenbrand, Clark, & Nearey, 2001). A lexical-distributional learner hearing reliable differences between sounds in different words might erroneously assign coarticulatory variants of the same phoneme to different categories, having no other mechanism to deal with context-dependent variability. Such variability may need to be represented explicitly if an interactive learner is to categorize coarticulatory variants together.

A second assumption concerns the lexicon used in the vowel simulations, which was generated from our model. Generating a lexicon from the model ensured that the learner’s expectations about the lexicon matched the structure of the lexicon being learned, and allowed us to examine the influence of lexical information in the best case scenario. However, several aspects of the lexicon, such as the assumption that phonemes in lexical items are selected independently of their neighbors, are unrealistic for natural language. In future work we hope to extend the present results using a lexicon based on child-directed speech.

Infants learn multiple levels of linguistic structure, and it is often implicitly assumed that these levels of structure are acquired sequentially. This paper has instead investigated the optimal learning outcome in an interactive system using a non-parametric Bayesian framework that permits simultaneous learning at multiple levels. Our results demonstrate that information from words can lead to more robust learning of phonetic categories, providing one example of how such interaction between domains might help make the learning problem more tractable.

Acknowledgments.¶

This research was supported by NSF grant BCS-0631518, AFOSR grant FA9550-07-1-0351, and NIH grant HD32005. We thank Joseph Williams for help in working out the model and Sheila Blumstein, Adam Darlow, Sharon Goldwater, Mark Johnson, and members of the computational modeling reading group for helpful comments and discussion.

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