1CS 188: Artificial IntelligenceFall 2006Lecture 21: Speech / Viterbi11/09/2006Dan Klein – UC BerkeleyAnnouncements Optional midterm On Tuesday 11/21 in class Review session 11/19, 7-9pm, in 306 Soda Projects 3.2 due 11/9 3.3 due 11/15 3.4 due 11/27 Contest Pacman contest details on web site this week Entries due 12/32Hidden Markov Models Hidden Markov models (HMMs) Underlying Markov chain over states X You observe outputs (effects) E at each time step As a Bayes’ net: Several questions you can answer for HMMs: Last time: filtering to track belief about current X given evidenceX5X2E1X1X3X4E2E3E4E5Speech Recognition [demos]3Digitizing SpeechSpeech in an Hour Speech input is an acoustic wave forms p ee ch l a bGraphs from Simon Arnfield’s web tutorial on speech, Sheffield:http://www.psyc.leeds.ac.uk/research/cogn/speech/tutorial/“l” to “a”transition:4She just had a baby What can we learn from a wavefile? Vowels are voiced, long, loud Length in time = length in space in waveform picture Voicing: regular peaks in amplitude When stops closed: no peaks: silence. Peaks = voicing: .46 to .58 (vowel [i], from second .65 to .74 (vowel [4]) and so on Silence of stop closure (1.06 to 1.08 for first [b], or 1.26 to 1.28 for second [b]) Fricatives like [6] intense irregular pattern; see .33 to .46 Frequency gives pitch; amplitude gives volume sampling at ~8 kHz phone, ~16 kHz mic (kHz=1000 cycles/sec) Fourier transform of wave displayed as a spectrogram darkness indicates energy at each frequencys p ee ch l a bfrequencyamplitudeSpectral Analysis5Adding 100 Hz + 1000 Hz WavesTime (s)00.05–0.96540.990Spectrum1001000Frequency in HzAmplitudeFrequency components (100 and 1000 Hz) on x-axis6Back to Spectra Spectrum represents these freq components Computed by Fourier transform, algorithm which separates out each frequency component of wave. x-axis shows frequency, y-axis shows magnitude (in decibels, a log measure of amplitude) Peaks at 930 Hz, 1860 Hz, and 3020 Hz.Vowel Formants7Resonances of the vocal tract The human vocal tract as an open tube Air in a tube of a given length will tend to vibrate at resonance frequency of tube. Constraint: Pressure differential should be maximal at (closed) glottal end and minimal at (open) lip end.Closed endOpen endLength 17.5 cm.Figure from W. Barry Speech Science slidesFromMarkLiberman’swebsite8Why these Peaks? Articulatory facts: Vocal cord vibrations create harmonics The mouth is a selective amplifier Depending on shape of mouth, some harmonics are amplified more than othersFigures from Ratree Wayland slides from his websiteVowel [i] sung at successively higher pitch. 12345679How to read spectrograms bab: closure of lips lowers all formants: so rapid increase in all formants at beginning of "bab” dad: first formant increases, but F2 and F3 slight fall gag: F2 and F3 come together: this is a characteristic of velars. Formant transitions take longer in velars than in alveolars or labialsFrom Ladefoged “A Course in Phonetics”Acoustic Feature Sequence Time slices are translated into acoustic feature vectors (~39 real numbers per slice) These are the observations, now we need the hidden states Xfrequency……………………………………………..e12e13e14e15e16………..10State Space P(E|X) encodes which acoustic vectors are appropriate for each phoneme (each kind of sound) P(X|X’) encodes how sounds can be strung together We will have one state for each sound in each word From some state x, can only: Stay in the same state (e.g. speaking slowly) Move to the next position in the word At the end of the word, move to the start of the next word We build a little state graph for each word and chain them together to form our state space XHMMs for Speech11ASR Lexicon: Markov ModelsMarkov Process with BigramsFigure from Huang et al page 61812Decoding While there are some practical issues, finding the words given the acoustics is an HMM inference problem We want to know which state sequence x1:Tis most likely given the evidence e1:T:Viterbi Algorithm Question: what is the most likely state sequence given the observations? Slow answer: enumerate all possibilities Better answer: cached incremental version13Viterbi with 2 Words + Unif. LMFigure from Huang et al page 612Next Class Final part of the course: machine learning We’ll start talking about how to learn model parameters (like probabilities) from data One of the most heavily used technologies in all of
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