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Berkeley COMPSCI 188 - Speech Recognition

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1CS 188: Artificial IntelligenceFall 2009Lecture 21: Speech Recognition11/10/2009Dan Klein – UC BerkeleyAnnouncements Written 3 due on Thursday night Extra OHs before then: see web page Review session? TBA Project 4 up! Due 11/19 Course contest update You can qualify for the final tournament starting tonight!2Today HMMs: Most likely explanation queries Speech recognition A massive HMM! Details of this section not required Start machine learning3Speech and Language Speech technologies Automatic speech recognition (ASR) Text-to-speech synthesis (TTS) Dialog systems Language processing technologies Machine translation Information extraction Web search, question answering Text classification, spam filtering, etc…HMMs: MLE Queries HMMs defined by States X Observations E Initial distr: Transitions: Emissions: Query: most likely explanation:XX2E1X1X3X4E2E3E4E5State Path Trellis State trellis: graph of states and transitions over time Each arc represents some transition Each arc has weight Each path is a sequence of states The product of weights on a path is the seq’s probability Can think of the Forward (and now Viterbi) algorithms as computing sums of all paths (best paths) in this graphsunrainsunrainsunrainsunrain62Viterbi Algorithmsunrainsunrainsunrainsunrain7Example8Digitizing Speech9Speech 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:10 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 bSpectral Analysis11Adding 100 Hz + 1000 Hz WavesTime (s)0 0.05–0.96540.990123Spectrum1001000Frequency in HzAmplitudeFrequency components (100 and 1000 Hz) on x-axis13Part of [ae] from “lab” Note complex wave repeating nine times in figure Plus smaller waves which repeats 4 times for every large pattern Large wave has frequency of 250 Hz (9 times in .036 seconds) Small wave roughly 4 times this, or roughly 1000 Hz Two little tiny waves on top of peak of 1000 Hz waves14Back 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.15[ demo ]Resonances 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 slides16FromMarkLiberman’swebsite17[ demo ]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 X……………………………………………..e12e13e14e15e16………..184State 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 X19HMMs for Speech20Transitions with BigramsFigure from Huang et al page 61821Decoding 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: From the sequence x, we can simply read off the words22End of Part II! Now we’re done with our unit on probabilistic reasoning Last part of class: machine learning23Parameter Estimation Estimating the distribution of a random variable Elicitation: ask a human! Usually need domain experts, and sophisticated ways of eliciting probabilities (e.g. betting games) Trouble calibrating Empirically: use training data For each outcome x, look at the empirical rate of that value: This is the estimate that maximizes the likelihood of the datar g g5Estimation: Smoothing Relative frequencies are the maximum likelihood estimates In Bayesian statistics, we think of the parameters as just another random variable, with its own distribution????Estimation: Laplace Smoothing Laplace’s estimate: Pretend you saw every outcome once more than you actually did Can derive this as a MAP estimate with Dirichlet priors (see cs281a)H H TEstimation: Laplace Smoothing Laplace’s estimate (extended): Pretend you saw every outcome k extra times What’s Laplace with k = 0? k is the strength of the prior Laplace for conditionals: Smooth each condition independently:H H


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Berkeley COMPSCI 188 - Speech Recognition

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