1CS 188: Artificial IntelligenceFall 2010Lecture 21: Speech / ML11/9/2010Dan Klein – UC BerkeleyAnnouncements Assignments: Project 2: In glookup Project 4: Due 11/17 Written 3: Out later this week Contest out now! Reminder: surveys (results next lecture)22Contest!3Today HMMs: Most likely explanation queries Speech recognition A massive HMM! Details of this section not required Start machine learning43Speech 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:XX2E1X1X3X4E2E3E4E64State 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 graphsunrainsunrainsunrainsunrain7Viterbi Algorithmsunrainsunrainsunrainsunrain85Digitizing 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:106 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 Analysis11Part of [ae] from “lab” Complex wave repeating nine times Plus smaller wave that repeats 4x for every large cycle Large wave: freq of 250 Hz (9 times in .036 seconds) Small wave roughly 4 times this, or roughly 1000 Hz12[ demo ]7Acoustic 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<<<..13State 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 X148HMMs for Speech15Transitions with BigramsFigure from Huang et al page 618198015222 the first194623024 the same168504105 the following158562063 the world<14112454 the door-----------------23135851162 the *Training Counts9Decoding 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 words17End of Part II! Now we’re done with our unit on probabilistic reasoning Last part of class: machine learning1810Machine Learning Up until now: how to reason in a model and how to make optimal decisions Machine learning: how to acquire a model on the basis of data / experience Learning parameters (e.g. probabilities) Learning structure (e.g. BN graphs) Learning hidden concepts (e.g. clustering)Parameter Estimation Estimating the distribution of a random variable Elicitation: ask a human (why is this hard?) Empirically: use training data (learning!) E.g.: for each outcome x, look at the empirical rate of that value: This is the estimate that maximizes the likelihood of the datar g gr g gr ggrggr ggrgg11Estimation: 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 T12Estimation: 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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