learning bit by bit hidden markov models. weighted fsa weather the is outside 1.0.7.3
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Learning Bit by Bit
Hidden Markov Models
Weighted FSA
weatherweatherTheThe isis
outsideoutside
1.0
.7
.3
Markov Chain
• Computing probability of an observed sequence of events
Markov Chain
weatherweather
TheThe
isis
outsideoutside
.7
.3
Observation = “The weather outside”
windwind
.5
.5
.1
.9
Parts of Speech
• Grammatical constructs like noun, verb
POS examples• N noun chair, bandwidth, pacing• V verb study, debate, munch• ADJ adjective purple, tall, ridiculous• ADV adverb unfortunately, slowly• P preposition of, by, to• PRO pronoun I, me, mine• DET determiner the, a, that, those
Parts of Speech-uses
• Speech recognition• Speech synthesis• Data mining• Translation
POS Tagging
• Words often have more than one POS: back– The back door = JJ– On my back = NN– Win the voters back = RB– Promised to back the bill = VB
• The POS tagging problem is to determine the POS tag for a particular instance of a word.
POS Tagging
• Sentence = sequence of observations• Ie. “Secretariat is expected to race tomorrow”
Disambiguating “race”
Hidden Markov Model
• Observed• Hidden
Hidden Markov Model
• 2 kinds of probabilities:– Tag transitions – Word likelihoods
Hidden Markov Model
• Tag transition prob = P( tag | previous tag)– ie. P(VB | TO)
Hidden Markov Model
• Word likelihood probability = P(word | tag)– ie. P(“race” | VB)
• Actual probabilities:– P (NN | TO) = .00047– P (VB | TO) = .83
• Actual probabilities:– P (NR| VB) = .0027– P (NR| NN) = .0012
• Actual probabilities:– P (race | NN) = .00057– P (race | VB) = .00012
Hidden Markov Model
• Probability “to race tomorrow” =“TO VB NR”• P(VB|TO) * P(NR|VB) * P(race|VB)• .83 * .0027 * .00012 = 0.00000026892
Hidden Markov Model
• Probability “to race tomorrow” =“TO NN NR”• P(NN|TO) * P(NR|NN) * P(race|NN)• .00047* .0012* .00057 = 0.00000000032148
Hidden Markov Model
• Probability “to race tomorrow” =“TO NN NR” = 0.00000000032148• Probability “to race tomorrow” =“TO VB NR”
= 0.00000026892
Bayesian Inference
• Correct answer = max (P (hypothesis | observed))
Bayesian Inference
• Prior probability = likelihood of the hypothesis
Bayesian Inference
• Likelihood = probability that the evidence matches the hypothesis
Bayesian Inference
• Bayesian vs. Frequentists• Subjectivity
Examples
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