Transcription of Lecture 9: Hidden Markov Models
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Lecture 9: Hidden Markov Models
Lecture 9: Hidden Markov Models Working with time series data Hidden Markov Models Inference and learning problems Forward-backward algorithm Baum-Welch algorithm for parameter fittingCOMP-652 and ECSE-608, Lecture 9 - February 9, 20161 Time series/sequence data Very important in practice: Speech recognition Text processing (taking into account the sequence of words) DNA analysis Heart-rate monitoring Financial market forecasting Mobile robot sensor processing .. Does this fit the machine learning paradigm as described so far? The sequences arenot all the same length(so we cannot just assumeone attribute per time step) The data at each time slice/index isnot independent The data distributionmay change over timeCOMP-652 and ECSE-608, Lecture 9 - February 9, 20162 Example: Robot position tracking1 Illustrative Example: Robot Localization!"Probt=0 Sensory model: never more than 1 mistakeMotion model: may not execute action with small Pfeiffer, 2004 COMP-652 and ECSE-608, Lecture 9 - February 9, 20163 Example (II)Illustrative Example: Robot Localization!
t(4) 0.0 0.25 0.0000 0.01562 0.00000 0.00098 0.00049 0.00037 0.00000 0.00000 t(5) 0.0 0.00 0.0625 0.00000 0.00391 0.00000 0.00000 0.00000 0.00009 0.00007 Note that probabilities decrease with the length of the sequence This is due to the fact that we are looking at a joint probability; this phenomenon would not happen for conditional probabilities
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