1. 1 Overview Motivation Basic definitions –Elements of an HMM –Markov chain example Three basic problems Sample application Cool terms and ideas Algorithms A big secret

2. 2 Motivation Applications include speech recognition And….? Other sequencing applications, such as protein research and gene finding

3. 3 Basic definitions Markov chain: each state depends unambiguously on the previous state –transitions are probabilistic –transitions depend only on current state Markov model: just another way of looking at Markov chains? –we can associate an observation with each state Hidden Markov Model (HMM): a Markov model in which observations are determined probabilistically from states

4. 4 Elements of an HMM N = number of states in model M = number of observation symbols per state A = state transition probability distribution B = observation symbol probability distribution  = initial state probability distribution

5. 5 uiuc.class.cs323 MP1 has completed executing thread threadC gets done, how can throw off Pending interrupts: off your function who's address your timer? But I am not necessarily increase functionality -- W. Top I don't they notice that we're both of the federal government's lifestyle choices to use stl without modification to go Ticks: total 510 threadC [...] I have been looking at time for a bug.

6. 6 talk.politics.misc surveillance system. This country must have a victim, they haven't gotten anyone and news group of productive life proves how to tax on land can disconnect one's computer and extent "Thief" is therefore to kill the invisible and abuse in surveillance station/system dislike. Roger Penrose has developed brain with the six years ago. Ten years and enjoying the most powerful electromagnetic waves in proportion to how corrupted situation of my reports are shot. Note. I mean that power, weapons to the people. People can be remotely controlled (powered) by many residents rejects the mind machine. Using the really cares about.

7. 7 alt.alien.visitors come to the proof. I'm like a fraction of the great deal were dreading from the operator in proportion to believe, and some time you choose to serve as proof that skeptics The Inter-dimensional Spectrum and our military has on March 25, 1896. Burial was gang-probed by Aliens, Gods, and thank you have any case, you are convinced with something else was handled pieces of those who have never seen "Experience something wrong somewhere they had only aware of Walt Disney and that Something Must Be Running In the red giant stars and the Tasmanian Tiger, we have to evolve a species find this process down, lightning hit bends the occasion that you have, I recall and non threatening manner. In earlier message news:39C05A9A.66A4@earthlink.net... In fact, I find people believe that an encounter.

8. 8 talk.politics.misc meets alt.alien.visitors The ego is happening. Secrets of crime. Because UFOs and nuclear weapon systems and applies them that FBI agents went across on the reality of a certain SF treated as well known as well! the middle or think of their lives. A psychotronic generator. The President can't convince us in a mental state whereby the curve for the involved LEO of a biological form, and conduct measurements and that was called Mankind's God's know. Therefore, the US citizen by invisible operatives. Yes and even if it both agreed, that his military greatness. He IS IT IS! I live dinosaurs I will begin the policeman again with you feel listless and groom were quotes your strap!!! outside of time. These include: various means, that I can no longer have been criminally eliminating guns are the I.Q. of an odd things. One size have a minimum of the cows were denied it, your brain functions without recompense, than Bill Gates Conspiracy

9. 9 Three basic problems 1: Given the observation sequence O and a model =(A, B,  ), how do we efficiently compute P(O| )? –scoring how well a given model matches a given observation sequence 2: Given O and, how do we choose corresponding state sequence Q which is optimal in some meaningful sense? –attempting to learn the structure of the model 3: How do we adjust the model parameters to maximize P(O| )? –training an HMM to recognize certain input patterns –most difficult of the problems, no optimal way

10. 10 Sample application Feature Analysis –spectral/temporal analysis of speech signal gives observation vectors for training HMMs Unit Matching –one HMM per unit Uh, other analysis –choosing which unit (HMM) best matches observation

11. 11 Terms and ideas Isolated word recognition vs connected word recognizers ergodic model –any state can be reached from any other state in a finite number of steps left-to-right (Bakis) model –transitions allowed only to self or to node to the right –obviously, not ergodic –very commonly used because it readily models changes over time optimality criteria (for Problem 2) –maximizing expected number of correct individual states –maximizing expected number of correct pairs or triples of states –single best state sequence (path) observations can be discrete or continuous observations may be associated with arcs instead of states parameter tieing to reduce number of independent parameters explicit modeling of state duration density comparison of HMMs implementation issues

12. 12 Algorithms Forward-Backward Procedure –greatly reduces number of calculations for Problem 1 –takes advantage of merging between sequences Viterbi Algorithm –for finding single best state sequence (Problem 2) –dynamic programming technique –iteratively finds most probable paths that output first symbol, then second, etc. Baum-Welch –reestimation procedure for solving Problem 3 –basically EM

13. 13 Guess the newsgroup I started the actual thread. The us-versus-them, highly negative attitude immediately assumes that an example: To induce sleep before invisible personnel successfully. Here are not possible radiation emitted 10-12 billion year here... But I am not necessarily increase functionality -- W. Top "I think an independent commission investigating the condemning the involved LEO have been found another blunder! Those who have a dozen urban legends. Can anyone tell if a direct way you want. I wish that in 1950s. This operation has been abusing this could be possible to some countries, the notes people underwent individual Souls still barabic. The fact slow to this honor. Behind the lose except 6 WEEKS WITH THY GOD? Holy Writ of the pyramids and see what you are you asking to you. I was because you will note your discernment, and believe in one unaware of you cannot help you are able to be determined by purposefully creating crafts are/and have been subtly, intentionally kept a horror writer? How can hear you! if they know if its actual priority? Read my time will stay within the Union of death (cancer & Goldhaber. (www.hagelin.org) You have incorporated the road. The reality of visible in a closer to at the right under high speed. Now, just the Shemakha astrophysics has stopped for these so quickly lost in the govt was hidden history of Poetry HITHER, AS TO EVERYONE ON YOUR MAILING LIST." Now if I'd mention the kittens I keep quiet about as I'm sure or not, situation. It's de rigueur to