Hidden Markov Models

Hello everyone, in this opportunity I want to share with you a powerful mathematic tool know as Hidden Markov Models, this kind o model allows us to model very problems in the real life, for example:

You’ve just picked up your brand new Watch from a bookstore. After marveling at the technological wonder on your wrist, you quickly realize it only really tells you the time and your heartbeat. Having just completed your semester in Artificial Intelligence, you know this can easily be enhanced. You have decided to take the incoming heartbeat signal and improve it to become an early detection system for various heart conditions. To keep your prototype simple, you decide to monitor for only 3 conditions at first.

To understand the incoming data:

1. The space between two vertical lines in the grid represents one-time slot.
2. The space between two large red lines represents one state.
3. A state can output either 1 or 0
   1. A state where the heartbeat signal stays at the baseline (flat), the output
      (emission) is 0.
4. There is a 10% chance a 1 is received instead.
   1. A state where the heartbeat signal deviates above and/or below the baseline
      (beat), the output (emission) is 1.
5. There is a 20% chance a 0 is received instead.
6. Assume a sequence will only ever start with the first state.

The HMMs below will be modeled using the following:

s = State Name
pp = Prior Probability
pst = Self Transition Probability
pt = Transition Probability
pe0 = Emission Probability of outputting a 0
pe1 = Emission Probability of outputting a 1

Normal Sinus Rhythm

Idioventricular Rhythm

Tachycardia Rhythm

I hope you enjoy it, do not forget to follow me @falcao12