Hidden Markov models and Kalman filters Flashcards
What is an Hmm?
It is a special type of temporal model, with hidden states
Having three main components as matices:
- prior probability matrix
- transition probability matrix
- observation probability matrix
Is the rain / umbrella example an HMM?
Yes - with one state variable Raint
What happens if you have a model with two or more state variables?
You can fit it into the HMM by creating one mega variable
which is a tuple of these values
What is the transition model in an HMM?
It is a S x S matrix where S is the number of different states X can be in.
We now call this model for T
What is the sensor model in an HMM?
https://gyazo.com/daf4ec44cd1bef3363500cdee1f3bce9
Here we have the matrix Ot
We must remember to only have values in the diagonal
this is for mathematical convenience.
What is the foward algorithm in HMMs?
By simple restructuring we can now get the following equation for the forward algorithm:
What is the backward algorithm in HMMs?
By restructuring we can now get the following for the backward algorithm:
What is the complexity of the forward-backward algorithm for HMMs?
Example of filtering in HMM
What do we use for HMMs with continuous values?
A gaussian function
or a mixture of gaussian functions
Example of an HMM with continuous values:
For linear models with continous values, we can use what?
Kalman filters
What is the purpose of the kalman filter?
By continously estimating the true value, position, velocity etc. of the object being measured. When the measured values contains unpredicted or random errors or variation.
What do we often use as a conditional density function for kalman filters?
A linear gaussian model
