Scala:Applied Machine Learning by Bugnion Pascal & Nicolas Patrick R. & Kozlov Alex

Author:Bugnion, Pascal & Nicolas, Patrick R. & Kozlov, Alex
Language: eng
Format: epub
Publisher: Packt Publishing
Published: 2017-02-23T05:00:00+00:00

Note

Normalization

Input states and observation data may have to be normalized and converted to probabilities before we initialize the A and B matrices.

The other two components of the HMM are the sequence of observations and the sequence of hidden states.

Design

The canonical forms of the HMM are implemented through dynamic programming techniques. These techniques rely on variables that define the state of the execution of the HMM for any of the canonical forms:

Alpha (the forward pass): The probability of observing the first t < T observations for a specific state at Si for the observation t is αt(i) = p(O0:t, qt=Si|λ)

Beta (the backward pass): The probability of observing the remainder of the sequence qt for a specific state is βt(i) =p(Ot+1:T-1|qt=Si,λ)

Gamma: The probability of being in a specific state given a sequence of observations and a model is γt(i) =p(qt=Si|O0:T-1, λ)

Delta: This is the sequence that has the highest probability path for the first i observations defined for a specific test δt(i)

Qstar: This is the optimum sequence q* of states Q0:T-1

DiGamma: The probability of being in a specific state at t and another defined state at t + 1 given the sequence of observations and the model is γt(i,j) = p(qt=Si,qt+1=Sj|O0:T-1, λ)

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