1. What is the Baum-Welch algorithm?
- the Baum-Welch (BW) algorithm is a special case of the Expectation-Maximization (EM) algorithm
- BW is also called forward-backward algorithm
- the BW algorithm attempts to find the unknown parameters in Hidden Markov Models (HMM’s)
- finds maximum likelihood (ML) estimates of the HMM parameters, given observations of the emitted symbols
- finds local maxima of the likelihood (initial values of the parameters are critical)
- parameters: start-, transition- and emission probabilities of the HMM
- hidden data: states of the HMM
- Baum-Welch cannot determine the structure of the HMM
2. Example: Dishonest casino
- see above: “The Hidden Markov Model: transition and emission probabilities”
- the states compass: F (fair die) and L (loaded die)
- symbols which can be emitted: 1, 2, 3, 4, 5, 6 (die rolls)
- using package HMM
![](data:image/png;base64,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)
library(HMM)
## Warning: package 'HMM' was built under R version 3.5.2
states = c("F", "L")
symbols = 1:6
3. Getting some observation
part1 = sample(symbols, 300, replace = TRUE) # fair
part2 = sample(symbols, 300, replace = TRUE, prob = c(rep(0.1,5), 0.5)) # loaded
part3 = sample(symbols, 300, replace = TRUE) # fair
observation <- c(part1, part2, part1)
observation
## [1] 1 3 2 1 2 1 1 3 6 2 5 2 3 3 4 5 2 4 5 3 3 1 2 5 1 1 3 3 1 4 5 6 4 2 6
## [36] 5 4 3 3 5 1 2 1 6 1 5 3 5 6 1 3 3 5 1 6 1 5 3 4 5 6 5 5 3 3 3 4 1 1 6
## [71] 5 6 3 5 6 6 4 1 2 1 6 5 2 5 1 3 5 3 2 3 5 1 4 5 3 4 3 3 3 4 5 5 3 1 1
## [106] 5 2 1 4 5 6 2 6 6 4 4 5 2 1 4 2 3 6 2 2 3 1 2 1 4 1 5 1 5 5 2 3 3 6 6
## [141] 6 4 1 4 4 1 6 4 1 6 2 3 6 2 4 2 6 3 3 1 1 3 1 2 1 6 1 6 3 5 2 5 3 1 1
## [176] 5 5 2 4 2 1 3 1 3 6 1 5 6 3 2 3 6 3 3 2 5 5 2 3 4 4 3 4 4 6 2 2 2 4 5
## [211] 5 4 1 3 1 4 3 3 6 1 2 3 1 6 5 4 1 6 2 6 6 2 6 5 4 3 5 4 6 3 1 6 2 5 1
## [246] 5 3 1 5 6 1 1 3 2 4 3 4 6 1 2 3 3 6 4 5 5 6 3 5 6 3 2 1 3 3 3 2 1 5 2
## [281] 5 5 6 3 6 5 6 2 5 6 1 5 4 2 6 4 3 4 1 2 6 2 2 2 1 6 6 6 5 4 6 6 5 6 6
## [316] 6 6 3 6 6 1 6 6 3 2 6 3 4 6 5 5 6 4 4 6 5 6 2 6 6 1 2 5 6 4 6 6 6 6 6
## [351] 3 6 2 4 6 5 6 4 3 6 4 6 2 2 3 4 6 6 2 6 3 5 5 6 6 6 5 5 6 3 6 6 6 4 4
## [386] 6 6 5 3 6 6 6 6 4 6 6 5 6 3 4 6 6 5 3 6 6 4 6 6 6 5 6 5 4 4 6 6 6 6 6
## [421] 5 6 2 3 5 4 6 4 6 6 1 6 6 6 3 6 6 6 6 6 6 6 6 5 6 3 4 4 4 5 6 6 6 6 6
## [456] 2 3 1 6 6 6 1 6 2 6 6 5 6 6 3 6 6 6 6 5 2 6 1 3 6 6 6 4 6 4 3 6 6 3 5
## [491] 5 6 1 6 3 6 5 3 6 6 6 2 6 6 4 2 6 6 6 5 6 6 6 5 1 2 6 6 6 6 6 2 6 6 6
## [526] 6 6 6 6 6 6 6 1 3 6 4 6 2 6 2 1 2 6 4 6 2 6 1 6 6 3 6 3 4 5 4 6 3 5 6
## [561] 5 6 5 6 3 6 2 6 6 5 2 3 6 6 6 6 3 3 5 6 6 3 6 5 4 2 4 4 6 6 6 6 6 6 5
## [596] 6 2 4 2 6 1 3 2 1 2 1 1 3 6 2 5 2 3 3 4 5 2 4 5 3 3 1 2 5 1 1 3 3 1 4
## [631] 5 6 4 2 6 5 4 3 3 5 1 2 1 6 1 5 3 5 6 1 3 3 5 1 6 1 5 3 4 5 6 5 5 3 3
## [666] 3 4 1 1 6 5 6 3 5 6 6 4 1 2 1 6 5 2 5 1 3 5 3 2 3 5 1 4 5 3 4 3 3 3 4
## [701] 5 5 3 1 1 5 2 1 4 5 6 2 6 6 4 4 5 2 1 4 2 3 6 2 2 3 1 2 1 4 1 5 1 5 5
## [736] 2 3 3 6 6 6 4 1 4 4 1 6 4 1 6 2 3 6 2 4 2 6 3 3 1 1 3 1 2 1 6 1 6 3 5
## [771] 2 5 3 1 1 5 5 2 4 2 1 3 1 3 6 1 5 6 3 2 3 6 3 3 2 5 5 2 3 4 4 3 4 4 6
## [806] 2 2 2 4 5 5 4 1 3 1 4 3 3 6 1 2 3 1 6 5 4 1 6 2 6 6 2 6 5 4 3 5 4 6 3
## [841] 1 6 2 5 1 5 3 1 5 6 1 1 3 2 4 3 4 6 1 2 3 3 6 4 5 5 6 3 5 6 3 2 1 3 3
## [876] 3 2 1 5 2 5 5 6 3 6 5 6 2 5 6 1 5 4 2 6 4 3 4 1 2
4. Initialization of the transition-, emission- , and start probabilities
trans_prob = matrix(c(0.95, 0.05, 0.1, 0.9), byrow = TRUE, nrow = 2) # transition probabilities
rownames(trans_prob) = states
colnames(trans_prob) = states
rowSums(trans_prob) # must be all one (stochastic matrix)
## F L
## 1 1
trans_prob
## F L
## F 0.95 0.05
## L 0.10 0.90
emission_prob = matrix(c(rep(1/6, 6), rep(0.1, 5), 0.5), byrow = TRUE, nrow = 2) # emission probabilities
rownames(emission_prob) = states
colnames(emission_prob) = symbols
rowSums(emission_prob) # must be all one (stochastic matrix)
## F L
## 1 1
emission_prob
## 1 2 3 4 5 6
## F 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
## L 0.1000000 0.1000000 0.1000000 0.1000000 0.1000000 0.5000000
start_prob = c(0.5, 0.5) # if we have no clue how it starts
names(start_prob) = states
sum(start_prob)
## [1] 1
start_prob
## F L
## 0.5 0.5
5. Running Baum-Welch
hmm = initHMM(states, symbols, startProbs = start_prob, transProbs = trans_prob, emissionProbs = emission_prob)
estimated_hmm <- baumWelch(hmm, observation, maxIterations = 100, delta = 1E-9, pseudoCount = 0)
round(estimated_hmm$hmm$transProbs, 4)
## to
## from F L
## F 0.9983 0.0017
## L 0.0036 0.9964
round(estimated_hmm$hmm$emissionProbs, 4)
## symbols
## states 1 2 3 4 5 6
## F 0.1856 0.1507 0.2044 0.1261 0.1749 0.1584
## L 0.0392 0.0806 0.1025 0.1075 0.1190 0.5512
# estimated_hmm$difference # sum of the distances between consecutive transition and emission matrices (L2-norm)
plot(estimated_hmm$difference, ylab = "Distance L2", xlab = "iteration-nr.", col = "red")
![](data:image/png;base64,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)
uwe.menzel@matstat.org