def __linearRegressionOnCountsOfCounts(self, countsOfCounts: list) -> list:
"""
Given counts of counts, this function will calculate the estimated counts of counts c$^*$ with
Good-Turing smoothing. First, the algorithm filters the non-zero counts from counts of counts array and constructs
c and r arrays. Then it constructs Z_n array with Z_n = (2C_n / (r_{n+1} - r_{n-1})). The algorithm then uses
simple linear regression on Z_n values to estimate w_1 and w_0, where log(N[i]) = w_1log(i) + w_0
PARAMETERS
----------
countsOfCounts : list
Counts of counts. countsOfCounts[1] is the number of words occurred once in the corpus. countsOfCounts[i] is
the number of words occurred i times in the corpus.
RETURNS
------
list
Estimated counts of counts array. N[1] is the estimated count for out of vocabulary words.
"""
N = [0.0] * len(countsOfCounts)
r = []
c = []
for i in range(1, len(countsOfCounts)):
if countsOfCounts[i] != 0:
r.append(i)
c.append(countsOfCounts[i])
A = Matrix(2, 2)
y = Vector(2, 0)
for i in range(len(r)):
xt = math.log(r[i])
if i == 0:
rt = math.log(c[i])
else:
if i == len(r) - 1:
rt = math.log((1.0 * c[i]) / (r[i] - r[i - 1]))
else:
rt = math.log((2.0 * c[i]) / (r[i + 1] - r[i - 1]))
A.addValue(0, 0, 1.0)
A.addValue(0, 1, xt)
A.addValue(1, 0, xt)
A.addValue(1, 1, xt * xt)
y.addValue(0, rt)
y.addValue(1, rt * xt)
A.inverse()
w = A.multiplyWithVectorFromRight(y)
w0 = w.getValue(0)
w1 = w.getValue(1)
for i in range(1, len(countsOfCounts)):
N[i] = math.exp(math.log(i) * w1 + w0)
return N
class Hmm1(Hmm):
__pi: Vector
def __init__(self, states: set, observations: list, emittedSymbols: list):
"""
A constructor of Hmm1 class which takes a Set of states, an array of observations (which also
consists of an array of states) and an array of instances (which also consists of an array of emitted symbols).
The constructor calls its super method to calculate the emission probabilities for those states.
PARAMETERS
----------
states : set
A Set of states, consisting of all possible states for this problem.
observations : list
An array of instances, where each instance consists of an array of states.
emittedSymbols : list
An array of instances, where each instance consists of an array of symbols.
"""
super().__init__(states, observations, emittedSymbols)
def calculatePi(self, observations: list):
"""
calculatePi calculates the prior probability vector (initial probabilities for each state) from a set of
observations. For each observation, the function extracts the first state in that observation. Normalizing the
counts of the states returns us the prior probabilities for each state.
PARAMETERS
----------
observations : list
A set of observations used to calculate the prior probabilities.
"""
self.__pi = Vector()
self.__pi.initAllSame(self.stateCount, 0.0)
for observation in observations:
index = self.stateIndexes[observation[0]]
self.__pi.addValue(index, 1.0)
self.__pi.l1Normalize()
def calculateTransitionProbabilities(self, observations: list):
"""
calculateTransitionProbabilities calculates the transition probabilities matrix from each state to another
state. For each observation and for each transition in each observation, the function gets the states.
Normalizing the counts of the pair of states returns us the transition probabilities.
PARAMETERS
----------
observations : list
A set of observations used to calculate the transition probabilities.
"""
self.transitionProbabilities = Matrix(self.stateCount, self.stateCount)
for current in observations:
for j in range(len(current) - 1):
fromIndex = self.stateIndexes[current[j]]
toIndex = self.stateIndexes[current[j + 1]]
self.transitionProbabilities.increment(fromIndex, toIndex)
self.transitionProbabilities.columnWiseNormalize()
def __logOfColumn(self, column: int) -> Vector:
"""
logOfColumn calculates the logarithm of each value in a specific column in the transition probability matrix.
PARAMETERS
----------
column : int
Column index of the transition probability matrix.
RETURNS
-------
Vector
A vector consisting of the logarithm of each value in the column in the transition probability matrix.
"""
result = Vector()
for i in range(self.stateCount):
result.add(self.safeLog(self.transitionProbabilities.getValue(i, column)))
return result
def viterbi(self, s: list) -> list:
"""
viterbi calculates the most probable state sequence for a set of observed symbols.
PARAMETERS
----------
s : list
A set of observed symbols.
RETURNS
-------
list
The most probable state sequence as an {@link ArrayList}.
"""
result = []
sequenceLength = len(s)
gamma = Matrix(sequenceLength, self.stateCount)
phi = Matrix(sequenceLength, self.stateCount)
qs = Vector(sequenceLength, 0)
emission = s[0]
for i in range(self.stateCount):
observationLikelihood = self.states[i].getEmitProb(emission)
gamma.setValue(0, i, self.safeLog(self.__pi.getValue(i)) + self.safeLog(observationLikelihood))
for t in range(1, sequenceLength):
emission = s[t]
for j in range(self.stateCount):
tempArray = self.__logOfColumn(j)
tempArray.addVector(gamma.getRowVector(t - 1))
maxIndex = tempArray.maxIndex()
observationLikelihood = self.states[j].getEmitProb(emission)
gamma.setValue(t, j, tempArray.getValue(maxIndex) + self.safeLog(observationLikelihood))
phi.setValue(t, j, maxIndex)
qs.setValue(sequenceLength - 1, gamma.getRowVector(sequenceLength - 1).maxIndex())
result.insert(0, self.states[int(qs.getValue(sequenceLength - 1))].getState())
for i in range(sequenceLength - 2, -1, -1):
qs.setValue(i, phi.getValue(i + 1, int(qs.getValue(i + 1))))
result.insert(0, self.states[int(qs.getValue(i))].getState())
return result
