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initial occupation and transition likelihoods

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aj 2020-12-24 14:58:45 +00:00
parent 08c130f020
commit 7f4775fc9c
4 changed files with 222 additions and 46 deletions
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67
markov.ipynb
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110
markov.py
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@ -1,22 +1,10 @@
from dataclasses import dataclass, field
from typing import List
import numpy as np
from numpy import log as ln
from maths import gaussian
@dataclass
class Likelihood:
forward: float # forward likelihood
backward: float # backward likelihood
@dataclass
class TimeStep:
states: List[Likelihood] = field(default_factory=list)
@dataclass
class Transition:
pass
class MarkovModel:
def __init__(self, states: list, observations: list = list(), state_transitions: list = list()):
@ -27,7 +15,12 @@ class MarkovModel:
# self.timesteps = list()
self.forward = np.zeros((len(states), len(observations)))
self.p_obs_forward = 0
self.backward = np.zeros((len(states), len(observations)))
self.p_obs_backward = 0
self.occupation = np.zeros((len(states), len(observations)))
def get_other_state_index(self, state_in):
"""For when state changes, get other index for retrieving state transitions (FOR 0 INDEXING)"""
@ -41,6 +34,13 @@ class MarkovModel:
def get_other_state_number(self, state_in):
"""For when state changes, get other number for retrieving state transitions (FOR 1 INDEXING)"""
return self.get_other_state_index(state_in - 1) + 1
def populate(self):
self.populate_forward()
self.calculate_p_obs_forward()
self.populate_backward()
self.calculate_p_obs_backward()
self.populate_occupation()
def populate_forward(self):
for t, observation in enumerate(self.observations): # iterate through observations (time)
@ -48,56 +48,112 @@ class MarkovModel:
state_number = state_index + 1 # for easier reading (arrays 0-indexed, numbers start at 1)
if t == 0: # calcualte initial
if t == 0: # calcualte initial, 0 = first row = initial
self.forward[state_index, t] = self.state_transitions[0, state_number] * gaussian(observation, state.mean, state.std_dev)
else:
# each state for each time has two paths leading to
# each state for each time has two paths leading to it, the same state (this) and the other state (other)
other_index = self.get_other_state_index(state_index)
other_number = other_index + 1 # for 1 indexing
# previous value prob of changing from previous state to current
# previous value * prob of changing from previous state to current
this_to_this = self.forward[state_index, t - 1] * self.state_transitions[state_number, state_number]
other_to_this = self.forward[other_index, t - 1] * self.state_transitions[other_number, state_number]
self.forward[state_index, t] = (this_to_this + other_to_this) * gaussian(observation, state.mean, state.std_dev)
@property
def p_observations_forward(self):
def observation_likelihood(self):
"""abstraction for getting p(obs|model) for future calculations (occupation/transition)"""
return self.p_obs_forward
def calculate_p_obs_forward(self):
sum = 0
for state_index, final_likelihood in enumerate(self.forward[:, -1]):
sum += final_likelihood * self.state_transitions[state_index + 1, -1] # get exit prob from state transitions
self.p_obs_forward = sum
return sum
#TODO finish
def populate_backward(self):
# initialise from exit probabilities
self.backward[:, -1] = self.state_transitions[1:len(self.states) + 1, -1]
for t, observation in list(enumerate(self.observations[1:]))[::-1]: # iterate backwards through observations (time)
print(t, observation)
# print(t, observation)
for state_index, state in enumerate(self.states):
state_number = state_index + 1 # for easier reading (arrays 0-indexed, numbers start at 1)
other_index = self.get_other_state_index(state_index)
other_number = other_index + 1 # for 1 indexing
# observation for transitions from the same state
this_state_gaussian = gaussian(observation, self.states[state_index].mean, self.states[state_index].std_dev)
# observation for transitions from the other state
other_state_gaussian = gaussian(observation, self.states[other_index].mean, self.states[other_index].std_dev)
# previous value prob of changing from previous state to current
this_to_this = self.backward[state_index, t + 1] * self.state_transitions[state_number, state_number]
other_to_this = self.backward[other_index, t + 1] * self.state_transitions[other_number, state_number]
# beta * a * b
this_from_this = self.backward[state_index, t + 1] * self.state_transitions[state_number, state_number] * this_state_gaussian
other_from_this = self.backward[other_index, t + 1] * self.state_transitions[other_number, state_number] * other_state_gaussian
self.backward[state_index, t] = (this_to_this + other_to_this) * gaussian(observation, state.mean, state.std_dev)
self.backward[state_index, t] = (this_from_this + other_from_this)
#TODO finish
@property
def p_observations_backward(self):
def calculate_p_obs_backward(self):
sum = 0
for state_index, initial_likelihood in enumerate(self.backward[:, 0]):
for state_index, initial_likelihood in enumerate(self.backward[:, 0]):
# pi * b * beta
sum += self.state_transitions[0, state_index + 1] * gaussian(self.observations[0], self.states[state_index].mean, self.states[state_index].std_dev) * initial_likelihood
self.p_obs_backward = sum
return sum
def populate_occupation(self):
for t, observation in enumerate(self.observations): # iterate through observations (time)
for state_index, state in enumerate(self.states):
forward_backward = self.forward[state_index, t] * self.backward[state_index, t]
self.occupation[state_index, t] = forward_backward / self.observation_likelihood
def transition_likelihood(self, from_index, to_index, t):
if t == 0:
print("no transition likelihood for t == 0")
forward = self.forward[from_index, t - 1]
transition = self.state_transitions[from_index + 1, to_index + 1]
emission = gaussian(self.observations[t], self.states[to_index].mean, self.states[to_index].std_dev)
backward = self.backward[to_index, t]
return (forward * transition * emission * backward) / self.observation_likelihood
def baum_welch_state_transitions(self):
new_transitions = np.zeros((len(self.states), len(self.states)))
# i
for from_index, from_state in enumerate(self.states):
# j
for to_index, to_state in enumerate(self.states):
transition_sum = 0
for t in range(1, len(self.observations)):
transition_sum += self.transition_likelihood(from_index, to_index, t)
occupation_sum = 0
for t in range(0, len(self.observations)):
occupation_sum = self.occupation[to_index, t]
new_transitions[from_index, to_index] = transition_sum / occupation_sum
return new_transitions
# child object to replace normal prob/likeli operations with log prob operations (normal prob for debugging)
class LogMarkovModel(MarkovModel):
def log_state_transitions(self):
self.state_transitions = ln(self.state_transitions)

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report/report.lyx
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@ -323,6 +323,17 @@ lstparams "language=Python,breaklines=true,frame=tb,otherkeywords={self},emph={S
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand lstinputlisting
filename "../maths.py"
lstparams "language=Python,breaklines=true,frame=tb,otherkeywords={self},emph={State},emphstyle={\\ttb\\color{darkred}},basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{darkblue}},emphstyle={\\color{red}},stringstyle={\\color{red}},caption={Maths utility file with definitions for a gaussian},label={maths-listing}"
\end_inset
\end_layout
\begin_layout Standard

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scratchpad.ipynb
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