/usr/share/pyshared/Bio/HMM/DynamicProgramming.py is in python-biopython 1.58-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 | """Dynamic Programming algorithms for general usage.
This module contains classes which implement Dynamic Programming
algorithms that can be used generally.
"""
class AbstractDPAlgorithms(object):
"""An abstract class to calculate forward and backward probabiliies.
This class should not be instantiated directly, but should be used
through a derived class which implements proper scaling of variables.
This class is just meant to encapsulate the basic foward and backward
algorithms, and allow derived classes to deal with the problems of
multiplying probabilities.
Derived class of this must implement:
o _forward_recursion -- Calculate the forward values in the recursion
using some kind of technique for preventing underflow errors.
o _backward_recursion -- Calculate the backward values in the recursion
step using some technique to prevent underflow errors.
"""
def __init__(self, markov_model, sequence):
"""Initialize to calculate foward and backward probabilities.
Arguments:
o markov_model -- The current Markov model we are working with.
o sequence -- A training sequence containing a set of emissions.
"""
self._mm = markov_model
self._seq = sequence
def _foward_recursion(self, cur_state, sequence_pos, forward_vars):
"""Calculate the forward recursion value.
"""
raise NotImplementedError("Subclasses must implement")
def forward_algorithm(self):
"""Calculate sequence probability using the forward algorithm.
This implements the foward algorithm, as described on p57-58 of
Durbin et al.
Returns:
o A dictionary containing the foward variables. This has keys of the
form (state letter, position in the training sequence), and values
containing the calculated forward variable.
o The calculated probability of the sequence.
"""
# all of the different letters that the state path can be in
state_letters = self._seq.states.alphabet.letters
# -- initialize the algorithm
#
# NOTE: My index numbers are one less than what is given in Durbin
# et al, since we are indexing the sequence going from 0 to
# (Length - 1) not 1 to Length, like in Durbin et al.
#
forward_var = {}
# f_{0}(0) = 1
forward_var[(state_letters[0], -1)] = 1
# f_{k}(0) = 0, for k > 0
for k in range(1, len(state_letters)):
forward_var[(state_letters[k], -1)] = 0
# -- now do the recursion step
# loop over the training sequence
# Recursion step: (i = 1 .. L)
for i in range(len(self._seq.emissions)):
# now loop over the letters in the state path
for main_state in state_letters:
# calculate the forward value using the appropriate
# method to prevent underflow errors
forward_value = self._forward_recursion(main_state, i,
forward_var)
if forward_value is not None:
forward_var[(main_state, i)] = forward_value
# -- termination step - calculate the probability of the sequence
first_state = state_letters[0]
seq_prob = 0
for state_item in state_letters:
# f_{k}(L)
forward_value = forward_var[(state_item,
len(self._seq.emissions) - 1)]
# a_{k0}
transition_value = self._mm.transition_prob[(state_item,
first_state)]
seq_prob += forward_value * transition_value
return forward_var, seq_prob
def _backward_recursion(self, cur_state, sequence_pos, forward_vars):
"""Calculate the backward recursion value.
"""
raise NotImplementedError("Subclasses must implement")
def backward_algorithm(self):
"""Calculate sequence probability using the backward algorithm.
This implements the backward algorithm, as described on p58-59 of
Durbin et al.
Returns:
o A dictionary containing the backwards variables. This has keys
of the form (state letter, position in the training sequence),
and values containing the calculated backward variable.
"""
# all of the different letters that the state path can be in
state_letters = self._seq.states.alphabet.letters
# -- initialize the algorithm
#
# NOTE: My index numbers are one less than what is given in Durbin
# et al, since we are indexing the sequence going from 0 to
# (Length - 1) not 1 to Length, like in Durbin et al.
#
backward_var = {}
first_letter = state_letters[0]
# b_{k}(L) = a_{k0} for all k
for state in state_letters:
backward_var[(state, len(self._seq.emissions) - 1)] = \
self._mm.transition_prob[(state, state_letters[0])]
# -- recursion
# first loop over the training sequence backwards
# Recursion step: (i = L - 1 ... 1)
all_indexes = range(len(self._seq.emissions) - 1)
all_indexes.reverse()
for i in all_indexes:
# now loop over the letters in the state path
for main_state in state_letters:
# calculate the backward value using the appropriate
# method to prevent underflow errors
backward_value = self._backward_recursion(main_state, i,
backward_var)
if backward_value is not None:
backward_var[(main_state, i)] = backward_value
# skip the termination step to avoid recalculations -- you should
# get sequence probabilities using the forward algorithm
return backward_var
class ScaledDPAlgorithms(AbstractDPAlgorithms):
"""Implement forward and backward algorithms using a rescaling approach.
This scales the f and b variables, so that they remain within a
manageable numerical interval during calculations. This approach is
described in Durbin et al. on p 78.
This approach is a little more straightfoward then log transformation
but may still give underflow errors for some types of models. In these
cases, the LogDPAlgorithms class should be used.
"""
def __init__(self, markov_model, sequence):
"""Initialize the scaled approach to calculating probabilities.
Arguments:
o markov_model -- The current Markov model we are working with.
o sequence -- A TrainingSequence object that must have a
set of emissions to work with.
"""
AbstractDPAlgorithms.__init__(self, markov_model, sequence)
self._s_values = {}
def _calculate_s_value(self, seq_pos, previous_vars):
"""Calculate the next scaling variable for a sequence position.
This utilizes the approach of choosing s values such that the
sum of all of the scaled f values is equal to 1.
Arguments:
o seq_pos -- The current position we are at in the sequence.
o previous_vars -- All of the forward or backward variables
calculated so far.
Returns:
o The calculated scaling variable for the sequence item.
"""
# all of the different letters the state can have
state_letters = self._seq.states.alphabet.letters
# loop over all of the possible states
s_value = 0
for main_state in state_letters:
emission = self._mm.emission_prob[(main_state,
self._seq.emissions[seq_pos])]
# now sum over all of the previous vars and transitions
trans_and_var_sum = 0
for second_state in self._mm.transitions_from(main_state):
# the value of the previous f or b value
var_value = previous_vars[(second_state, seq_pos - 1)]
# the transition probability
trans_value = self._mm.transition_prob[(second_state,
main_state)]
trans_and_var_sum += (var_value * trans_value)
s_value += (emission * trans_and_var_sum)
return s_value
def _forward_recursion(self, cur_state, sequence_pos, forward_vars):
"""Calculate the value of the forward recursion.
Arguments:
o cur_state -- The letter of the state we are calculating the
forward variable for.
o sequence_pos -- The position we are at in the training seq.
o forward_vars -- The current set of forward variables
"""
# calculate the s value, if we haven't done so already (ie. during
# a previous forward or backward recursion)
if sequence_pos not in self._s_values:
self._s_values[sequence_pos] = \
self._calculate_s_value(sequence_pos, forward_vars)
# e_{l}(x_{i})
seq_letter = self._seq.emissions[sequence_pos]
cur_emission_prob = self._mm.emission_prob[(cur_state, seq_letter)]
# divide by the scaling value
scale_emission_prob = (float(cur_emission_prob) /
float(self._s_values[sequence_pos]))
# loop over all of the possible states at the position
state_pos_sum = 0
have_transition = 0
for second_state in self._mm.transitions_from(cur_state):
have_transition = 1
# get the previous forward_var values
# f_{k}(i - 1)
prev_forward = forward_vars[(second_state, sequence_pos - 1)]
# a_{kl}
cur_trans_prob = self._mm.transition_prob[(second_state,
cur_state)]
state_pos_sum += prev_forward * cur_trans_prob
# if we have the possiblity of having a transition
# return the recursion value
if have_transition:
return (scale_emission_prob * state_pos_sum)
else:
return None
def _backward_recursion(self, cur_state, sequence_pos, backward_vars):
"""Calculate the value of the backward recursion
Arguments:
o cur_state -- The letter of the state we are calculating the
forward variable for.
o sequence_pos -- The position we are at in the training seq.
o backward_vars -- The current set of backward variables
"""
# calculate the s value, if we haven't done so already (ie. during
# a previous forward or backward recursion)
if sequence_pos not in self._s_values:
self._s_values[sequence_pos] = \
self._calculate_s_value(sequence_pos, backward_vars)
# loop over all of the possible states at the position
state_pos_sum = 0
have_transition = 0
for second_state in self._mm.transitions_from(cur_state):
have_transition = 1
# e_{l}(x_{i + 1})
seq_letter = self._seq.emissions[sequence_pos + 1]
cur_emission_prob = self._mm.emission_prob[(cur_state, seq_letter)]
# get the previous backward_var value
# b_{l}(i + 1)
prev_backward = backward_vars[(second_state, sequence_pos + 1)]
# the transition probability -- a_{kl}
cur_transition_prob = self._mm.transition_prob[(cur_state,
second_state)]
state_pos_sum += (cur_emission_prob * prev_backward *
cur_transition_prob)
# if we have a probability for a transition, return it
if have_transition:
return (state_pos_sum / float(self._s_values[sequence_pos]))
# otherwise we have no probability (ie. we can't do this transition)
# and return None
else:
return None
class LogDPAlgorithms(AbstractDPAlgorithms):
"""Implement forward and backward algorithms using a log approach.
This uses the approach of calculating the sum of log probabilities
using a lookup table for common values.
XXX This is not implemented yet!
"""
def __init__(self, markov_model, sequence):
raise NotImplementedError("Haven't coded this yet...")
|