Hidden Markov Models – Utility functions#
AUTHOR:
William Stein, 2010-03
- class sage.stats.hmm.util.HMM_Util#
Bases:
object
A class used in order to share cdef’s methods between different files.
- initial_probs_to_TimeSeries(pi, normalize)#
This function is used internally by the __init__ methods of various Hidden Markov Models.
INPUT:
pi
– vector, list, orTimeSeries
normalize
– ifTrue
, replace negative entries by 0 and rescale to ensure that the sum of the entries in each row is equal to 1. If the sum of the entries in a row is 0, replace them all by \(1/N\).
OUTPUT:
a
TimeSeries
of length \(N\)
EXAMPLES:
sage: import sage.stats.hmm.util sage: u = sage.stats.hmm.util.HMM_Util() sage: u.initial_probs_to_TimeSeries([0.1,0.2,0.9], True) [0.0833, 0.1667, 0.7500] sage: u.initial_probs_to_TimeSeries([0.1,0.2,0.9], False) [0.1000, 0.2000, 0.9000]
- normalize_probability_TimeSeries(T, i, j)#
This function is used internally by the Hidden Markov Models code.
Replace entries of T[i:j] in place so that they are all nonnegative and sum to 1. Negative entries are replaced by 0 and T[i:j] is then rescaled to ensure that the sum of the entries in each row is equal to 1. If all entries are 0, replace them by 1/(j-i).
INPUT:
T
– aTimeSeries
i
– nonnegative integerj
– nonnegative integer
OUTPUT:
T
is modified
EXAMPLES:
sage: import sage.stats.hmm.util sage: T = stats.TimeSeries([.1, .3, .7, .5]) sage: u = sage.stats.hmm.util.HMM_Util() sage: u.normalize_probability_TimeSeries(T,0,3) sage: T [0.0909, 0.2727, 0.6364, 0.5000] sage: u.normalize_probability_TimeSeries(T,0,4) sage: T [0.0606, 0.1818, 0.4242, 0.3333] sage: abs(T.sum()-1) < 1e-8 # might not exactly equal 1 due to rounding True
- state_matrix_to_TimeSeries(A, N, normalize)#
This function is used internally by the
__init__
methods of Hidden Markov Models to make a transition matrix fromA
.INPUT:
A
– matrix, list, list of lists, orTimeSeries
N
– number of statesnormalize
– ifTrue
, replace negative entries by 0 and rescale to ensure that the sum of the entries in each row is equal to 1. If the sum of the entries in a row is 0, replace them all by \(1/N\).
OUTPUT:
a
TimeSeries
EXAMPLES:
sage: import sage.stats.hmm.util sage: u = sage.stats.hmm.util.HMM_Util() sage: u.state_matrix_to_TimeSeries([[.1,.7],[3/7,4/7]], 2, True) [0.1250, 0.8750, 0.4286, 0.5714] sage: u.state_matrix_to_TimeSeries([[.1,.7],[3/7,4/7]], 2, False) [0.1000, 0.7000, 0.4286, 0.5714]