lineage.BaumWelch
=================

.. py:module:: lineage.BaumWelch

.. autoapi-nested-parse::

   Re-calculates the tHMM parameters of pi, T, and emissions using Baum Welch.



Functions
---------

.. autoapisummary::

   lineage.BaumWelch.do_E_step
   lineage.BaumWelch.calculate_log_likelihood
   lineage.BaumWelch.calculate_stationary
   lineage.BaumWelch.do_M_step
   lineage.BaumWelch.do_M_pi_step
   lineage.BaumWelch.do_M_T_step
   lineage.BaumWelch.do_M_E_step
   lineage.BaumWelch.do_M_E_step_atonce


Module Contents
---------------

.. py:function:: do_E_step(tHMMobj)

   Calculate MSD, EL, NF, gamma, beta, LL from tHMM model.

   :param tHMMobj: A tHMM object with properties of the lineages of cells.
   :return MSD: Marginal state distribution
   :return NF: normalizing factor
   :return betas: beta values (conditional probability of cell states given cell observations)
   :return gammas: gamma values (used to calculate the downward reursion)


.. py:function:: calculate_log_likelihood(NF)

   Calculates log likelihood of NF for each lineage.

   :param NF: list of normalizing factors
   :return: the sum of log likelihoods for each lineage


.. py:function:: calculate_stationary(T)

   Calculate the stationary distribution of states from T.
   Note that this does not take into account potential influences of the emissions.

   :param T: transition matrix, a square matrix with probabilities of transitioning from one state to the other
   :return: The stationary distribution of states which can be obtained by solving w = w * T


.. py:function:: do_M_step(tHMMobj, MSD, betas, gammas)

   Calculates the maximization step of the Baum Welch algorithm
   given output of the expectation step.
   The individual parameter estimations are performed in
   separate functions.

   :param tHMMobj: A class object with properties of the lineages of cells
   :type tHMMobj: list
   :param MSD: The marginal state distribution P(z_n = k)
   :param betas: beta values. The conditional probability of states, given observations of the sub-tree rooted in cell_n
   :param gammas: gamma values. The conditional probability of states, given the observation of the whole tree


.. py:function:: do_M_pi_step(tHMMobj, gammas)

   Calculates the M-step of the Baum Welch algorithm
   given output of the E step.
   Does the parameter estimation for the pi
   initial probability vector.

   :param tHMMobj: A class object with properties of the lineages of cells
   :type tHMMobj: object
   :param gammas: gamma values. The conditional probability of states, given the observation of the whole tree


.. py:function:: do_M_T_step(tHMMobj, MSD, betas, gammas)

   Calculates the M-step of the Baum Welch algorithm
   given output of the E step.
   Does the parameter estimation for the T
   Markov stochastic transition matrix.

   :param tHMMobj: A class object with properties of the lineages of cells
   :type tHMMobj: list of tHMMobj s
   :param MSD: The marginal state distribution P(z_n = k)
   :param betas: beta values. The conditional probability of states, given observations of the sub-tree rooted in cell_n
   :param gammas: gamma values. The conditional probability of states, given the observation of the whole tree


.. py:function:: do_M_E_step(tHMMobj, gammas)

   Calculates the M-step of the Baum Welch algorithm
   given output of the E step.
   Does the parameter estimation for the E
   Emissions matrix (state probabilistic distributions).

   :param tHMMobj: A class object with properties of the lineages of cells
   :type tHMMobj: object
   :param gammas: gamma values. The conditional probability of states, given the observation of the whole tree


.. py:function:: do_M_E_step_atonce(all_tHMMobj, all_gammas)

   Performs the maximization step for emission estimation when data for all the concentrations are given at once for all the states.
   After reshaping, we will have a list of lists for each state.
   This function is specifically written for the experimental data of G1 and S-G2 cell cycle fates and durations.