lineage.BaumWelch

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

Functions

do_E_step(tHMMobj)

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

calculate_log_likelihood(NF)

Calculates log likelihood of NF for each lineage.

calculate_stationary(T)

Calculate the stationary distribution of states from T.

do_M_step(tHMMobj, MSD, betas, gammas)

Calculates the maximization step of the Baum Welch algorithm

do_M_pi_step(tHMMobj, gammas)

Calculates the M-step of the Baum Welch algorithm

do_M_T_step(tHMMobj, MSD, betas, gammas)

Calculates the M-step of the Baum Welch algorithm

do_M_E_step(tHMMobj, gammas)

Calculates the M-step of the Baum Welch algorithm

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.

Module Contents

lineage.BaumWelch.do_E_step(tHMMobj)

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

Parameters:

tHMMobj (lineage.tHMM.tHMM) -- 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)

Return type:

tuple[list, list, list, list]

lineage.BaumWelch.calculate_log_likelihood(NF)

Calculates log likelihood of NF for each lineage.

Parameters:

NF (list[numpy.ndarray] | list[list[numpy.ndarray]] | list[Any]) -- list of normalizing factors

Returns:

the sum of log likelihoods for each lineage

Return type:

float

lineage.BaumWelch.calculate_stationary(T)

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

Parameters:

T (numpy.ndarray) -- transition matrix, a square matrix with probabilities of transitioning from one state to the other

Returns:

The stationary distribution of states which can be obtained by solving w = w * T

Return type:

numpy.ndarray

lineage.BaumWelch.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.

Parameters:

  • tHMMobj (list) -- A class object with properties of the lineages of cells

  • MSD (list) -- The marginal state distribution P(z_n = k)

  • betas (list) -- beta values. The conditional probability of states, given observations of the sub-tree rooted in cell_n

  • gammas (list) -- gamma values. The conditional probability of states, given the observation of the whole tree

lineage.BaumWelch.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.

Parameters:

  • tHMMobj (object) -- A class object with properties of the lineages of cells

  • gammas (list[numpy.ndarray]) -- gamma values. The conditional probability of states, given the observation of the whole tree

Return type:

numpy.ndarray

lineage.BaumWelch.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.

Parameters:

  • tHMMobj (list of tHMMobj s) -- A class object with properties of the lineages of cells

  • MSD (list[list[numpy.ndarray]]) -- The marginal state distribution P(z_n = k)

  • betas (list[list[numpy.ndarray]]) -- beta values. The conditional probability of states, given observations of the sub-tree rooted in cell_n

  • gammas (list[list[numpy.ndarray]]) -- gamma values. The conditional probability of states, given the observation of the whole tree

Return type:

numpy.ndarray

lineage.BaumWelch.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).

Parameters:

  • tHMMobj (object) -- A class object with properties of the lineages of cells

  • gammas (list[numpy.ndarray]) -- gamma values. The conditional probability of states, given the observation of the whole tree

lineage.BaumWelch.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.

Parameters: