lineage.BaumWelch¶
Re-calculates the tHMM parameters of pi, T, and emissions using Baum Welch.
Module Contents¶
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lineage.BaumWelch.do_E_step(tHMMobj: tHMM) → Tuple[list, list, list, list]¶ Calculate MSD, EL, NF, gamma, beta, LL from tHMM model.
- Parameters
tHMMobj – A tHMM object with properties of the lineages of cells, such as
- 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)
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lineage.BaumWelch.calculate_log_likelihood(NF: list) → float¶ Calculates log likelihood of NF for each lineage.
- Parameters
NF – list of normalizing factors
return: the sum of log likelihoods for each lineage
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lineage.BaumWelch.calculate_stationary(T: np.ndarray) → np.ndarray¶ Calculate the stationary distribution of states from T. Note that this does not take into account potential influences of the emissions.
- Parameters
T – 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
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lineage.BaumWelch.do_M_step(tHMMobj: list[tHMM], MSD: list, betas: list, gammas: list)¶ 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 – The marginal state distribution P(z_n = k)
betas – beta values. The conditional probability of states, given observations of the sub-tree rooted in cell_n
gammas – gamma values. The conditional probability of states, given the observation of the whole tree
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lineage.BaumWelch.do_M_pi_step(tHMMobj: list[tHMM], gammas: list[np.ndarray]) → np.ndarray¶ 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 – gamma values. The conditional probability of states, given the observation of the whole tree
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lineage.BaumWelch.do_M_T_step(tHMMobj: list[tHMM], MSD: list[list[np.ndarray]], betas: list[list[np.ndarray]], gammas: list[list[np.ndarray]]) → np.ndarray¶ 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 – The marginal state distribution P(z_n = k)
betas – beta values. The conditional probability of states, given observations of the sub-tree rooted in cell_n
gammas – gamma values. The conditional probability of states, given the observation of the whole tree
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lineage.BaumWelch.do_M_E_step(tHMMobj: tHMM, gammas: list[np.ndarray])¶ 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 – gamma values. The conditional probability of states, given the observation of the whole tree
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lineage.BaumWelch.do_M_E_step_atonce(all_tHMMobj: list[tHMM], all_gammas: list[list[np.ndarray]])¶ 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.