How to use the pomegranate.NormalDistribution function in pomegranate

Returns
    -------
    model :
        A pomegranate HiddenMarkovModel trained on the given dataset.
    """
    assert method in ('hmm-tumor', 'hmm-germline', 'hmm')
    observations = as_observation_matrix(cnarr.autosomes())

    # Estimate standard deviation from the full distribution, robustly
    stdev = biweight_midvariance(np.concatenate(observations), initial=0)
    if method == 'hmm-germline':
        state_names = ["loss", "neutral", "gain"]
        distributions = [
            pom.NormalDistribution(-1.0, stdev, frozen=True),
            pom.NormalDistribution(0.0, stdev, frozen=True),
            pom.NormalDistribution(0.585, stdev, frozen=True),
        ]
    elif method == 'hmm-tumor':
        state_names = ["del", "loss", "neutral", "gain", "amp"]
        distributions = [
            pom.NormalDistribution(-2.0, stdev, frozen=False),
            pom.NormalDistribution(-0.5, stdev, frozen=False),
            pom.NormalDistribution(0.0, stdev, frozen=True),
            pom.NormalDistribution(0.3, stdev, frozen=False),
            pom.NormalDistribution(1.0, stdev, frozen=False),
        ]
    else:
        state_names = ["loss", "neutral", "gain"]
        distributions = [
            pom.NormalDistribution(-1.0, stdev, frozen=False),
            pom.NormalDistribution(0.0, stdev, frozen=False),
            pom.NormalDistribution(0.585, stdev, frozen=False),

assert method in ('hmm-tumor', 'hmm-germline', 'hmm')
    observations = as_observation_matrix(cnarr.autosomes())

    # Estimate standard deviation from the full distribution, robustly
    stdev = biweight_midvariance(np.concatenate(observations), initial=0)
    if method == 'hmm-germline':
        state_names = ["loss", "neutral", "gain"]
        distributions = [
            pom.NormalDistribution(-1.0, stdev, frozen=True),
            pom.NormalDistribution(0.0, stdev, frozen=True),
            pom.NormalDistribution(0.585, stdev, frozen=True),
        ]
    elif method == 'hmm-tumor':
        state_names = ["del", "loss", "neutral", "gain", "amp"]
        distributions = [
            pom.NormalDistribution(-2.0, stdev, frozen=False),
            pom.NormalDistribution(-0.5, stdev, frozen=False),
            pom.NormalDistribution(0.0, stdev, frozen=True),
            pom.NormalDistribution(0.3, stdev, frozen=False),
            pom.NormalDistribution(1.0, stdev, frozen=False),
        ]
    else:
        state_names = ["loss", "neutral", "gain"]
        distributions = [
            pom.NormalDistribution(-1.0, stdev, frozen=False),
            pom.NormalDistribution(0.0, stdev, frozen=False),
            pom.NormalDistribution(0.585, stdev, frozen=False),
        ]

    n_states = len(distributions)
    # Starts -- prefer neutral
    binom_coefs = scipy.special.binom(n_states - 1, range(n_states))

# Estimate standard deviation from the full distribution, robustly
    stdev = biweight_midvariance(np.concatenate(observations), initial=0)
    if method == 'hmm-germline':
        state_names = ["loss", "neutral", "gain"]
        distributions = [
            pom.NormalDistribution(-1.0, stdev, frozen=True),
            pom.NormalDistribution(0.0, stdev, frozen=True),
            pom.NormalDistribution(0.585, stdev, frozen=True),
        ]
    elif method == 'hmm-tumor':
        state_names = ["del", "loss", "neutral", "gain", "amp"]
        distributions = [
            pom.NormalDistribution(-2.0, stdev, frozen=False),
            pom.NormalDistribution(-0.5, stdev, frozen=False),
            pom.NormalDistribution(0.0, stdev, frozen=True),
            pom.NormalDistribution(0.3, stdev, frozen=False),
            pom.NormalDistribution(1.0, stdev, frozen=False),
        ]
    else:
        state_names = ["loss", "neutral", "gain"]
        distributions = [
            pom.NormalDistribution(-1.0, stdev, frozen=False),
            pom.NormalDistribution(0.0, stdev, frozen=False),
            pom.NormalDistribution(0.585, stdev, frozen=False),
        ]

    n_states = len(distributions)
    # Starts -- prefer neutral
    binom_coefs = scipy.special.binom(n_states - 1, range(n_states))
    start_probabilities = binom_coefs / binom_coefs.sum()

def load_segmentation_model(modeldata):
    model = HiddenMarkovModel('model')

    states = {}
    for s in modeldata:
        if len(s['emission']) == 1:
            emission = NormalDistribution(*s['emission'][0][:2])
        else:
            weights = np.array([w for _, _, w in s['emission']])
            dists = [NormalDistribution(mu, sigma)
                     for mu, sigma, _ in s['emission']]
            emission = GeneralMixtureModel(dists, weights=weights)
        state = State(emission, name=s['name'])

        states[s['name']] = state
        model.add_state(state)
        if 'start_prob' in s:
            model.add_transition(model.start, state, s['start_prob'])

    for s in modeldata:
        current = states[s['name']]
        for nextstate, prob in s['transition']:
            model.add_transition(current, states[nextstate], prob)

Returns
    -------
    model :
        A pomegranate HiddenMarkovModel trained on the given dataset.
    """
    assert method in ('hmm-tumor', 'hmm-germline', 'hmm')
    observations = as_observation_matrix(cnarr.autosomes())

    # Estimate standard deviation from the full distribution, robustly
    stdev = biweight_midvariance(np.concatenate(observations), initial=0)
    if method == 'hmm-germline':
        state_names = ["loss", "neutral", "gain"]
        distributions = [
            pom.NormalDistribution(-1.0, stdev, frozen=True),
            pom.NormalDistribution(0.0, stdev, frozen=True),
            pom.NormalDistribution(0.585, stdev, frozen=True),
        ]
    elif method == 'hmm-tumor':
        state_names = ["del", "loss", "neutral", "gain", "amp"]
        distributions = [
            pom.NormalDistribution(-2.0, stdev, frozen=False),
            pom.NormalDistribution(-0.5, stdev, frozen=False),
            pom.NormalDistribution(0.0, stdev, frozen=True),
            pom.NormalDistribution(0.3, stdev, frozen=False),
            pom.NormalDistribution(1.0, stdev, frozen=False),
        ]
    else:
        state_names = ["loss", "neutral", "gain"]
        distributions = [
            pom.NormalDistribution(-1.0, stdev, frozen=False),
            pom.NormalDistribution(0.0, stdev, frozen=False),

stdev = biweight_midvariance(np.concatenate(observations), initial=0)
    if method == 'hmm-germline':
        state_names = ["loss", "neutral", "gain"]
        distributions = [
            pom.NormalDistribution(-1.0, stdev, frozen=True),
            pom.NormalDistribution(0.0, stdev, frozen=True),
            pom.NormalDistribution(0.585, stdev, frozen=True),
        ]
    elif method == 'hmm-tumor':
        state_names = ["del", "loss", "neutral", "gain", "amp"]
        distributions = [
            pom.NormalDistribution(-2.0, stdev, frozen=False),
            pom.NormalDistribution(-0.5, stdev, frozen=False),
            pom.NormalDistribution(0.0, stdev, frozen=True),
            pom.NormalDistribution(0.3, stdev, frozen=False),
            pom.NormalDistribution(1.0, stdev, frozen=False),
        ]
    else:
        state_names = ["loss", "neutral", "gain"]
        distributions = [
            pom.NormalDistribution(-1.0, stdev, frozen=False),
            pom.NormalDistribution(0.0, stdev, frozen=False),
            pom.NormalDistribution(0.585, stdev, frozen=False),
        ]

    n_states = len(distributions)
    # Starts -- prefer neutral
    binom_coefs = scipy.special.binom(n_states - 1, range(n_states))
    start_probabilities = binom_coefs / binom_coefs.sum()

    # Prefer to keep the current state in each transition
    # All other transitions are equally likely, to start

def load_segmentation_model(modeldata):
    model = HiddenMarkovModel('model')

    states = {}
    for s in modeldata:
        if len(s['emission']) == 1:
            emission = NormalDistribution(*s['emission'][0][:2])
        else:
            weights = np.array([w for _, _, w in s['emission']])
            dists = [NormalDistribution(mu, sigma)
                     for mu, sigma, _ in s['emission']]
            emission = GeneralMixtureModel(dists, weights=weights)
        state = State(emission, name=s['name'])

        states[s['name']] = state
        model.add_state(state)
        if 'start_prob' in s:
            model.add_transition(model.start, state, s['start_prob'])

    for s in modeldata:
        current = states[s['name']]
        for nextstate, prob in s['transition']:
            model.add_transition(current, states[nextstate], prob)

    model.bake()

# GMM emissions
        # 4 Hidden States:
        # 0--start, 1--downstream, 2--upstream, 3--end
        numdists = 3 # Three-distribution Gaussian Mixtures
        var = 7.5 / (numdists - 1)
        means = [[], [], [], []]
        for i in range(numdists):
            means[3].append(i * 7.5 / ( numdists - 1 ) + 2.5)
            means[2].append(i * 7.5 / ( numdists - 1 ))
            means[1].append(-i * 7.5 / ( numdists - 1 ))
            means[0].append(-i * 7.5 / ( numdists - 1 ) - 2.5)
        states = []
        for i, m in enumerate(means):
            tmp = []
            for j in m:
                tmp.append(NormalDistribution(j, var))
            mixture = GeneralMixtureModel(tmp)
            states.append(State(mixture, name=str(i)))
        hmm.add_states(*tuple(states))

        # Transmission matrix
        #A = [[0., 1., 0., 0.],
        #    [0., 0.5, 0.5, 0.],
        #    [0., 0., 0.5, 0.5],
        #    [1., 0., 0., 0.]]
        hmm.add_transition(states[0], states[1], 1)
        hmm.add_transition(states[1], states[1], 0.5)
        hmm.add_transition(states[1], states[2], 0.5)
        hmm.add_transition(states[2], states[2], 0.5)
        hmm.add_transition(states[2], states[3], 0.5)
        hmm.add_transition(states[3], states[0], 1)

# Estimate standard deviation from the full distribution, robustly
    stdev = biweight_midvariance(np.concatenate(observations), initial=0)
    if method == 'hmm-germline':
        state_names = ["loss", "neutral", "gain"]
        distributions = [
            pom.NormalDistribution(-1.0, stdev, frozen=True),
            pom.NormalDistribution(0.0, stdev, frozen=True),
            pom.NormalDistribution(0.585, stdev, frozen=True),
        ]
    elif method == 'hmm-tumor':
        state_names = ["del", "loss", "neutral", "gain", "amp"]
        distributions = [
            pom.NormalDistribution(-2.0, stdev, frozen=False),
            pom.NormalDistribution(-0.5, stdev, frozen=False),
            pom.NormalDistribution(0.0, stdev, frozen=True),
            pom.NormalDistribution(0.3, stdev, frozen=False),
            pom.NormalDistribution(1.0, stdev, frozen=False),
        ]
    else:
        state_names = ["loss", "neutral", "gain"]
        distributions = [
            pom.NormalDistribution(-1.0, stdev, frozen=False),
            pom.NormalDistribution(0.0, stdev, frozen=False),
            pom.NormalDistribution(0.585, stdev, frozen=False),
        ]

    n_states = len(distributions)
    # Starts -- prefer neutral
    binom_coefs = scipy.special.binom(n_states - 1, range(n_states))
    start_probabilities = binom_coefs / binom_coefs.sum()

    # Prefer to keep the current state in each transition