BoghdadyJR/codesearch_python · Datasets at Hugging Face

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def predict(self, X): """Predict label for data. Parameters ---------- X : array-like, shape = [n_samples, n_features] Returns ------- C : array, shape = (n_samples,) """ logprob, responsibilities = self.score_samples(X) return responsibi...
def sample(self, n_samples=1, random_state=None): """Generate random samples from the model. Parameters ---------- n_samples : int, optional Number of samples to generate. Defaults to 1. Returns ------- X : array_like, shape (n_samples, n_features) ...
def fit(self, X, y=None): """Estimate model parameters with the expectation-maximization algorithm. A initialization step is performed before entering the em algorithm. If you want to avoid this step, set the keyword argument init_params to the empty string '' when creating the ...
def _do_mstep(self, X, responsibilities, params, min_covar=0): """ Perform the Mstep of the EM algorithm and return the class weihgts. """ weights = responsibilities.sum(axis=0) weighted_X_sum = np.dot(responsibilities.T, X) inverse_weights = 1.0 / (weights[:, np.newaxis] + 10 * ...
def _n_parameters(self): """Return the number of free parameters in the model.""" ndim = self.means_.shape[1] if self.covariance_type == 'full': cov_params = self.n_components * ndim * (ndim + 1) / 2. elif self.covariance_type == 'diag': cov_params = self.n_compon...
def bic(self, X): """Bayesian information criterion for the current model fit and the proposed data Parameters ---------- X : array of shape(n_samples, n_dimensions) Returns ------- bic: float (the lower the better) """ return (-2 * self....
def _get_param_names(cls): """Get parameter names for the estimator""" # fetch the constructor or the original constructor before # deprecation wrapping if any init = getattr(cls.__init__, 'deprecated_original', cls.__init__) if init is object.__init__: # No explicit ...
def set_params(self, **params): """Set the parameters of this estimator. The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form ``<component>__<parameter>`` so that it's possible to update each component of ...
def init_model_gaussian1d(observations, nstates, reversible=True): """Generate an initial model with 1D-Gaussian output densities Parameters ---------- observations : list of ndarray((T_i), dtype=float) list of arrays of length T_i with observation data nstates : int The number of s...
def _p_o(self, o): """ Returns the output probability for symbol o from all hidden states Parameters ---------- o : float A single observation. Return ------ p_o : ndarray (N) p_o[i] is the probability density of the observation o...
def p_obs(self, obs, out=None): """ Returns the output probabilities for an entire trajectory and all hidden states Parameters ---------- oobs : ndarray((T), dtype=int) a discrete trajectory of length T Return ------ p_o : ndarray (T,N) ...
def estimate(self, observations, weights): """ Fits the output model given the observations and weights Parameters ---------- observations : [ ndarray(T_k,) ] with K elements A list of K observation trajectories, each having length T_k and d dimensions weight...
def sample(self, observations, prior=None): """ Sample a new set of distribution parameters given a sample of observations from the given state. Both the internal parameters and the attached HMM model are updated. Parameters ---------- observations : [ numpy.array with...
def generate_observation_from_state(self, state_index): """ Generate a single synthetic observation data from a given state. Parameters ---------- state_index : int Index of the state from which observations are to be generated. Returns ------- ...
def generate_observations_from_state(self, state_index, nobs): """ Generate synthetic observation data from a given state. Parameters ---------- state_index : int Index of the state from which observations are to be generated. nobs : int The numbe...
def generate_observation_trajectory(self, s_t): """ Generate synthetic observation data from a given state sequence. Parameters ---------- s_t : numpy.array with shape (T,) of int type s_t[t] is the hidden state sampled at time t Returns ------- ...
def initial_distribution_samples(self): r""" Samples of the initial distribution """ res = np.empty((self.nsamples, self.nstates), dtype=config.dtype) for i in range(self.nsamples): res[i, :] = self._sampled_hmms[i].stationary_distribution return res
def transition_matrix_samples(self): r""" Samples of the transition matrix """ res = np.empty((self.nsamples, self.nstates, self.nstates), dtype=config.dtype) for i in range(self.nsamples): res[i, :, :] = self._sampled_hmms[i].transition_matrix return res
def eigenvalues_samples(self): r""" Samples of the eigenvalues """ res = np.empty((self.nsamples, self.nstates), dtype=config.dtype) for i in range(self.nsamples): res[i, :] = self._sampled_hmms[i].eigenvalues return res
def eigenvectors_left_samples(self): r""" Samples of the left eigenvectors of the hidden transition matrix """ res = np.empty((self.nsamples, self.nstates, self.nstates), dtype=config.dtype) for i in range(self.nsamples): res[i, :, :] = self._sampled_hmms[i].eigenvectors_left ...
def eigenvectors_right_samples(self): r""" Samples of the right eigenvectors of the hidden transition matrix """ res = np.empty((self.nsamples, self.nstates, self.nstates), dtype=config.dtype) for i in range(self.nsamples): res[i, :, :] = self._sampled_hmms[i].eigenvectors_right ...
def timescales_samples(self): r""" Samples of the timescales """ res = np.empty((self.nsamples, self.nstates-1), dtype=config.dtype) for i in range(self.nsamples): res[i, :] = self._sampled_hmms[i].timescales return res
def lifetimes_samples(self): r""" Samples of the timescales """ res = np.empty((self.nsamples, self.nstates), dtype=config.dtype) for i in range(self.nsamples): res[i, :] = self._sampled_hmms[i].lifetimes return res
def set_implementation(self, impl): """ Sets the implementation of this module Parameters ---------- impl : str One of ["python", "c"] """ if impl.lower() == 'python': self.__impl__ = self.__IMPL_PYTHON__ elif impl.lower() == 'c':...
def log_p_obs(self, obs, out=None, dtype=np.float32): """ Returns the element-wise logarithm of the output probabilities for an entire trajectory and all hidden states This is a default implementation that will take the log of p_obs(obs) and should only be used if p_obs(obs) is numerica...
def _handle_outliers(self, p_o): """ Sets observation probabilities of outliers to uniform if ignore_outliers is set. Parameters ---------- p_o : ndarray((T, N)) output probabilities """ if self.ignore_outliers: outliers = np.where(p_o.sum(axis=1)=...
def forward(A, pobs, pi, T=None, alpha_out=None, dtype=np.float32): """Compute P( obs \| A, B, pi ) and all forward coefficients. Parameters ---------- A : ndarray((N,N), dtype = float) transition matrix of the hidden states pobs : ndarray((T,N), dtype = float) pobs[t,i] is the obser...
def backward(A, pobs, T=None, beta_out=None, dtype=np.float32): """Compute all backward coefficients. With scaling! Parameters ---------- A : ndarray((N,N), dtype = float) transition matrix of the hidden states pobs : ndarray((T,N), dtype = float) pobs[t,i] is the observation probab...
def transition_counts(alpha, beta, A, pobs, T=None, out=None, dtype=np.float32): """ Sum for all t the probability to transition from state i to state j. Parameters ---------- alpha : ndarray((T,N), dtype = float), optional, default = None alpha[t,i] is the ith forward coefficient of time t. ...
def viterbi(A, pobs, pi, dtype=np.float32): """ Estimate the hidden pathway of maximum likelihood using the Viterbi algorithm. Parameters ---------- A : ndarray((N,N), dtype = float) transition matrix of the hidden states pobs : ndarray((T,N), dtype = float) pobs[t,i] is the observa...
def sample_path(alpha, A, pobs, T=None, dtype=np.float32): """ alpha : ndarray((T,N), dtype = float), optional, default = None alpha[t,i] is the ith forward coefficient of time t. beta : ndarray((T,N), dtype = float), optional, default = None beta[t,i] is the ith forward coefficient of time ...
def coarse_grain_transition_matrix(P, M): """ Coarse grain transition matrix P using memberships M Computes .. math: Pc = (M' M)^-1 M' P M Parameters ---------- P : ndarray(n, n) microstate transition matrix M : ndarray(n, m) membership matrix. Membership to macros...
def regularize_hidden(p0, P, reversible=True, stationary=False, C=None, eps=None): """ Regularizes the hidden initial distribution and transition matrix. Makes sure that the hidden initial distribution and transition matrix have nonzero probabilities by setting them to eps and then renormalizing. Avoid...
def regularize_pobs(B, nonempty=None, separate=None, eps=None): """ Regularizes the output probabilities. Makes sure that the output probability distributions has nonzero probabilities by setting them to eps and then renormalizing. Avoids zeros that would cause estimation algorithms to crash or get stu...
def init_discrete_hmm_spectral(C_full, nstates, reversible=True, stationary=True, active_set=None, P=None, eps_A=None, eps_B=None, separate=None): """Initializes discrete HMM using spectral clustering of observation counts Initializes HMM as described in [1]_. First estimates a M...
def init_discrete_hmm_ml(C_full, nstates, reversible=True, stationary=True, active_set=None, P=None, eps_A=None, eps_B=None, separate=None): """Initializes discrete HMM using maximum likelihood of observation counts""" raise NotImplementedError('ML-initialization not yet implemented')
def update(self, Pi, Tij): r""" Updates the transition matrix and recomputes all derived quantities """ from msmtools import analysis as msmana # update transition matrix by copy self._Tij = np.array(Tij) assert msmana.is_transition_matrix(self._Tij), 'Given transition matrix is...
def is_stationary(self): r""" Whether the MSM is stationary, i.e. whether the initial distribution is the stationary distribution of the hidden transition matrix. """ # for disconnected matrices, the stationary distribution depends on the estimator, so we can't compute # it directly. Th...
def stationary_distribution(self): r""" Compute stationary distribution of hidden states if possible. Raises ------ ValueError if the HMM is not stationary """ assert _tmatrix_disconnected.is_connected(self._Tij, strong=False), \ 'No unique stationary distri...
def timescales(self): r""" Relaxation timescales of the hidden transition matrix Returns ------- ts : ndarray(m) relaxation timescales in units of the input trajectory time step, defined by :math:`-tau / ln \| \lambda_i \|, i = 2,...,nstates`, where :ma...
def lifetimes(self): r""" Lifetimes of states of the hidden transition matrix Returns ------- l : ndarray(nstates) state lifetimes in units of the input trajectory time step, defined by :math:`-tau / ln \| p_{ii} \|, i = 1,...,nstates`, where :math:`p_{...
def sub_hmm(self, states): r""" Returns HMM on a subset of states Returns the HMM restricted to the selected subset of states. Will raise exception if the hidden transition matrix cannot be normalized on this subset """ # restrict initial distribution pi_sub = self._Pi[...
def count_matrix(self): # TODO: does this belong here or to the BHMM sampler, or in a subclass containing HMM with data? """Compute the transition count matrix from hidden state trajectory. Returns ------- C : numpy.array with shape (nstates,nstates) C[i,j] is the nu...
def count_init(self): """Compute the counts at the first time step Returns ------- n : ndarray(nstates) n[i] is the number of trajectories starting in state i """ if self.hidden_state_trajectories is None: raise RuntimeError('HMM model does not h...
def collect_observations_in_state(self, observations, state_index): # TODO: this would work well in a subclass with data """Collect a vector of all observations belonging to a specified hidden state. Parameters ---------- observations : list of numpy.array List of ob...
def generate_synthetic_state_trajectory(self, nsteps, initial_Pi=None, start=None, stop=None, dtype=np.int32): """Generate a synthetic state trajectory. Parameters ---------- nsteps : int Number of steps in the synthetic state trajectory to be generated. initial_Pi :...
def generate_synthetic_observation_trajectory(self, length, initial_Pi=None): """Generate a synthetic realization of observables. Parameters ---------- length : int Length of synthetic state trajectory to be generated. initial_Pi : np.array of shape (nstates,), optio...
def generate_synthetic_observation_trajectories(self, ntrajectories, length, initial_Pi=None): """Generate a number of synthetic realization of observables from this model. Parameters ---------- ntrajectories : int The number of trajectories to be generated. length :...
def nb_to_python(nb_path): """convert notebook to python script""" exporter = python.PythonExporter() output, resources = exporter.from_filename(nb_path) return output
def nb_to_html(nb_path): """convert notebook to html""" exporter = html.HTMLExporter(template_file='full') output, resources = exporter.from_filename(nb_path) header = output.split('<head>', 1)[1].split('</head>',1)[0] body = output.split('<body>', 1)[1].split('</body>',1)[0] # http://imgur.com...
def p_obs(self, obs, out=None): """ Returns the output probabilities for an entire trajectory and all hidden states Parameters ---------- obs : ndarray((T), dtype=int) a discrete trajectory of length T Return ------ p_o : ndarray (T,N) ...
def estimate(self, observations, weights): """ Maximum likelihood estimation of output model given the observations and weights Parameters ---------- observations : [ ndarray(T_k) ] with K elements A list of K observation trajectories, each having length T_k ...
def sample(self, observations_by_state): """ Sample a new set of distribution parameters given a sample of observations from the given state. The internal parameters are updated. Parameters ---------- observations : [ numpy.array with shape (N_k,) ] with nstates elemen...
def generate_observation_from_state(self, state_index): """ Generate a single synthetic observation data from a given state. Parameters ---------- state_index : int Index of the state from which observations are to be generated. Returns ------- ...
def generate_observations_from_state(self, state_index, nobs): """ Generate synthetic observation data from a given state. Parameters ---------- state_index : int Index of the state from which observations are to be generated. nobs : int The numbe...
def generate_observation_trajectory(self, s_t, dtype=None): """ Generate synthetic observation data from a given state sequence. Parameters ---------- s_t : numpy.array with shape (T,) of int type s_t[t] is the hidden state sampled at time t Returns ...
def set_implementation(impl): """ Sets the implementation of this module Parameters ---------- impl : str One of ["python", "c"] """ global __impl__ if impl.lower() == 'python': __impl__ = __IMPL_PYTHON__ elif impl.lower() == 'c': __impl__ = __IMPL_C__ e...
def forward(A, pobs, pi, T=None, alpha_out=None): """Compute P( obs \| A, B, pi ) and all forward coefficients. Parameters ---------- A : ndarray((N,N), dtype = float) transition matrix of the hidden states pobs : ndarray((T,N), dtype = float) pobs[t,i] is the observation probability...
def backward(A, pobs, T=None, beta_out=None): """Compute all backward coefficients. With scaling! Parameters ---------- A : ndarray((N,N), dtype = float) transition matrix of the hidden states pobs : ndarray((T,N), dtype = float) pobs[t,i] is the observation probability for observat...
def state_probabilities(alpha, beta, T=None, gamma_out=None): """ Calculate the (T,N)-probabilty matrix for being in state i at time t. Parameters ---------- alpha : ndarray((T,N), dtype = float), optional, default = None alpha[t,i] is the ith forward coefficient of time t. beta : ndarray((...
def state_counts(gamma, T, out=None): """ Sum the probabilities of being in state i to time t Parameters ---------- gamma : ndarray((T,N), dtype = float), optional, default = None gamma[t,i] is the probabilty at time t to be in state i ! T : int number of time steps Returns ...
def transition_counts(alpha, beta, A, pobs, T=None, out=None): """ Sum for all t the probability to transition from state i to state j. Parameters ---------- alpha : ndarray((T,N), dtype = float), optional, default = None alpha[t,i] is the ith forward coefficient of time t. beta : ndarray((...
def viterbi(A, pobs, pi): """ Estimate the hidden pathway of maximum likelihood using the Viterbi algorithm. Parameters ---------- A : ndarray((N,N), dtype = float) transition matrix of the hidden states pobs : ndarray((T,N), dtype = float) pobs[t,i] is the observation probability f...
def sample_path(alpha, A, pobs, T=None): """ Sample the hidden pathway S from the conditional distribution P ( S \| Parameters, Observations ) Parameters ---------- alpha : ndarray((T,N), dtype = float), optional, default = None alpha[t,i] is the ith forward coefficient of time t. A : ndarra...
def logger(name='BHMM', pattern='%(asctime)s %(levelname)s %(name)s: %(message)s', date_format='%H:%M:%S', handler=logging.StreamHandler(sys.stdout)): """ Retrieves the logger instance associated to the given name. :param name: The name of the logger instance. :type name: str :param patt...
def sample(self, nsamples, nburn=0, nthin=1, save_hidden_state_trajectory=False, call_back=None): """Sample from the BHMM posterior. Parameters ---------- nsamples : int The number of samples to generate. nburn : int, optional, default=0 Th...
def _update(self): """Update the current model using one round of Gibbs sampling. """ initial_time = time.time() self._updateHiddenStateTrajectories() self._updateEmissionProbabilities() self._updateTransitionMatrix() final_time = time.time() elapsed_ti...
def _updateHiddenStateTrajectories(self): """Sample a new set of state trajectories from the conditional distribution P(S \| T, E, O) """ self.model.hidden_state_trajectories = list() for trajectory_index in range(self.nobs): hidden_state_trajectory = self._sampleHiddenStateT...
def _sampleHiddenStateTrajectory(self, obs, dtype=np.int32): """Sample a hidden state trajectory from the conditional distribution P(s \| T, E, o) Parameters ---------- o_t : numpy.array with dimensions (T,) observation[n] is the nth observation dtype : numpy.dtype, o...
def _updateEmissionProbabilities(self): """Sample a new set of emission probabilites from the conditional distribution P(E \| S, O) """ observations_by_state = [self.model.collect_observations_in_state(self.observations, state) for state in range(self.model.nstat...
def _updateTransitionMatrix(self): """ Updates the hidden-state transition matrix and the initial distribution """ # TRANSITION MATRIX C = self.model.count_matrix() + self.prior_C # posterior count matrix # check if we work with these options if self.reversible...
def _generateInitialModel(self, output_model_type): """Initialize using an MLHMM. """ logger().info("Generating initial model for BHMM using MLHMM...") from bhmm.estimators.maximum_likelihood import MaximumLikelihoodEstimator mlhmm = MaximumLikelihoodEstimator(self.observations,...
def ensure_dtraj(dtraj): r"""Makes sure that dtraj is a discrete trajectory (array of int) """ if is_int_vector(dtraj): return dtraj elif is_list_of_int(dtraj): return np.array(dtraj, dtype=int) else: raise TypeError('Argument dtraj is not a discrete trajectory - only list o...
def ensure_dtraj_list(dtrajs): r"""Makes sure that dtrajs is a list of discrete trajectories (array of int) """ if isinstance(dtrajs, list): # elements are ints? then wrap into a list if is_list_of_int(dtrajs): return [np.array(dtrajs, dtype=int)] else: for i...
def connected_sets(C, mincount_connectivity=0, strong=True): """ Computes the connected sets of C. C : count matrix mincount_connectivity : float Minimum count which counts as a connection. strong : boolean True: Seek strongly connected sets. False: Seek weakly connected sets. """ ...
def closed_sets(C, mincount_connectivity=0): """ Computes the strongly connected closed sets of C """ n = np.shape(C)[0] S = connected_sets(C, mincount_connectivity=mincount_connectivity, strong=True) closed = [] for s in S: mask = np.zeros(n, dtype=bool) mask[s] = True if C[...
def nonempty_set(C, mincount_connectivity=0): """ Returns the set of states that have at least one incoming or outgoing count """ # truncate to states with at least one observed incoming or outgoing count. if mincount_connectivity > 0: C = C.copy() C[np.where(C < mincount_connectivity)] = 0 ...
def estimate_P(C, reversible=True, fixed_statdist=None, maxiter=1000000, maxerr=1e-8, mincount_connectivity=0): """ Estimates full transition matrix for general connectivity structure Parameters ---------- C : ndarray count matrix reversible : bool estimate reversible? fixed_sta...
def transition_matrix_partial_rev(C, P, S, maxiter=1000000, maxerr=1e-8): """Maximum likelihood estimation of transition matrix which is reversible on parts Partially-reversible estimation of transition matrix. Maximizes the likelihood: .. math: P_S &=& arg max prod_{S, :} (p_ij)^c_ij \\ \...
def enforce_reversible_on_closed(P): """ Enforces transition matrix P to be reversible on its closed sets. """ import msmtools.analysis as msmana n = np.shape(P)[0] Prev = P.copy() # treat each weakly connected set separately sets = closed_sets(P) for s in sets: I = np.ix_(s, s) ...
def is_reversible(P): """ Returns if P is reversible on its weakly connected sets """ import msmtools.analysis as msmana # treat each weakly connected set separately sets = connected_sets(P, strong=False) for s in sets: Ps = P[s, :][:, s] if not msmana.is_transition_matrix(Ps): ...
def stationary_distribution(P, C=None, mincount_connectivity=0): """ Simple estimator for stationary distribution for multiple strongly connected sets """ # can be replaced by msmtools.analysis.stationary_distribution in next msmtools release from msmtools.analysis.dense.stationary_vector import stationary_...
def means_samples(self): r""" Samples of the Gaussian distribution means """ res = np.empty((self.nsamples, self.nstates, self.dimension), dtype=config.dtype) for i in range(self.nsamples): for j in range(self.nstates): res[i, j, :] = self._sampled_hmms[i].means[j] ...
def sigmas_samples(self): r""" Samples of the Gaussian distribution standard deviations """ res = np.empty((self.nsamples, self.nstates, self.dimension), dtype=config.dtype) for i in range(self.nsamples): for j in range(self.nstates): res[i, j, :] = self._sampled_hmms...
def _guess_output_type(observations): """ Suggests a HMM model type based on the observation data Uses simple rules in order to decide which HMM model type makes sense based on observation data. If observations consist of arrays/lists of integer numbers (irrespective of whether the python type is int o...
def lag_observations(observations, lag, stride=1): r""" Create new trajectories that are subsampled at lag but shifted Given a trajectory (s0, s1, s2, s3, s4, ...) and lag 3, this function will generate 3 trajectories (s0, s3, s6, ...), (s1, s4, s7, ...) and (s2, s5, s8, ...). Use this function in order to...
def gaussian_hmm(pi, P, means, sigmas): """ Initializes a 1D-Gaussian HMM Parameters ---------- pi : ndarray(nstates, ) Initial distribution. P : ndarray(nstates,nstates) Hidden transition matrix means : ndarray(nstates, ) Means of Gaussian output distributions sigma...
def discrete_hmm(pi, P, pout): """ Initializes a discrete HMM Parameters ---------- pi : ndarray(nstates, ) Initial distribution. P : ndarray(nstates,nstates) Hidden transition matrix pout : ndarray(nstates,nsymbols) Output matrix from hidden states to observable symbols...
def init_hmm(observations, nstates, lag=1, output=None, reversible=True): """Use a heuristic scheme to generate an initial model. Parameters ---------- observations : list of ndarray((T_i)) list of arrays of length T_i with observation data nstates : int The number of states. ou...
def init_gaussian_hmm(observations, nstates, lag=1, reversible=True): """ Use a heuristic scheme to generate an initial model. Parameters ---------- observations : list of ndarray((T_i)) list of arrays of length T_i with observation data nstates : int The number of states. Exam...
def init_discrete_hmm(observations, nstates, lag=1, reversible=True, stationary=True, regularize=True, method='connect-spectral', separate=None): """Use a heuristic scheme to generate an initial model. Parameters ---------- observations : list of ndarray((T_i)) list of arr...
def estimate_hmm(observations, nstates, lag=1, initial_model=None, output=None, reversible=True, stationary=False, p=None, accuracy=1e-3, maxit=1000, maxit_P=100000, mincount_connectivity=1e-2): r""" Estimate maximum-likelihood HMM Generic maximum-likelihood estimation of HMMs...
def bayesian_hmm(observations, estimated_hmm, nsample=100, reversible=True, stationary=False, p0_prior='mixed', transition_matrix_prior='mixed', store_hidden=False, call_back=None): r""" Bayesian HMM based on sampling the posterior Generic maximum-likelihood estimation of HMMs Parameters ...
def logsumexp(arr, axis=0): """Computes the sum of arr assuming arr is in the log domain. Returns log(sum(exp(arr))) while minimizing the possibility of over/underflow. Examples -------- >>> import numpy as np >>> from sklearn.utils.extmath import logsumexp >>> a = np.arange(10) >...
def _ensure_sparse_format(spmatrix, accept_sparse, dtype, order, copy, force_all_finite): """Convert a sparse matrix to a given format. Checks the sparse format of spmatrix and converts if necessary. Parameters ---------- spmatrix : scipy sparse matrix Input to va...
def check_array(array, accept_sparse=None, dtype="numeric", order=None, copy=False, force_all_finite=True, ensure_2d=True, allow_nd=False, ensure_min_samples=1, ensure_min_features=1): """Input validation on an array, list, sparse matrix or similar. By default, the input is conv...
def beta_confidence_intervals(ci_X, ntrials, ci=0.95): """ Compute confidence intervals of beta distributions. Parameters ---------- ci_X : numpy.array Computed confidence interval estimate from `ntrials` experiments ntrials : int The number of trials that were run. ci : flo...
def empirical_confidence_interval(sample, interval=0.95): """ Compute specified symmetric confidence interval for empirical sample. Parameters ---------- sample : numpy.array The empirical samples. interval : float, optional, default=0.95 Size of desired symmetric confidence int...
def generate_latex_table(sampled_hmm, conf=0.95, dt=1, time_unit='ms', obs_name='force', obs_units='pN', caption='', outfile=None): """ Generate a LaTeX column-wide table showing various computed properties and uncertainties. Parameters ---------- conf : float confi...
def confidence_interval(data, alpha): """ Computes the mean and alpha-confidence interval of the given sample set Parameters ---------- data : ndarray a 1D-array of samples alpha : float in [0,1] the confidence level, i.e. percentage of data included in the interval ...

def predict(self, X): """Predict label for data. Parameters ---------- X : array-like, shape = [n_samples, n_features] Returns ------- C : array, shape = (n_samples,) """ logprob, responsibilities = self.score_samples(X) return responsibi...

def sample(self, n_samples=1, random_state=None): """Generate random samples from the model. Parameters ---------- n_samples : int, optional Number of samples to generate. Defaults to 1. Returns ------- X : array_like, shape (n_samples, n_features) ...

def fit(self, X, y=None): """Estimate model parameters with the expectation-maximization algorithm. A initialization step is performed before entering the em algorithm. If you want to avoid this step, set the keyword argument init_params to the empty string '' when creating the ...

def _do_mstep(self, X, responsibilities, params, min_covar=0): """ Perform the Mstep of the EM algorithm and return the class weihgts. """ weights = responsibilities.sum(axis=0) weighted_X_sum = np.dot(responsibilities.T, X) inverse_weights = 1.0 / (weights[:, np.newaxis] + 10 * ...

def _n_parameters(self): """Return the number of free parameters in the model.""" ndim = self.means_.shape[1] if self.covariance_type == 'full': cov_params = self.n_components * ndim * (ndim + 1) / 2. elif self.covariance_type == 'diag': cov_params = self.n_compon...

def bic(self, X): """Bayesian information criterion for the current model fit and the proposed data Parameters ---------- X : array of shape(n_samples, n_dimensions) Returns ------- bic: float (the lower the better) """ return (-2 * self....

def _get_param_names(cls): """Get parameter names for the estimator""" # fetch the constructor or the original constructor before # deprecation wrapping if any init = getattr(cls.__init__, 'deprecated_original', cls.__init__) if init is object.__init__: # No explicit ...

def set_params(self, **params): """Set the parameters of this estimator. The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form ``<component>__<parameter>`` so that it's possible to update each component of ...

def init_model_gaussian1d(observations, nstates, reversible=True): """Generate an initial model with 1D-Gaussian output densities Parameters ---------- observations : list of ndarray((T_i), dtype=float) list of arrays of length T_i with observation data nstates : int The number of s...

def _p_o(self, o): """ Returns the output probability for symbol o from all hidden states Parameters ---------- o : float A single observation. Return ------ p_o : ndarray (N) p_o[i] is the probability density of the observation o...

def p_obs(self, obs, out=None): """ Returns the output probabilities for an entire trajectory and all hidden states Parameters ---------- oobs : ndarray((T), dtype=int) a discrete trajectory of length T Return ------ p_o : ndarray (T,N) ...

def estimate(self, observations, weights): """ Fits the output model given the observations and weights Parameters ---------- observations : [ ndarray(T_k,) ] with K elements A list of K observation trajectories, each having length T_k and d dimensions weight...

def sample(self, observations, prior=None): """ Sample a new set of distribution parameters given a sample of observations from the given state. Both the internal parameters and the attached HMM model are updated. Parameters ---------- observations : [ numpy.array with...

def generate_observation_from_state(self, state_index): """ Generate a single synthetic observation data from a given state. Parameters ---------- state_index : int Index of the state from which observations are to be generated. Returns ------- ...

def generate_observations_from_state(self, state_index, nobs): """ Generate synthetic observation data from a given state. Parameters ---------- state_index : int Index of the state from which observations are to be generated. nobs : int The numbe...

def generate_observation_trajectory(self, s_t): """ Generate synthetic observation data from a given state sequence. Parameters ---------- s_t : numpy.array with shape (T,) of int type s_t[t] is the hidden state sampled at time t Returns ------- ...

def initial_distribution_samples(self): r""" Samples of the initial distribution """ res = np.empty((self.nsamples, self.nstates), dtype=config.dtype) for i in range(self.nsamples): res[i, :] = self._sampled_hmms[i].stationary_distribution return res

def transition_matrix_samples(self): r""" Samples of the transition matrix """ res = np.empty((self.nsamples, self.nstates, self.nstates), dtype=config.dtype) for i in range(self.nsamples): res[i, :, :] = self._sampled_hmms[i].transition_matrix return res

def eigenvalues_samples(self): r""" Samples of the eigenvalues """ res = np.empty((self.nsamples, self.nstates), dtype=config.dtype) for i in range(self.nsamples): res[i, :] = self._sampled_hmms[i].eigenvalues return res

def eigenvectors_left_samples(self): r""" Samples of the left eigenvectors of the hidden transition matrix """ res = np.empty((self.nsamples, self.nstates, self.nstates), dtype=config.dtype) for i in range(self.nsamples): res[i, :, :] = self._sampled_hmms[i].eigenvectors_left ...

def eigenvectors_right_samples(self): r""" Samples of the right eigenvectors of the hidden transition matrix """ res = np.empty((self.nsamples, self.nstates, self.nstates), dtype=config.dtype) for i in range(self.nsamples): res[i, :, :] = self._sampled_hmms[i].eigenvectors_right ...

def timescales_samples(self): r""" Samples of the timescales """ res = np.empty((self.nsamples, self.nstates-1), dtype=config.dtype) for i in range(self.nsamples): res[i, :] = self._sampled_hmms[i].timescales return res

def lifetimes_samples(self): r""" Samples of the timescales """ res = np.empty((self.nsamples, self.nstates), dtype=config.dtype) for i in range(self.nsamples): res[i, :] = self._sampled_hmms[i].lifetimes return res

def set_implementation(self, impl): """ Sets the implementation of this module Parameters ---------- impl : str One of ["python", "c"] """ if impl.lower() == 'python': self.__impl__ = self.__IMPL_PYTHON__ elif impl.lower() == 'c':...

def log_p_obs(self, obs, out=None, dtype=np.float32): """ Returns the element-wise logarithm of the output probabilities for an entire trajectory and all hidden states This is a default implementation that will take the log of p_obs(obs) and should only be used if p_obs(obs) is numerica...

def _handle_outliers(self, p_o): """ Sets observation probabilities of outliers to uniform if ignore_outliers is set. Parameters ---------- p_o : ndarray((T, N)) output probabilities """ if self.ignore_outliers: outliers = np.where(p_o.sum(axis=1)=...

def forward(A, pobs, pi, T=None, alpha_out=None, dtype=np.float32): """Compute P( obs | A, B, pi ) and all forward coefficients. Parameters ---------- A : ndarray((N,N), dtype = float) transition matrix of the hidden states pobs : ndarray((T,N), dtype = float) pobs[t,i] is the obser...

def backward(A, pobs, T=None, beta_out=None, dtype=np.float32): """Compute all backward coefficients. With scaling! Parameters ---------- A : ndarray((N,N), dtype = float) transition matrix of the hidden states pobs : ndarray((T,N), dtype = float) pobs[t,i] is the observation probab...

def transition_counts(alpha, beta, A, pobs, T=None, out=None, dtype=np.float32): """ Sum for all t the probability to transition from state i to state j. Parameters ---------- alpha : ndarray((T,N), dtype = float), optional, default = None alpha[t,i] is the ith forward coefficient of time t. ...

def viterbi(A, pobs, pi, dtype=np.float32): """ Estimate the hidden pathway of maximum likelihood using the Viterbi algorithm. Parameters ---------- A : ndarray((N,N), dtype = float) transition matrix of the hidden states pobs : ndarray((T,N), dtype = float) pobs[t,i] is the observa...

def sample_path(alpha, A, pobs, T=None, dtype=np.float32): """ alpha : ndarray((T,N), dtype = float), optional, default = None alpha[t,i] is the ith forward coefficient of time t. beta : ndarray((T,N), dtype = float), optional, default = None beta[t,i] is the ith forward coefficient of time ...

def coarse_grain_transition_matrix(P, M): """ Coarse grain transition matrix P using memberships M Computes .. math: Pc = (M' M)^-1 M' P M Parameters ---------- P : ndarray(n, n) microstate transition matrix M : ndarray(n, m) membership matrix. Membership to macros...

def regularize_hidden(p0, P, reversible=True, stationary=False, C=None, eps=None): """ Regularizes the hidden initial distribution and transition matrix. Makes sure that the hidden initial distribution and transition matrix have nonzero probabilities by setting them to eps and then renormalizing. Avoid...

def regularize_pobs(B, nonempty=None, separate=None, eps=None): """ Regularizes the output probabilities. Makes sure that the output probability distributions has nonzero probabilities by setting them to eps and then renormalizing. Avoids zeros that would cause estimation algorithms to crash or get stu...

def init_discrete_hmm_spectral(C_full, nstates, reversible=True, stationary=True, active_set=None, P=None, eps_A=None, eps_B=None, separate=None): """Initializes discrete HMM using spectral clustering of observation counts Initializes HMM as described in [1]_. First estimates a M...

def init_discrete_hmm_ml(C_full, nstates, reversible=True, stationary=True, active_set=None, P=None, eps_A=None, eps_B=None, separate=None): """Initializes discrete HMM using maximum likelihood of observation counts""" raise NotImplementedError('ML-initialization not yet implemented')

def update(self, Pi, Tij): r""" Updates the transition matrix and recomputes all derived quantities """ from msmtools import analysis as msmana # update transition matrix by copy self._Tij = np.array(Tij) assert msmana.is_transition_matrix(self._Tij), 'Given transition matrix is...

def is_stationary(self): r""" Whether the MSM is stationary, i.e. whether the initial distribution is the stationary distribution of the hidden transition matrix. """ # for disconnected matrices, the stationary distribution depends on the estimator, so we can't compute # it directly. Th...

def stationary_distribution(self): r""" Compute stationary distribution of hidden states if possible. Raises ------ ValueError if the HMM is not stationary """ assert _tmatrix_disconnected.is_connected(self._Tij, strong=False), \ 'No unique stationary distri...

def timescales(self): r""" Relaxation timescales of the hidden transition matrix Returns ------- ts : ndarray(m) relaxation timescales in units of the input trajectory time step, defined by :math:`-tau / ln | \lambda_i |, i = 2,...,nstates`, where :ma...

def lifetimes(self): r""" Lifetimes of states of the hidden transition matrix Returns ------- l : ndarray(nstates) state lifetimes in units of the input trajectory time step, defined by :math:`-tau / ln | p_{ii} |, i = 1,...,nstates`, where :math:`p_{...

def sub_hmm(self, states): r""" Returns HMM on a subset of states Returns the HMM restricted to the selected subset of states. Will raise exception if the hidden transition matrix cannot be normalized on this subset """ # restrict initial distribution pi_sub = self._Pi[...

def count_matrix(self): # TODO: does this belong here or to the BHMM sampler, or in a subclass containing HMM with data? """Compute the transition count matrix from hidden state trajectory. Returns ------- C : numpy.array with shape (nstates,nstates) C[i,j] is the nu...

def count_init(self): """Compute the counts at the first time step Returns ------- n : ndarray(nstates) n[i] is the number of trajectories starting in state i """ if self.hidden_state_trajectories is None: raise RuntimeError('HMM model does not h...

def collect_observations_in_state(self, observations, state_index): # TODO: this would work well in a subclass with data """Collect a vector of all observations belonging to a specified hidden state. Parameters ---------- observations : list of numpy.array List of ob...

def generate_synthetic_state_trajectory(self, nsteps, initial_Pi=None, start=None, stop=None, dtype=np.int32): """Generate a synthetic state trajectory. Parameters ---------- nsteps : int Number of steps in the synthetic state trajectory to be generated. initial_Pi :...

def generate_synthetic_observation_trajectory(self, length, initial_Pi=None): """Generate a synthetic realization of observables. Parameters ---------- length : int Length of synthetic state trajectory to be generated. initial_Pi : np.array of shape (nstates,), optio...

def generate_synthetic_observation_trajectories(self, ntrajectories, length, initial_Pi=None): """Generate a number of synthetic realization of observables from this model. Parameters ---------- ntrajectories : int The number of trajectories to be generated. length :...

def nb_to_python(nb_path): """convert notebook to python script""" exporter = python.PythonExporter() output, resources = exporter.from_filename(nb_path) return output

def nb_to_html(nb_path): """convert notebook to html""" exporter = html.HTMLExporter(template_file='full') output, resources = exporter.from_filename(nb_path) header = output.split('<head>', 1)[1].split('</head>',1)[0] body = output.split('<body>', 1)[1].split('</body>',1)[0] # http://imgur.com...

def p_obs(self, obs, out=None): """ Returns the output probabilities for an entire trajectory and all hidden states Parameters ---------- obs : ndarray((T), dtype=int) a discrete trajectory of length T Return ------ p_o : ndarray (T,N) ...

def estimate(self, observations, weights): """ Maximum likelihood estimation of output model given the observations and weights Parameters ---------- observations : [ ndarray(T_k) ] with K elements A list of K observation trajectories, each having length T_k ...

def sample(self, observations_by_state): """ Sample a new set of distribution parameters given a sample of observations from the given state. The internal parameters are updated. Parameters ---------- observations : [ numpy.array with shape (N_k,) ] with nstates elemen...

def generate_observation_from_state(self, state_index): """ Generate a single synthetic observation data from a given state. Parameters ---------- state_index : int Index of the state from which observations are to be generated. Returns ------- ...

def generate_observations_from_state(self, state_index, nobs): """ Generate synthetic observation data from a given state. Parameters ---------- state_index : int Index of the state from which observations are to be generated. nobs : int The numbe...

def generate_observation_trajectory(self, s_t, dtype=None): """ Generate synthetic observation data from a given state sequence. Parameters ---------- s_t : numpy.array with shape (T,) of int type s_t[t] is the hidden state sampled at time t Returns ...

def set_implementation(impl): """ Sets the implementation of this module Parameters ---------- impl : str One of ["python", "c"] """ global __impl__ if impl.lower() == 'python': __impl__ = __IMPL_PYTHON__ elif impl.lower() == 'c': __impl__ = __IMPL_C__ e...

def forward(A, pobs, pi, T=None, alpha_out=None): """Compute P( obs | A, B, pi ) and all forward coefficients. Parameters ---------- A : ndarray((N,N), dtype = float) transition matrix of the hidden states pobs : ndarray((T,N), dtype = float) pobs[t,i] is the observation probability...

def backward(A, pobs, T=None, beta_out=None): """Compute all backward coefficients. With scaling! Parameters ---------- A : ndarray((N,N), dtype = float) transition matrix of the hidden states pobs : ndarray((T,N), dtype = float) pobs[t,i] is the observation probability for observat...

def state_probabilities(alpha, beta, T=None, gamma_out=None): """ Calculate the (T,N)-probabilty matrix for being in state i at time t. Parameters ---------- alpha : ndarray((T,N), dtype = float), optional, default = None alpha[t,i] is the ith forward coefficient of time t. beta : ndarray((...

def state_counts(gamma, T, out=None): """ Sum the probabilities of being in state i to time t Parameters ---------- gamma : ndarray((T,N), dtype = float), optional, default = None gamma[t,i] is the probabilty at time t to be in state i ! T : int number of time steps Returns ...

def transition_counts(alpha, beta, A, pobs, T=None, out=None): """ Sum for all t the probability to transition from state i to state j. Parameters ---------- alpha : ndarray((T,N), dtype = float), optional, default = None alpha[t,i] is the ith forward coefficient of time t. beta : ndarray((...

def viterbi(A, pobs, pi): """ Estimate the hidden pathway of maximum likelihood using the Viterbi algorithm. Parameters ---------- A : ndarray((N,N), dtype = float) transition matrix of the hidden states pobs : ndarray((T,N), dtype = float) pobs[t,i] is the observation probability f...

def sample_path(alpha, A, pobs, T=None): """ Sample the hidden pathway S from the conditional distribution P ( S | Parameters, Observations ) Parameters ---------- alpha : ndarray((T,N), dtype = float), optional, default = None alpha[t,i] is the ith forward coefficient of time t. A : ndarra...

def logger(name='BHMM', pattern='%(asctime)s %(levelname)s %(name)s: %(message)s', date_format='%H:%M:%S', handler=logging.StreamHandler(sys.stdout)): """ Retrieves the logger instance associated to the given name. :param name: The name of the logger instance. :type name: str :param patt...

def sample(self, nsamples, nburn=0, nthin=1, save_hidden_state_trajectory=False, call_back=None): """Sample from the BHMM posterior. Parameters ---------- nsamples : int The number of samples to generate. nburn : int, optional, default=0 Th...

def _update(self): """Update the current model using one round of Gibbs sampling. """ initial_time = time.time() self._updateHiddenStateTrajectories() self._updateEmissionProbabilities() self._updateTransitionMatrix() final_time = time.time() elapsed_ti...

def _updateHiddenStateTrajectories(self): """Sample a new set of state trajectories from the conditional distribution P(S | T, E, O) """ self.model.hidden_state_trajectories = list() for trajectory_index in range(self.nobs): hidden_state_trajectory = self._sampleHiddenStateT...

def _sampleHiddenStateTrajectory(self, obs, dtype=np.int32): """Sample a hidden state trajectory from the conditional distribution P(s | T, E, o) Parameters ---------- o_t : numpy.array with dimensions (T,) observation[n] is the nth observation dtype : numpy.dtype, o...

def _updateEmissionProbabilities(self): """Sample a new set of emission probabilites from the conditional distribution P(E | S, O) """ observations_by_state = [self.model.collect_observations_in_state(self.observations, state) for state in range(self.model.nstat...

def _updateTransitionMatrix(self): """ Updates the hidden-state transition matrix and the initial distribution """ # TRANSITION MATRIX C = self.model.count_matrix() + self.prior_C # posterior count matrix # check if we work with these options if self.reversible...

def _generateInitialModel(self, output_model_type): """Initialize using an MLHMM. """ logger().info("Generating initial model for BHMM using MLHMM...") from bhmm.estimators.maximum_likelihood import MaximumLikelihoodEstimator mlhmm = MaximumLikelihoodEstimator(self.observations,...

def ensure_dtraj(dtraj): r"""Makes sure that dtraj is a discrete trajectory (array of int) """ if is_int_vector(dtraj): return dtraj elif is_list_of_int(dtraj): return np.array(dtraj, dtype=int) else: raise TypeError('Argument dtraj is not a discrete trajectory - only list o...

def ensure_dtraj_list(dtrajs): r"""Makes sure that dtrajs is a list of discrete trajectories (array of int) """ if isinstance(dtrajs, list): # elements are ints? then wrap into a list if is_list_of_int(dtrajs): return [np.array(dtrajs, dtype=int)] else: for i...

def connected_sets(C, mincount_connectivity=0, strong=True): """ Computes the connected sets of C. C : count matrix mincount_connectivity : float Minimum count which counts as a connection. strong : boolean True: Seek strongly connected sets. False: Seek weakly connected sets. """ ...

def closed_sets(C, mincount_connectivity=0): """ Computes the strongly connected closed sets of C """ n = np.shape(C)[0] S = connected_sets(C, mincount_connectivity=mincount_connectivity, strong=True) closed = [] for s in S: mask = np.zeros(n, dtype=bool) mask[s] = True if C[...

def nonempty_set(C, mincount_connectivity=0): """ Returns the set of states that have at least one incoming or outgoing count """ # truncate to states with at least one observed incoming or outgoing count. if mincount_connectivity > 0: C = C.copy() C[np.where(C < mincount_connectivity)] = 0 ...

def estimate_P(C, reversible=True, fixed_statdist=None, maxiter=1000000, maxerr=1e-8, mincount_connectivity=0): """ Estimates full transition matrix for general connectivity structure Parameters ---------- C : ndarray count matrix reversible : bool estimate reversible? fixed_sta...

def transition_matrix_partial_rev(C, P, S, maxiter=1000000, maxerr=1e-8): """Maximum likelihood estimation of transition matrix which is reversible on parts Partially-reversible estimation of transition matrix. Maximizes the likelihood: .. math: P_S &=& arg max prod_{S, :} (p_ij)^c_ij \\ \...

def enforce_reversible_on_closed(P): """ Enforces transition matrix P to be reversible on its closed sets. """ import msmtools.analysis as msmana n = np.shape(P)[0] Prev = P.copy() # treat each weakly connected set separately sets = closed_sets(P) for s in sets: I = np.ix_(s, s) ...

def is_reversible(P): """ Returns if P is reversible on its weakly connected sets """ import msmtools.analysis as msmana # treat each weakly connected set separately sets = connected_sets(P, strong=False) for s in sets: Ps = P[s, :][:, s] if not msmana.is_transition_matrix(Ps): ...

def stationary_distribution(P, C=None, mincount_connectivity=0): """ Simple estimator for stationary distribution for multiple strongly connected sets """ # can be replaced by msmtools.analysis.stationary_distribution in next msmtools release from msmtools.analysis.dense.stationary_vector import stationary_...

def means_samples(self): r""" Samples of the Gaussian distribution means """ res = np.empty((self.nsamples, self.nstates, self.dimension), dtype=config.dtype) for i in range(self.nsamples): for j in range(self.nstates): res[i, j, :] = self._sampled_hmms[i].means[j] ...

def sigmas_samples(self): r""" Samples of the Gaussian distribution standard deviations """ res = np.empty((self.nsamples, self.nstates, self.dimension), dtype=config.dtype) for i in range(self.nsamples): for j in range(self.nstates): res[i, j, :] = self._sampled_hmms...

def _guess_output_type(observations): """ Suggests a HMM model type based on the observation data Uses simple rules in order to decide which HMM model type makes sense based on observation data. If observations consist of arrays/lists of integer numbers (irrespective of whether the python type is int o...

def lag_observations(observations, lag, stride=1): r""" Create new trajectories that are subsampled at lag but shifted Given a trajectory (s0, s1, s2, s3, s4, ...) and lag 3, this function will generate 3 trajectories (s0, s3, s6, ...), (s1, s4, s7, ...) and (s2, s5, s8, ...). Use this function in order to...

def gaussian_hmm(pi, P, means, sigmas): """ Initializes a 1D-Gaussian HMM Parameters ---------- pi : ndarray(nstates, ) Initial distribution. P : ndarray(nstates,nstates) Hidden transition matrix means : ndarray(nstates, ) Means of Gaussian output distributions sigma...

def discrete_hmm(pi, P, pout): """ Initializes a discrete HMM Parameters ---------- pi : ndarray(nstates, ) Initial distribution. P : ndarray(nstates,nstates) Hidden transition matrix pout : ndarray(nstates,nsymbols) Output matrix from hidden states to observable symbols...

def init_hmm(observations, nstates, lag=1, output=None, reversible=True): """Use a heuristic scheme to generate an initial model. Parameters ---------- observations : list of ndarray((T_i)) list of arrays of length T_i with observation data nstates : int The number of states. ou...

def init_gaussian_hmm(observations, nstates, lag=1, reversible=True): """ Use a heuristic scheme to generate an initial model. Parameters ---------- observations : list of ndarray((T_i)) list of arrays of length T_i with observation data nstates : int The number of states. Exam...

def init_discrete_hmm(observations, nstates, lag=1, reversible=True, stationary=True, regularize=True, method='connect-spectral', separate=None): """Use a heuristic scheme to generate an initial model. Parameters ---------- observations : list of ndarray((T_i)) list of arr...

def estimate_hmm(observations, nstates, lag=1, initial_model=None, output=None, reversible=True, stationary=False, p=None, accuracy=1e-3, maxit=1000, maxit_P=100000, mincount_connectivity=1e-2): r""" Estimate maximum-likelihood HMM Generic maximum-likelihood estimation of HMMs...

def bayesian_hmm(observations, estimated_hmm, nsample=100, reversible=True, stationary=False, p0_prior='mixed', transition_matrix_prior='mixed', store_hidden=False, call_back=None): r""" Bayesian HMM based on sampling the posterior Generic maximum-likelihood estimation of HMMs Parameters ...

def logsumexp(arr, axis=0): """Computes the sum of arr assuming arr is in the log domain. Returns log(sum(exp(arr))) while minimizing the possibility of over/underflow. Examples -------- >>> import numpy as np >>> from sklearn.utils.extmath import logsumexp >>> a = np.arange(10) >...

def _ensure_sparse_format(spmatrix, accept_sparse, dtype, order, copy, force_all_finite): """Convert a sparse matrix to a given format. Checks the sparse format of spmatrix and converts if necessary. Parameters ---------- spmatrix : scipy sparse matrix Input to va...

def check_array(array, accept_sparse=None, dtype="numeric", order=None, copy=False, force_all_finite=True, ensure_2d=True, allow_nd=False, ensure_min_samples=1, ensure_min_features=1): """Input validation on an array, list, sparse matrix or similar. By default, the input is conv...

def beta_confidence_intervals(ci_X, ntrials, ci=0.95): """ Compute confidence intervals of beta distributions. Parameters ---------- ci_X : numpy.array Computed confidence interval estimate from `ntrials` experiments ntrials : int The number of trials that were run. ci : flo...

def empirical_confidence_interval(sample, interval=0.95): """ Compute specified symmetric confidence interval for empirical sample. Parameters ---------- sample : numpy.array The empirical samples. interval : float, optional, default=0.95 Size of desired symmetric confidence int...

def generate_latex_table(sampled_hmm, conf=0.95, dt=1, time_unit='ms', obs_name='force', obs_units='pN', caption='', outfile=None): """ Generate a LaTeX column-wide table showing various computed properties and uncertainties. Parameters ---------- conf : float confi...

def confidence_interval(data, alpha): """ Computes the mean and alpha-confidence interval of the given sample set Parameters ---------- data : ndarray a 1D-array of samples alpha : float in [0,1] the confidence level, i.e. percentage of data included in the interval ...