Transitions (Perturbation Kernels)¶
Perturbation strategies. The classes defined here transition the current population to the next one. pyABC implements global and local transitions. Proposals for the subsequent generation are generated from the current generation density estimates of the current generations. This is equivalent to perturbing randomly chosen particles.
These can be passed to pyabc.smc.ABCSMC
via the transitions
keyword argument.

class
pyabc.transition.
Transition
¶ Bases:
sklearn.base.BaseEstimator
Abstract Transition base class. Derive all Transitions from this class
Note
This class does a little bit of metaprogramming.
The fit, pdf and rvs methods are automatically wrapped to handle the special case of no parameters.
Hence, you can safely assume that you encounter at least one parameter. All the defined transitions will then automatically generalize to the case of no paramter.

fit
(X: pandas.core.frame.DataFrame, w: numpy.ndarray)¶ Fit the density estimator (perturber) to the sampled data. Concrete implementations might do something like fitting a KDE.
The parameters given as
X
andw
are automatically stored inself.X
andself.w
.Parameters:  X (pd.DataFrame) – The parameters.
 w (array) – The corresponding weights

mean_cv
(n_samples: Union[None, int] = None) → float¶ Estimate the uncertainty on the KDE.
Parameters: n_samples (int, optional) – Estimate the CV for n_samples
samples. If this parameter is not given, the sample size of the last fit is used.Returns: mean_cv – The estimated average coefficient of variation. Return type: float Note
A call to this method, as a side effect, also sets the attributes
test_points_
,test_weights_
andvariation_at_test_points_
. These are the individual points, weights and varations used to calculate the mean.

pdf
(x: Union[pandas.core.series.Series, pandas.core.frame.DataFrame]) → Union[float, numpy.ndarray]¶ Evaluate the probability density function (PDF) at x.
Parameters: x (pd.Series, pd.DataFrame) – Parameter. If x is a series, then x should have the the columns from X passed to the fit method as indices. If x is a DataFrame, then x should have the same columns as X passed before to the fit method. The order of the columns is not important Returns: density – Probability density at x. Return type: float

rvs
(size=None)¶ Sample from the density.
Parameters: size (int, optional) – Number of independent samples to draw. Defaults to 1 and is in this case equivalent to calling “rvs_single”. Returns: samples Return type: The samples as pandas DataFrame Note
This method can be overridden for efficient implementations. The default is to call rvs_single repeatedly (which might not be the most efficient way).

rvs_single
() → pandas.core.series.Series¶ Random variable sample (rvs).
Sample from the fitted distribution.
Returns: sample – A sample from the fitted model. Return type: pd.Series


class
pyabc.transition.
MultivariateNormalTransition
(scaling=1, bandwidth_selector=<function silverman_rule_of_thumb>)¶ Bases:
pyabc.transition.base.Transition
Transition via a multivariate Gaussian KDE estimate.
Parameters:  scaling (float) – Scaling is a factor which additionally multiplies the covariance with. Since Silverman and Scott usually have too large bandwidths, it should make most sense to have 0 < scaling <= 1
 bandwidth_selector (optional) – Defaults to silverman_rule_of_thumb. The bandwidth selector is a function of the form f(n_samples: float, dimension: int), where n_samples denotes the (effective) samples size (and is therefore) a float and dimension is the parameter dimension.

fit
(X: pandas.core.frame.DataFrame, w: numpy.ndarray)¶ Fit the density estimator (perturber) to the sampled data. Concrete implementations might do something like fitting a KDE.
The parameters given as
X
andw
are automatically stored inself.X
andself.w
.Parameters:  X (pd.DataFrame) – The parameters.
 w (array) – The corresponding weights

pdf
(x: Union[pandas.core.series.Series, pandas.core.frame.DataFrame])¶ Evaluate the probability density function (PDF) at x.
Parameters: x (pd.Series, pd.DataFrame) – Parameter. If x is a series, then x should have the the columns from X passed to the fit method as indices. If x is a DataFrame, then x should have the same columns as X passed before to the fit method. The order of the columns is not important Returns: density – Probability density at x. Return type: float

rvs_single
()¶ Random variable sample (rvs).
Sample from the fitted distribution.
Returns: sample – A sample from the fitted model. Return type: pd.Series

class
pyabc.transition.
GridSearchCV
(estimator, param_grid, scoring=None, fit_params=None, n_jobs=1, iid=True, refit=True, cv=5, verbose=0, pre_dispatch='2*n_jobs', error_score='raise', return_train_score=True)¶ Bases:
sklearn.model_selection._search.GridSearchCV
Do a grid search to automatically select the best parameters for transition classes such as the
pyabc.transition.MultivariateNormalTransition
.This is essentially a thin wrapper around ‘sklearn.model_selection.GridSearchCV’. It translates the scikitlearn interface to the interface used in pyABC. It implements hence a thin adapter pattern.

fit
(X, y=None, groups=None)¶ Run fit with all sets of parameters.
Parameters:  X (arraylike, shape = [n_samples, n_features]) – Training vector, where n_samples is the number of samples and n_features is the number of features.
 y (arraylike, shape = [n_samples] or [n_samples, n_output], optional) – Target relative to X for classification or regression; None for unsupervised learning.
 groups (arraylike, with shape (n_samples,), optional) – Group labels for the samples used while splitting the dataset into train/test set.
 **fit_params (dict of string > object) – Parameters passed to the
fit
method of the estimator


exception
pyabc.transition.
NotEnoughParticles
¶ Bases:
Exception

class
pyabc.transition.
LocalTransition
(k=None, k_fraction=0.25, scaling=1)¶ Bases:
pyabc.transition.base.Transition
Local KDE fit. Takes into account only the k nearest neighbors, similar to [Filippi].
Parameters:  k (int) – Number of nearest neighbors for local covariance calculation.
 scaling (float) – Scaling factor for the local covariance matrices.
 k_fraction (float, optional) – Calculate number of nearest neighbors to use according to
k = k_fraction * population_size
(and rounds it).

EPS
¶ Scaling of the identity matrix to be added to the covariance in case the covariances are not invertible.
Type: float
[Filippi] Filippi, Sarah, Chris P. Barnes, Julien Cornebise, and Michael P.H. Stumpf. “On Optimality of Kernels for Approximate Bayesian Computation Using Sequential Monte Carlo.” Statistical Applications in Genetics and Molecular Biology 12, no. 1 (2013): 87–107. doi:10.1515/sagmb20120069. 
fit
(X, w)¶ Fit the density estimator (perturber) to the sampled data. Concrete implementations might do something like fitting a KDE.
The parameters given as
X
andw
are automatically stored inself.X
andself.w
.Parameters:  X (pd.DataFrame) – The parameters.
 w (array) – The corresponding weights

pdf
(x)¶ Evaluate the probability density function (PDF) at x.
Parameters: x (pd.Series, pd.DataFrame) – Parameter. If x is a series, then x should have the the columns from X passed to the fit method as indices. If x is a DataFrame, then x should have the same columns as X passed before to the fit method. The order of the columns is not important Returns: density – Probability density at x. Return type: float

rvs_single
()¶ Random variable sample (rvs).
Sample from the fitted distribution.
Returns: sample – A sample from the fitted model. Return type: pd.Series

pyabc.transition.
scott_rule_of_thumb
(n_samples, dimension)¶ Scott’s rule of thumb.
\[\left ( \frac{1}{n} \right ) ^{\frac{1}{d+4}}\](see also scipy.stats.kde.gaussian_kde.scotts_factor)

pyabc.transition.
silverman_rule_of_thumb
(n_samples, dimension)¶ Silverman’s rule of thumb.
\[\left ( \frac{4}{n (d+2)} \right ) ^ {\frac{1}{d + 4}}\](see also scipy.stats.kde.gaussian_kde.silverman_factor)