API¶
This file describes the classes and methods available in ELFI.
Modelling API¶
Below is the API for creating generative models.
elfi.ElfiModel ([name, observed, source_net]) 
A container for the inference model. 
General model nodes
elfi.Constant (value, **kwargs) 
A node holding a constant value. 
elfi.Operation (fn, *parents, **kwargs) 
A generic deterministic operation node. 
elfi.RandomVariable (distribution, *params[, …]) 
A node that draws values from a random distribution. 
LFI nodes
elfi.Prior (distribution, *params[, size]) 
A parameter node of an ELFI graph. 
elfi.Simulator (fn, *params, **kwargs) 
A simulator node of an ELFI graph. 
elfi.Summary (fn, *parents, **kwargs) 
A summary node of an ELFI graph. 
elfi.Discrepancy (discrepancy, *parents, **kwargs) 
A discrepancy node of an ELFI graph. 
elfi.Distance (distance, *summaries, **kwargs) 
A convenience class for the discrepancy node. 
Other
elfi.new_model ([name, set_default]) 
Create a new ElfiModel instance. 
elfi.load_model (name[, prefix, set_default]) 
Load the pickled ElfiModel. 
elfi.get_default_model () 
Return the current default ElfiModel instance. 
elfi.set_default_model ([model]) 
Set the current default ElfiModel instance. 
elfi.draw (G[, internal, param_names, …]) 
Draw the ElfiModel. 
elfi.plot_params_vs_node (node[, n_samples, …]) 
Plot some realizations of parameters vs. 
Inference API¶
Below is a list of inference methods included in ELFI.
elfi.Rejection (model[, discrepancy_name, …]) 
Parallel ABC rejection sampler. 
elfi.SMC (model[, discrepancy_name, output_names]) 
Sequential Monte Carlo ABC sampler. 
elfi.BayesianOptimization (model[, …]) 
Bayesian Optimization of an unknown target function. 
elfi.BOLFI (model[, target_name, bounds, …]) 
Bayesian Optimization for LikelihoodFree Inference (BOLFI). 
Result objects
OptimizationResult (x_min, **kwargs) 
Base class for results from optimization. 
Sample (method_name, outputs, parameter_names) 
Sampling results from inference methods. 
SmcSample (method_name, outputs, …) 
Container for results from SMCABC. 
BolfiSample (method_name, chains, …) 
Container for results from BOLFI. 
Postprocessing
elfi.adjust_posterior (sample, model, …[, …]) 
Adjust the posterior using local regression. 
LinearAdjustment (**kwargs) 
Regression adjustment using a local linear model. 
Diagnostics
elfi.TwoStageSelection (simulator, fn_distance) 
Perform the summarystatistics selection proposed by Nunes and Balding (2010). 
Acquisition methods
LCBSC (*args[, delta]) 
Lower Confidence Bound Selection Criterion. 
MaxVar ([quantile_eps]) 
The maximum variance acquisition method. 
RandMaxVar ([quantile_eps, sampler, …]) 
The randomised maximum variance acquisition method. 
ExpIntVar ([quantile_eps, integration, …]) 
The Expected Integrated Variance (ExpIntVar) acquisition method. 
UniformAcquisition (model[, prior, n_inits, …]) 
Acquisition from uniform distribution. 
Other¶
Data pools
elfi.OutputPool ([outputs, name, prefix]) 
Store node outputs to dictionarylike stores. 
elfi.ArrayPool ([outputs, name, prefix]) 
OutputPool that uses binary .npy files as default stores. 
Module functions
elfi.get_client () 
Get the current ELFI client instance. 
elfi.set_client ([client]) 
Set the current ELFI client instance. 
Tools
elfi.tools.vectorize (operation[, constants, …]) 
Vectorize an operation. 
elfi.tools.external_operation (command[, …]) 
Wrap an external command as a Python callable (function). 
Class documentations¶
Modelling API classes¶

class
elfi.
ElfiModel
(name=None, observed=None, source_net=None)[source]¶ A container for the inference model.
The ElfiModel is a directed acyclic graph (DAG), whose nodes represent parts of the inference task, for example the parameters to be inferred, the simulator or a summary statistic.
Initialize the inference model.
Parameters:  name (str, optional) –
 observed (dict, optional) – Observed data with node names as keys.
 source_net (nx.DiGraph, optional) –
 set_current (bool, optional) – Sets this model as the current (default) ELFI model

generate
(batch_size=1, outputs=None, with_values=None, seed=None)[source]¶ Generate a batch of outputs.
This method is useful for testing that the ELFI graph works.
Parameters:  batch_size (int, optional) –
 outputs (list, optional) –
 with_values (dict, optional) – You can specify values for nodes to use when generating data
 seed (int, optional) – Defaults to global numpy seed.

get_reference
(name)[source]¶ Return a new reference object for a node in the model.
Parameters: name (str) –

classmethod
load
(name, prefix)[source]¶ Load the pickled ElfiModel.
Assumes there exists a file “name.pkl” in the current directory.
Parameters:  name (str) – Name of the model file to load (without the .pkl extension).
 prefix (str) – Path to directory where the model file is located, optional.
Returns: Return type:

name
¶ Return name of the model.

observed
¶ Return the observed data for the nodes in a dictionary.

parameter_names
¶ Return a list of model parameter names in an alphabetical order.

class
elfi.
Constant
(value, **kwargs)[source]¶ A node holding a constant value.
Initialize a node holding a constant value.
Parameters: value – The constant value of the node. 
become
(other_node)¶ Make this node become the other_node.
The children of this node will be preserved.
Parameters: other_node (NodeReference) –

generate
(batch_size=1, with_values=None)¶ Generate output from this node.
Useful for testing.
Parameters:  batch_size (int, optional) –
 with_values (dict, optional) –

parents
¶ Get all positional parent nodes (inputs) of this node.
Returns: parents – List of positional parents Return type: list

classmethod
reference
(name, model)¶ Construct a reference for an existing node in the model.
Parameters:  name (string) – name of the node
 model (ElfiModel) –
Returns: Return type: NodePointer instance

state
¶ Return the state dictionary of the node.


class
elfi.
Operation
(fn, *parents, **kwargs)[source]¶ A generic deterministic operation node.
Initialize a node that performs an operation.
Parameters: fn (callable) – The operation of the node. 
become
(other_node)¶ Make this node become the other_node.
The children of this node will be preserved.
Parameters: other_node (NodeReference) –

generate
(batch_size=1, with_values=None)¶ Generate output from this node.
Useful for testing.
Parameters:  batch_size (int, optional) –
 with_values (dict, optional) –

parents
¶ Get all positional parent nodes (inputs) of this node.
Returns: parents – List of positional parents Return type: list

classmethod
reference
(name, model)¶ Construct a reference for an existing node in the model.
Parameters:  name (string) – name of the node
 model (ElfiModel) –
Returns: Return type: NodePointer instance

state
¶ Return the state dictionary of the node.


class
elfi.
RandomVariable
(distribution, *params, size=None, **kwargs)[source]¶ A node that draws values from a random distribution.
Initialize a node that represents a random variable.
Parameters:  distribution (str or scipylike distribution object) –
 params (params of the distribution) –
 size (int, tuple or None, optional) – Output size of a single random draw.

become
(other_node)¶ Make this node become the other_node.
The children of this node will be preserved.
Parameters: other_node (NodeReference) –

static
compile_operation
(state)[source]¶ Compile a callable operation that samples the associated distribution.
Parameters: state (dict) –

distribution
¶ Return the distribution object.

generate
(batch_size=1, with_values=None)¶ Generate output from this node.
Useful for testing.
Parameters:  batch_size (int, optional) –
 with_values (dict, optional) –

parents
¶ Get all positional parent nodes (inputs) of this node.
Returns: parents – List of positional parents Return type: list

classmethod
reference
(name, model)¶ Construct a reference for an existing node in the model.
Parameters:  name (string) – name of the node
 model (ElfiModel) –
Returns: Return type: NodePointer instance

size
¶ Return the size of the output from the distribution.

state
¶ Return the state dictionary of the node.

class
elfi.
Prior
(distribution, *params, size=None, **kwargs)[source]¶ A parameter node of an ELFI graph.
Initialize a Prior.
Parameters:  distribution (str, object) – Any distribution from scipy.stats, either as a string or an object. Objects must implement at least an rvs method with signature rvs(*parameters, size, random_state). Can also be a custom distribution object that implements at least an rvs method. Many of the algorithms also require the pdf and logpdf methods to be available.
 size (int, tuple or None, optional) – Output size of a single random draw.
 params – Parameters of the prior distribution
 kwargs –
Notes
The parameters of the scipy distributions (typically loc and scale) must be given as positional arguments.
Many algorithms (e.g. SMC) also require a pdf method for the distribution. In general the definition of the distribution is a subset of scipy.stats.rv_continuous.
Scipy distributions: https://docs.scipy.org/doc/scipy0.19.0/reference/stats.html

become
(other_node)¶ Make this node become the other_node.
The children of this node will be preserved.
Parameters: other_node (NodeReference) –

static
compile_operation
(state)¶ Compile a callable operation that samples the associated distribution.
Parameters: state (dict) –

distribution
¶ Return the distribution object.

generate
(batch_size=1, with_values=None)¶ Generate output from this node.
Useful for testing.
Parameters:  batch_size (int, optional) –
 with_values (dict, optional) –

parents
¶ Get all positional parent nodes (inputs) of this node.
Returns: parents – List of positional parents Return type: list

classmethod
reference
(name, model)¶ Construct a reference for an existing node in the model.
Parameters:  name (string) – name of the node
 model (ElfiModel) –
Returns: Return type: NodePointer instance

size
¶ Return the size of the output from the distribution.

state
¶ Return the state dictionary of the node.

class
elfi.
Simulator
(fn, *params, **kwargs)[source]¶ A simulator node of an ELFI graph.
Simulator nodes are stochastic and may have observed data in the model.
Initialize a Simulator.
Parameters:  fn (callable) – Simulator function with a signature sim(*params, batch_size, random_state)
 params – Input parameters for the simulator.
 kwargs –

become
(other_node)¶ Make this node become the other_node.
The children of this node will be preserved.
Parameters: other_node (NodeReference) –

generate
(batch_size=1, with_values=None)¶ Generate output from this node.
Useful for testing.
Parameters:  batch_size (int, optional) –
 with_values (dict, optional) –

parents
¶ Get all positional parent nodes (inputs) of this node.
Returns: parents – List of positional parents Return type: list

classmethod
reference
(name, model)¶ Construct a reference for an existing node in the model.
Parameters:  name (string) – name of the node
 model (ElfiModel) –
Returns: Return type: NodePointer instance

state
¶ Return the state dictionary of the node.

class
elfi.
Summary
(fn, *parents, **kwargs)[source]¶ A summary node of an ELFI graph.
Summary nodes are deterministic operations associated with the observed data. if their parents hold observed data it will be automatically transformed.
Initialize a Summary.
Parameters:  fn (callable) – Summary function with a signature summary(*parents)
 parents – Input data for the summary function.
 kwargs –

become
(other_node)¶ Make this node become the other_node.
The children of this node will be preserved.
Parameters: other_node (NodeReference) –

generate
(batch_size=1, with_values=None)¶ Generate output from this node.
Useful for testing.
Parameters:  batch_size (int, optional) –
 with_values (dict, optional) –

parents
¶ Get all positional parent nodes (inputs) of this node.
Returns: parents – List of positional parents Return type: list

classmethod
reference
(name, model)¶ Construct a reference for an existing node in the model.
Parameters:  name (string) – name of the node
 model (ElfiModel) –
Returns: Return type: NodePointer instance

state
¶ Return the state dictionary of the node.

class
elfi.
Discrepancy
(discrepancy, *parents, **kwargs)[source]¶ A discrepancy node of an ELFI graph.
This class provides a convenience node for custom distance operations.
Initialize a Discrepancy.
Parameters:  discrepancy (callable) – Signature of the discrepancy function is of the form: discrepancy(summary_1, summary_2, …, observed), where summaries are arrays containing batch_size simulated values and observed is a tuple (observed_summary_1, observed_summary_2, …). The callable object should return a vector of discrepancies between the simulated summaries and the observed summaries.
 *parents – Typically the summaries for the discrepancy function.
 **kwargs –
See also
elfi.Distance
 creating common distance discrepancies.

become
(other_node)¶ Make this node become the other_node.
The children of this node will be preserved.
Parameters: other_node (NodeReference) –

generate
(batch_size=1, with_values=None)¶ Generate output from this node.
Useful for testing.
Parameters:  batch_size (int, optional) –
 with_values (dict, optional) –

parents
¶ Get all positional parent nodes (inputs) of this node.
Returns: parents – List of positional parents Return type: list

classmethod
reference
(name, model)¶ Construct a reference for an existing node in the model.
Parameters:  name (string) – name of the node
 model (ElfiModel) –
Returns: Return type: NodePointer instance

state
¶ Return the state dictionary of the node.

class
elfi.
Distance
(distance, *summaries, **kwargs)[source]¶ A convenience class for the discrepancy node.
Initialize a distance node of an ELFI graph.
This class contains many common distance implementations through scipy.
Parameters:  distance (str, callable) –
If string it must be a valid metric from scipy.spatial.distance.cdist.
Is a callable, the signature must be distance(X, Y), where X is a n x m array containing n simulated values (summaries) in rows and Y is a 1 x m array that contains the observed values (summaries). The callable should return a vector of distances between the simulated summaries and the observed summaries.
 *summaries – Summary nodes of the model.
 **kwargs – Additional parameters may be required depending on the chosen distance. See the scipy documentation. (The support is not exhaustive.) ELFIrelated kwargs are passed on to elfi.Discrepancy.
Examples
>>> d = elfi.Distance('euclidean', summary1, summary2...)
>>> d = elfi.Distance('minkowski', summary, p=1)
Notes
Your summaries need to be scalars or vectors for this method to work. The summaries will be first stacked to a single 2D array with the simulated summaries in the rows for every simulation and the distance is taken row wise against the corresponding observed summary vector.
Scipy distances: https://docs.scipy.org/doc/scipy/reference/generated/generated/scipy.spatial.distance.cdist.html # noqa
See also
elfi.Discrepancy
 A general discrepancy node

become
(other_node)¶ Make this node become the other_node.
The children of this node will be preserved.
Parameters: other_node (NodeReference) –

generate
(batch_size=1, with_values=None)¶ Generate output from this node.
Useful for testing.
Parameters:  batch_size (int, optional) –
 with_values (dict, optional) –

parents
¶ Get all positional parent nodes (inputs) of this node.
Returns: parents – List of positional parents Return type: list

classmethod
reference
(name, model)¶ Construct a reference for an existing node in the model.
Parameters:  name (string) – name of the node
 model (ElfiModel) –
Returns: Return type: NodePointer instance

state
¶ Return the state dictionary of the node.
 distance (str, callable) –
Other

elfi.
new_model
(name=None, set_default=True)[source]¶ Create a new
ElfiModel
instance.In addition to making a new ElfiModel instance, this method sets the new instance as the default for new nodes.
Parameters:  name (str, optional) –
 set_default (bool, optional) – Whether to set the newly created model as the current model.

elfi.
load_model
(name, prefix=None, set_default=True)[source]¶ Load the pickled ElfiModel.
Assumes there exists a file “name.pkl” in the current directory. Also sets the loaded model as the default model for new nodes.
Parameters:  name (str) – Name of the model file to load (without the .pkl extension).
 prefix (str) – Path to directory where the model file is located, optional.
 set_default (bool, optional) – Set the loaded model as the default model. Default is True.
Returns: Return type:

elfi.
get_default_model
()[source]¶ Return the current default
ElfiModel
instance.New nodes will be added to this model by default.

elfi.
set_default_model
(model=None)[source]¶ Set the current default
ElfiModel
instance.New nodes will be placed the given model by default.
Parameters: model (ElfiModel, optional) – If None, creates a new ElfiModel
.

elfi.
draw
(G, internal=False, param_names=False, filename=None, format=None)¶ Draw the ElfiModel.
Parameters:  G (nx.DiGraph or ElfiModel) – Graph or model to draw
 internal (boolean, optional) – Whether to draw internal nodes (starting with an underscore)
 param_names (bool, optional) – Show param names on edges
 filename (str, optional) – If given, save the dot file into the given filename.
 format (str, optional) – format of the file
Notes
Requires the optional ‘graphviz’ library.
Returns: A GraphViz dot representation of the model. Return type: dot

elfi.
plot_params_vs_node
(node, n_samples=100, func=None, seed=None, axes=None, **kwargs)[source]¶ Plot some realizations of parameters vs. node.
Useful e.g. for exploring how a summary statistic varies with parameters. Currently only nodes with scalar output are supported, though a function func can be given to reduce node output. This allows giving the simulator as the node and applying a summarizing function without incorporating it into the ELFI graph.
If node is one of the model parameters, its histogram is plotted.
Parameters:  node (elfi.NodeReference) – The node which to evaluate. Its output must be scalar (shape=(batch_size,1)).
 n_samples (int, optional) – How many samples to plot.
 func (callable, optional) – A function to apply to node output.
 seed (int, optional) –
 axes (one or an iterable of plt.Axes, optional) –
Returns: axes
Return type: np.array of plt.Axes
Inference API classes¶

class
elfi.
Rejection
(model, discrepancy_name=None, output_names=None, **kwargs)[source]¶ Parallel ABC rejection sampler.
For a description of the rejection sampler and a general introduction to ABC, see e.g. Lintusaari et al. 2016.
References
Lintusaari J, Gutmann M U, Dutta R, Kaski S, Corander J (2016). Fundamentals and Recent Developments in Approximate Bayesian Computation. Systematic Biology. http://dx.doi.org/10.1093/sysbio/syw077.
Initialize the Rejection sampler.
Parameters:  model (ElfiModel or NodeReference) –
 discrepancy_name (str, NodeReference, optional) – Only needed if model is an ElfiModel
 output_names (list, optional) – Additional outputs from the model to be included in the inference result, e.g. corresponding summaries to the acquired samples
 kwargs – See InferenceMethod

batch_size
¶ Return the current batch_size.

extract_result
()[source]¶ Extract the result from the current state.
Returns: result Return type: Sample

infer
(*args, vis=None, bar=True, **kwargs)¶ Set the objective and start the iterate loop until the inference is finished.
See the other arguments from the set_objective method.
Parameters:  vis (dict, optional) – Plotting options. More info in self.plot_state method
 bar (bool, optional) – Flag to remove (False) or keep (True) the progress bar from/in output.
Returns: result
Return type:

iterate
()¶ Advance the inference by one iteration.
This is a way to manually progress the inference. One iteration consists of waiting and processing the result of the next batch in succession and possibly submitting new batches.
Notes
If the next batch is ready, it will be processed immediately and no new batches are submitted.
New batches are submitted only while waiting for the next one to complete. There will never be more batches submitted in parallel than the max_parallel_batches setting allows.
Returns: Return type: None

parameter_names
¶ Return the parameters to be inferred.

plot_state
(**options)[source]¶ Plot the current state of the inference algorithm.
This feature is still experimental and only supports 1d or 2d cases.

pool
¶ Return the output pool of the inference.

prepare_new_batch
(batch_index)¶ Prepare values for a new batch.
ELFI calls this method before submitting a new batch with an increasing index batch_index. This is an optional method to override. Use this if you have a need do do preparations, e.g. in Bayesian optimization algorithm, the next acquisition points would be acquired here.
If you need provide values for certain nodes, you can do so by constructing a batch dictionary and returning it. See e.g. BayesianOptimization for an example.
Parameters: batch_index (int) – next batch_index to be submitted Returns: batch – Keys should match to node names in the model. These values will override any default values or operations in those nodes. Return type: dict or None

sample
(n_samples, *args, **kwargs)¶ Sample from the approximate posterior.
See the other arguments from the set_objective method.
Parameters:  n_samples (int) – Number of samples to generate from the (approximate) posterior
 *args –
 **kwargs –
Returns: result
Return type:

seed
¶ Return the seed of the inference.

set_objective
(n_samples, threshold=None, quantile=None, n_sim=None)[source]¶ Set objective for inference.
Parameters:  n_samples (int) – number of samples to generate
 threshold (float) – Acceptance threshold
 quantile (float) – In between (0,1). Define the threshold as the pquantile of all the simulations. n_sim = n_samples/quantile.
 n_sim (int) – Total number of simulations. The threshold will be the n_samples smallest discrepancy among n_sim simulations.

class
elfi.
SMC
(model, discrepancy_name=None, output_names=None, **kwargs)[source]¶ Sequential Monte Carlo ABC sampler.
Initialize the SMCABC sampler.
Parameters:  model (ElfiModel or NodeReference) –
 discrepancy_name (str, NodeReference, optional) – Only needed if model is an ElfiModel
 output_names (list, optional) – Additional outputs from the model to be included in the inference result, e.g. corresponding summaries to the acquired samples
 kwargs – See InferenceMethod

batch_size
¶ Return the current batch_size.

current_population_threshold
¶ Return the threshold for current population.

infer
(*args, vis=None, bar=True, **kwargs)¶ Set the objective and start the iterate loop until the inference is finished.
See the other arguments from the set_objective method.
Parameters:  vis (dict, optional) – Plotting options. More info in self.plot_state method
 bar (bool, optional) – Flag to remove (False) or keep (True) the progress bar from/in output.
Returns: result
Return type:

iterate
()¶ Advance the inference by one iteration.
This is a way to manually progress the inference. One iteration consists of waiting and processing the result of the next batch in succession and possibly submitting new batches.
Notes
If the next batch is ready, it will be processed immediately and no new batches are submitted.
New batches are submitted only while waiting for the next one to complete. There will never be more batches submitted in parallel than the max_parallel_batches setting allows.
Returns: Return type: None

parameter_names
¶ Return the parameters to be inferred.

plot_state
(**kwargs)¶ Plot the current state of the algorithm.
Parameters:  axes (matplotlib.axes.Axes (optional)) –
 figure (matplotlib.figure.Figure (optional)) –
 xlim – xaxis limits
 ylim – yaxis limits
 interactive (bool (default False)) – If true, uses IPython.display to update the cell figure
 close – Close figure in the end of plotting. Used in the end of interactive mode.
Returns: Return type: None

pool
¶ Return the output pool of the inference.

prepare_new_batch
(batch_index)[source]¶ Prepare values for a new batch.
Parameters: batch_index (int) – next batch_index to be submitted Returns: batch – Keys should match to node names in the model. These values will override any default values or operations in those nodes. Return type: dict or None

sample
(n_samples, *args, **kwargs)¶ Sample from the approximate posterior.
See the other arguments from the set_objective method.
Parameters:  n_samples (int) – Number of samples to generate from the (approximate) posterior
 *args –
 **kwargs –
Returns: result
Return type:

seed
¶ Return the seed of the inference.

class
elfi.
BayesianOptimization
(model, target_name=None, bounds=None, initial_evidence=None, update_interval=10, target_model=None, acquisition_method=None, acq_noise_var=0, exploration_rate=10, batch_size=1, batches_per_acquisition=None, async=False, **kwargs)[source]¶ Bayesian Optimization of an unknown target function.
Initialize Bayesian optimization.
Parameters:  model (ElfiModel or NodeReference) –
 target_name (str or NodeReference) – Only needed if model is an ElfiModel
 bounds (dict, optional) – The region where to estimate the posterior for each parameter in model.parameters: dict(‘parameter_name’:(lower, upper), … )`. Not used if custom target_model is given.
 initial_evidence (int, dict, optional) – Number of initial evidence or a precomputed batch dict containing parameter and discrepancy values. Default value depends on the dimensionality.
 update_interval (int, optional) – How often to update the GP hyperparameters of the target_model
 target_model (GPyRegression, optional) –
 acquisition_method (Acquisition, optional) – Method of acquiring evidence points. Defaults to LCBSC.
 acq_noise_var (float or np.array, optional) – Variance(s) of the noise added in the default LCBSC acquisition method. If an array, should be 1d specifying the variance for each dimension.
 exploration_rate (float, optional) – Exploration rate of the acquisition method
 batch_size (int, optional) – Elfi batch size. Defaults to 1.
 batches_per_acquisition (int, optional) – How many batches will be requested from the acquisition function at one go. Defaults to max_parallel_batches.
 async (bool, optional) – Allow acquisitions to be made asynchronously, i.e. do not wait for all the results from the previous acquisition before making the next. This can be more efficient with a large amount of workers (e.g. in cluster environments) but forgoes the guarantee for the exactly same result with the same initial conditions (e.g. the seed). Default False.
 **kwargs –

acq_batch_size
¶ Return the total number of acquisition per iteration.

batch_size
¶ Return the current batch_size.

extract_result
()[source]¶ Extract the result from the current state.
Returns: Return type: OptimizationResult

infer
(*args, vis=None, bar=True, **kwargs)¶ Set the objective and start the iterate loop until the inference is finished.
See the other arguments from the set_objective method.
Parameters:  vis (dict, optional) – Plotting options. More info in self.plot_state method
 bar (bool, optional) – Flag to remove (False) or keep (True) the progress bar from/in output.
Returns: result
Return type:

iterate
()¶ Advance the inference by one iteration.
This is a way to manually progress the inference. One iteration consists of waiting and processing the result of the next batch in succession and possibly submitting new batches.
Notes
If the next batch is ready, it will be processed immediately and no new batches are submitted.
New batches are submitted only while waiting for the next one to complete. There will never be more batches submitted in parallel than the max_parallel_batches setting allows.
Returns: Return type: None

n_evidence
¶ Return the number of acquired evidence points.

parameter_names
¶ Return the parameters to be inferred.

plot_discrepancy
(axes=None, **kwargs)[source]¶ Plot acquired parameters vs. resulting discrepancy.
TODO: refactor

plot_state
(**options)[source]¶ Plot the GP surface.
This feature is still experimental and currently supports only 2D cases.

pool
¶ Return the output pool of the inference.

prepare_new_batch
(batch_index)[source]¶ Prepare values for a new batch.
Parameters: batch_index (int) – next batch_index to be submitted Returns: batch – Keys should match to node names in the model. These values will override any default values or operations in those nodes. Return type: dict or None

seed
¶ Return the seed of the inference.

class
elfi.
BOLFI
(model, target_name=None, bounds=None, initial_evidence=None, update_interval=10, target_model=None, acquisition_method=None, acq_noise_var=0, exploration_rate=10, batch_size=1, batches_per_acquisition=None, async=False, **kwargs)[source]¶ Bayesian Optimization for LikelihoodFree Inference (BOLFI).
Approximates the discrepancy function by a stochastic regression model. Discrepancy model is fit by sampling the discrepancy function at points decided by the acquisition function.
The method implements the framework introduced in Gutmann & Corander, 2016.
References
Gutmann M U, Corander J (2016). Bayesian Optimization for LikelihoodFree Inference of SimulatorBased Statistical Models. JMLR 17(125):1−47, 2016. http://jmlr.org/papers/v17/15017.html
Initialize Bayesian optimization.
Parameters:  model (ElfiModel or NodeReference) –
 target_name (str or NodeReference) – Only needed if model is an ElfiModel
 bounds (dict, optional) – The region where to estimate the posterior for each parameter in model.parameters: dict(‘parameter_name’:(lower, upper), … )`. Not used if custom target_model is given.
 initial_evidence (int, dict, optional) – Number of initial evidence or a precomputed batch dict containing parameter and discrepancy values. Default value depends on the dimensionality.
 update_interval (int, optional) – How often to update the GP hyperparameters of the target_model
 target_model (GPyRegression, optional) –
 acquisition_method (Acquisition, optional) – Method of acquiring evidence points. Defaults to LCBSC.
 acq_noise_var (float or np.array, optional) – Variance(s) of the noise added in the default LCBSC acquisition method. If an array, should be 1d specifying the variance for each dimension.
 exploration_rate (float, optional) – Exploration rate of the acquisition method
 batch_size (int, optional) – Elfi batch size. Defaults to 1.
 batches_per_acquisition (int, optional) – How many batches will be requested from the acquisition function at one go. Defaults to max_parallel_batches.
 async (bool, optional) – Allow acquisitions to be made asynchronously, i.e. do not wait for all the results from the previous acquisition before making the next. This can be more efficient with a large amount of workers (e.g. in cluster environments) but forgoes the guarantee for the exactly same result with the same initial conditions (e.g. the seed). Default False.
 **kwargs –

acq_batch_size
¶ Return the total number of acquisition per iteration.

batch_size
¶ Return the current batch_size.

extract_posterior
(threshold=None)[source]¶ Return an object representing the approximate posterior.
The approximation is based on surrogate model regression.
Parameters: threshold (float, optional) – Discrepancy threshold for creating the posterior (log with log discrepancy). Returns: posterior Return type: elfi.methods.posteriors.BolfiPosterior

extract_result
()¶ Extract the result from the current state.
Returns: Return type: OptimizationResult

fit
(n_evidence, threshold=None, bar=True)[source]¶ Fit the surrogate model.
Generates a regression model for the discrepancy given the parameters.
Currently only Gaussian processes are supported as surrogate models.
Parameters:  n_evidence (int, required) – Number of evidence for fitting
 threshold (float, optional) – Discrepancy threshold for creating the posterior (log with log discrepancy).
 bar (bool, optional) – Flag to remove (False) the progress bar from output.

infer
(*args, vis=None, bar=True, **kwargs)¶ Set the objective and start the iterate loop until the inference is finished.
See the other arguments from the set_objective method.
Parameters:  vis (dict, optional) – Plotting options. More info in self.plot_state method
 bar (bool, optional) – Flag to remove (False) or keep (True) the progress bar from/in output.
Returns: result
Return type:

iterate
()¶ Advance the inference by one iteration.
This is a way to manually progress the inference. One iteration consists of waiting and processing the result of the next batch in succession and possibly submitting new batches.
Notes
If the next batch is ready, it will be processed immediately and no new batches are submitted.
New batches are submitted only while waiting for the next one to complete. There will never be more batches submitted in parallel than the max_parallel_batches setting allows.
Returns: Return type: None

n_evidence
¶ Return the number of acquired evidence points.

parameter_names
¶ Return the parameters to be inferred.

plot_discrepancy
(axes=None, **kwargs)¶ Plot acquired parameters vs. resulting discrepancy.
TODO: refactor

plot_state
(**options)¶ Plot the GP surface.
This feature is still experimental and currently supports only 2D cases.

pool
¶ Return the output pool of the inference.

prepare_new_batch
(batch_index)¶ Prepare values for a new batch.
Parameters: batch_index (int) – next batch_index to be submitted Returns: batch – Keys should match to node names in the model. These values will override any default values or operations in those nodes. Return type: dict or None

sample
(n_samples, warmup=None, n_chains=4, threshold=None, initials=None, algorithm='nuts', n_evidence=None, **kwargs)[source]¶ Sample the posterior distribution of BOLFI.
Here the likelihood is defined through the cumulative density function of the standard normal distribution:
L(theta) propto F((hmu(theta)) / sigma(theta))
where h is the threshold, and mu(theta) and sigma(theta) are the posterior mean and (noisy) standard deviation of the associated Gaussian process.
The sampling is performed with an MCMC sampler (the NoUTurn Sampler, NUTS).
Parameters:  n_samples (int) – Number of requested samples from the posterior for each chain. This includes warmup, and note that the effective sample size is usually considerably smaller.
 warmpup (int, optional) – Length of warmup sequence in MCMC sampling. Defaults to n_samples//2.
 n_chains (int, optional) – Number of independent chains.
 threshold (float, optional) – The threshold (bandwidth) for posterior (give as log if log discrepancy).
 initials (np.array of shape (n_chains, n_params), optional) – Initial values for the sampled parameters for each chain. Defaults to best evidence points.
 algorithm (string, optional) – Sampling algorithm to use. Currently only ‘nuts’ is supported.
 n_evidence (int) – If the regression model is not fitted yet, specify the amount of evidence
Returns: Return type:

seed
¶ Return the seed of the inference.

set_objective
(n_evidence=None)¶ Set objective for inference.
You can continue BO by giving a larger n_evidence.
Parameters: n_evidence (int) – Number of total evidence for the GP fitting. This includes any initial evidence.

update
(batch, batch_index)¶ Update the GP regression model of the target node with a new batch.
Parameters:  batch (dict) – dict with self.outputs as keys and the corresponding outputs for the batch as values
 batch_index (int) –
Result objects

class
elfi.methods.results.
OptimizationResult
(x_min, **kwargs)[source]¶ Base class for results from optimization.
Initialize result.
Parameters:  x_min – The optimized parameters
 **kwargs – See ParameterInferenceResult

is_multivariate
¶ Check whether the result contains multivariate parameters.

class
elfi.methods.results.
Sample
(method_name, outputs, parameter_names, discrepancy_name=None, weights=None, **kwargs)[source]¶ Sampling results from inference methods.
Initialize result.
Parameters:  method_name (string) – Name of inference method.
 outputs (dict) – Dictionary with outputs from the nodes, e.g. samples.
 parameter_names (list) – Names of the parameter nodes
 discrepancy_name (string, optional) – Name of the discrepancy in outputs.
 weights (array_like) –
 **kwargs – Other meta information for the result

dim
¶ Return the number of parameters.

discrepancies
¶ Return the discrepancy values.

is_multivariate
¶ Check whether the result contains multivariate parameters.

n_samples
¶ Return the number of samples.

plot_marginals
(selector=None, bins=20, axes=None, **kwargs)[source]¶ Plot marginal distributions for parameters.
Supports only univariate distributions.
Parameters:  selector (iterable of ints or strings, optional) – Indices or keys to use from samples. Default to all.
 bins (int, optional) – Number of bins in histograms.
 axes (one or an iterable of plt.Axes, optional) –
Returns: axes
Return type: np.array of plt.Axes

plot_pairs
(selector=None, bins=20, axes=None, **kwargs)[source]¶ Plot pairwise relationships as a matrix with marginals on the diagonal.
The yaxis of marginal histograms are scaled. Supports only univariate distributions.
Parameters:  selector (iterable of ints or strings, optional) – Indices or keys to use from samples. Default to all.
 bins (int, optional) – Number of bins in histograms.
 axes (one or an iterable of plt.Axes, optional) –
Returns: axes
Return type: np.array of plt.Axes

sample_means
¶ Evaluate weighted averages of sampled parameters.
Returns: Return type: OrderedDict

sample_means_array
¶ Evaluate weighted averages of sampled parameters.
Returns: Return type: np.array

samples_array
¶ Return the samples as an array.
The columns are in the same order as in self.parameter_names.
Returns: Return type: list of np.arrays

save
(fname=None)[source]¶ Save samples in csv, json or pickle file formats.
Clarification: csv saves only samples, json saves the whole object’s dictionary except outputs key and pickle saves the whole object.
Parameters: fname (str, required) – File name to be saved. The type is inferred from extension (‘csv’, ‘json’ or ‘pkl’).

class
elfi.methods.results.
SmcSample
(method_name, outputs, parameter_names, populations, *args, **kwargs)[source]¶ Container for results from SMCABC.
Initialize result.
Parameters:  method_name (str) –
 outputs (dict) –
 parameter_names (list) –
 populations (list[Sample]) – List of Sample objects
 args –
 kwargs –

dim
¶ Return the number of parameters.

discrepancies
¶ Return the discrepancy values.

is_multivariate
¶ Check whether the result contains multivariate parameters.

n_populations
¶ Return the number of populations.

n_samples
¶ Return the number of samples.

plot_marginals
(selector=None, bins=20, axes=None, all=False, **kwargs)[source]¶ Plot marginal distributions for parameters for all populations.
Parameters:  selector (iterable of ints or strings, optional) – Indices or keys to use from samples. Default to all.
 bins (int, optional) – Number of bins in histograms.
 axes (one or an iterable of plt.Axes, optional) –
 all (bool, optional) – Plot the marginals of all populations

plot_pairs
(selector=None, bins=20, axes=None, all=False, **kwargs)[source]¶ Plot pairwise relationships as a matrix with marginals on the diagonal.
The yaxis of marginal histograms are scaled.
Parameters:  selector (iterable of ints or strings, optional) – Indices or keys to use from samples. Default to all.
 bins (int, optional) – Number of bins in histograms.
 axes (one or an iterable of plt.Axes, optional) –
 all (bool, optional) – Plot for all populations

sample_means
¶ Evaluate weighted averages of sampled parameters.
Returns: Return type: OrderedDict

sample_means_array
¶ Evaluate weighted averages of sampled parameters.
Returns: Return type: np.array

sample_means_summary
(all=False)[source]¶ Print a representation of sample means.
Parameters: all (bool, optional) – Whether to print the means for all populations separately, or just the final population (default).

samples_array
¶ Return the samples as an array.
The columns are in the same order as in self.parameter_names.
Returns: Return type: list of np.arrays

save
(fname=None)¶ Save samples in csv, json or pickle file formats.
Clarification: csv saves only samples, json saves the whole object’s dictionary except outputs key and pickle saves the whole object.
Parameters: fname (str, required) – File name to be saved. The type is inferred from extension (‘csv’, ‘json’ or ‘pkl’).

class
elfi.methods.results.
BolfiSample
(method_name, chains, parameter_names, warmup, **kwargs)[source]¶ Container for results from BOLFI.
Initialize result.
Parameters:  method_name (string) – Name of inference method.
 chains (np.array) – Chains from sampling, warmup included. Shape: (n_chains, n_samples, n_parameters).
 parameter_names (list : list of strings) – List of names in the outputs dict that refer to model parameters.
 warmup (int) – Number of warmup iterations in chains.

dim
¶ Return the number of parameters.

discrepancies
¶ Return the discrepancy values.

is_multivariate
¶ Check whether the result contains multivariate parameters.

n_samples
¶ Return the number of samples.

plot_marginals
(selector=None, bins=20, axes=None, **kwargs)¶ Plot marginal distributions for parameters.
Supports only univariate distributions.
Parameters:  selector (iterable of ints or strings, optional) – Indices or keys to use from samples. Default to all.
 bins (int, optional) – Number of bins in histograms.
 axes (one or an iterable of plt.Axes, optional) –
Returns: axes
Return type: np.array of plt.Axes

plot_pairs
(selector=None, bins=20, axes=None, **kwargs)¶ Plot pairwise relationships as a matrix with marginals on the diagonal.
The yaxis of marginal histograms are scaled. Supports only univariate distributions.
Parameters:  selector (iterable of ints or strings, optional) – Indices or keys to use from samples. Default to all.
 bins (int, optional) – Number of bins in histograms.
 axes (one or an iterable of plt.Axes, optional) –
Returns: axes
Return type: np.array of plt.Axes

sample_means
¶ Evaluate weighted averages of sampled parameters.
Returns: Return type: OrderedDict

sample_means_array
¶ Evaluate weighted averages of sampled parameters.
Returns: Return type: np.array

sample_means_summary
()¶ Print a representation of sample means.

samples_array
¶ Return the samples as an array.
The columns are in the same order as in self.parameter_names.
Returns: Return type: list of np.arrays

save
(fname=None)¶ Save samples in csv, json or pickle file formats.
Clarification: csv saves only samples, json saves the whole object’s dictionary except outputs key and pickle saves the whole object.
Parameters: fname (str, required) – File name to be saved. The type is inferred from extension (‘csv’, ‘json’ or ‘pkl’).

summary
()¶ Print a verbose summary of contained results.
Postprocessing

elfi.
adjust_posterior
(sample, model, summary_names, parameter_names=None, adjustment='linear')[source]¶ Adjust the posterior using local regression.
Note that the summary nodes need to be explicitly included to the sample object with the output_names keyword argument when performing the inference.
Parameters:  sample (elfi.methods.results.Sample) – a sample object from an ABC algorithm
 model (elfi.ElfiModel) – the inference model
 summary_names (list[str]) – names of the summary nodes
 parameter_names (list[str] (optional)) – names of the parameters
 adjustment (RegressionAdjustment or string) –
a regression adjustment object or a string specification
 Accepted values for the string specification:
 ’linear’
Returns: a Sample object with the adjusted posterior
Return type: Examples
import elfi from elfi.examples import gauss m = gauss.get_model() res = elfi.Rejection(m[‘d’], output_names=[‘ss_mean’, ‘ss_var’]).sample(1000) adj = adjust_posterior(res, m, [‘ss_mean’, ‘ss_var’], [‘mu’], LinearAdjustment())

class
elfi.methods.post_processing.
LinearAdjustment
(**kwargs)[source]¶ Regression adjustment using a local linear model.

adjust
()¶ Adjust the posterior.
Only the nonfinite values used to fit the regression model will be adjusted.
Returns: Return type: a Sample object containing the adjusted posterior

fit
(sample, model, summary_names, parameter_names=None)¶ Fit a regression adjustment model to the posterior sample.
Nonfinite values in the summary statistics and parameters will be omitted.
Parameters:  sample (elfi.methods.Sample) – a sample object from an ABC method
 model (elfi.ElfiModel) – the inference model
 summary_names (list[str]) – a list of names for the summary nodes
 parameter_names (list[str] (optional)) – a list of parameter names

Diagnostics

class
elfi.
TwoStageSelection
(simulator, fn_distance, list_ss=None, prepared_ss=None, max_cardinality=4, seed=0)[source]¶ Perform the summarystatistics selection proposed by Nunes and Balding (2010).
The user can provide a list of summary statistics as list_ss, and let ELFI to combine them, or provide some already combined summary statistics as prepared_ss.
The rationale of the Two Stage procedure procedure is the following:
 First, the module computes or accepts the combinations of the candidate summary statistics.
 In Stage 1, each summarystatistics combination is evaluated using the Minimum Entropy algorithm.
 In Stage 2, the minimumentropy combination is selected, and the ‘closest’ datasets are identified.
 Further in Stage 2, for each summarystatistics combination, the mean root sum of squared errors (MRSSE) is calculated over all ‘closest datasets’, and the minimumMRSSE combination is chosen as the one with the optimal performance.
References
[1] Nunes, M. A., & Balding, D. J. (2010). On optimal selection of summary statistics for approximate Bayesian computation. Statistical applications in genetics and molecular biology, 9(1). [2] Blum, M. G., Nunes, M. A., Prangle, D., & Sisson, S. A. (2013). A comparative review of dimension reduction methods in approximate Bayesian computation. Statistical Science, 28(2), 189208.
Initialise the summarystatistics selection for the Two Stage Procedure.
Parameters:  simulator (elfi.Node) – Node (often elfi.Simulator) for which the summary statistics will be applied. The node is the final node of a coherent ElfiModel (i.e. it has no child nodes).
 fn_distance (str or callable function) – Distance metric, consult the elfi.Distance documentation for calling as a string.
 list_ss (List of callable functions, optional) – List of candidate summary statistics.
 prepared_ss (List of lists of callable functions, optional) – List of prepared combinations of candidate summary statistics. No other combinations will be evaluated.
 max_cardinality (int, optional) – Maximum cardinality of a candidate summarystatistics combination.
 seed (int, optional) –

run
(n_sim, n_acc=None, n_closest=None, batch_size=1, k=4)[source]¶ Run the Two Stage Procedure for identifying relevant summary statistics.
Parameters:  n_sim (int) – Number of the total ABCrejection simulations.
 n_acc (int, optional) – Number of the accepted ABCrejection simulations.
 n_closest (int, optional) – Number of the ‘closest’ datasets (i.e., the closest n simulation datasets w.r.t the observations).
 batch_size (int, optional) – Number of samples per batch.
 k (int, optional) – Parameter for the kthnearestneighbour search performed in the minimumentropy step (in Nunes & Balding, 2010 it is fixed to 4).
Returns: Summarystatistics combination showing the optimal performance.
Return type: array_like
Acquisition methods

class
elfi.methods.bo.acquisition.
LCBSC
(*args, delta=None, **kwargs)[source]¶ Lower Confidence Bound Selection Criterion.
Srinivas et al. call this GPLCB.
LCBSC uses the parameter delta which is here equivalent to 1/exploration_rate.
Parameter delta should be in (0, 1) for the theoretical results to hold. The theoretical upper bound for total regret in Srinivas et al. has a probability greater or equal to 1  delta, so values of delta very close to 1 or over it do not make much sense in that respect.
Delta is roughly the exploitation tendency of the acquisition function.
References
N. Srinivas, A. Krause, S. M. Kakade, and M. Seeger. Gaussian process optimization in the bandit setting: No regret and experimental design. In Proc. International Conference on Machine Learning (ICML), 2010
E. Brochu, V.M. Cora, and N. de Freitas. A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. arXiv:1012.2599, 2010.
Notes
The formula presented in Brochu (pp. 15) seems to be from Srinivas et al. Theorem 2. However, instead of having t**(d/2 + 2) in beta_t, it seems that the correct form would be t**(2d + 2).
Initialize LCBSC.
Parameters:  args –
 delta (float, optional) – In between (0, 1). Default is 1/exploration_rate. If given, overrides the exploration_rate.
 kwargs –

acquire
(n, t=None)¶ Return the next batch of acquisition points.
Gaussian noise ~N(0, self.noise_var) is added to the acquired points.
Parameters:  n (int) – Number of acquisition points to return.
 t (int) – Current acq_batch_index (starting from 0).
Returns: x – The shape is (n, input_dim)
Return type: np.ndarray

delta
¶ Return the inverse of exploration rate.

class
elfi.methods.bo.acquisition.
MaxVar
(quantile_eps=0.01, *args, **opts)[source]¶ The maximum variance acquisition method.
The next evaluation point is acquired in the maximiser of the variance of the unnormalised approximate posterior.
theta_{t+1} = arg max Var(p(theta) * p_a(theta)),
where the unnormalised likelihood p_a is defined using the CDF of normal distribution, Phi, as follows:
 p_a(theta) =
 (Phi((epsilon  mu_{1:t}(theta)) / sqrt(v_{1:t}(theta) + sigma2_n))),
where epsilon is the ABC threshold, mu_{1:t} and v_{1:t} are determined by the Gaussian process, sigma2_n is the noise.
References
[1] Järvenpää et al. (2017). arXiv:1704.00520 [2] Gutmann M U, Corander J (2016). Bayesian Optimization for LikelihoodFree Inference of SimulatorBased Statistical Models. JMLR 17(125):1−47, 2016. http://jmlr.org/papers/v17/15017.html
Initialise MaxVar.
Parameters: quantile_eps (int, optional) – Quantile of the observed discrepancies used in setting the ABC threshold. 
acquire
(n, t=None)[source]¶ Acquire a batch of acquisition points.
Parameters:  n (int) – Number of acquisitions.
 t (int, optional) – Current iteration, (unused).
Returns: Coordinates of the yielded acquisition points.
Return type: array_like

evaluate
(theta_new, t=None)[source]¶ Evaluate the acquisition function at the location theta_new.
Parameters:  theta_new (array_like) – Evaluation coordinates.
 t (int, optional) – Current iteration, (unused).
Returns: Variance of the approximate posterior.
Return type: array_like

evaluate_gradient
(theta_new, t=None)[source]¶ Evaluate the acquisition function’s gradient at the location theta_new.
Parameters:  theta_new (array_like) – Evaluation coordinates.
 t (int, optional) – Current iteration, (unused).
Returns: Gradient of the variance of the approximate posterior
Return type: array_like

class
elfi.methods.bo.acquisition.
RandMaxVar
(quantile_eps=0.01, sampler='nuts', n_samples=50, limit_faulty_init=10, sigma_proposals_metropolis=None, *args, **opts)[source]¶ The randomised maximum variance acquisition method.
The next evaluation point is sampled from the density corresponding to the variance of the unnormalised approximate posterior (The MaxVar acquisition function).
theta_{t+1} ~ q(theta),
where q(theta) propto Var(p(theta) * p_a(theta)) and the unnormalised likelihood p_a is defined using the CDF of normal distribution, Phi, as follows:
 p_a(theta) =
 (Phi((epsilon  mu_{1:t}(theta)) / sqrt(v_{1:t}(theta) + sigma2_n))),
where epsilon is the ABC threshold, mu_{1:t} and v_{1:t} are determined by the Gaussian process, sigma2_n is the noise.
References
[1] arXiv:1704.00520 (Järvenpää et al., 2017)
Initialise RandMaxVar.
Parameters:  quantile_eps (int, optional) – Quantile of the observed discrepancies used in setting the ABC threshold.
 sampler (string, optional) – Name of the sampler (options: metropolis, nuts).
 n_samples (int, optional) – Length of the sampler’s chain for obtaining the acquisitions.
 limit_faulty_init (int, optional) – Limit for the iterations used to obtain the sampler’s initial points.
 sigma_proposals_metropolis (array_like, optional) – Standard deviation proposals for tuning the metropolis sampler. For the default settings, the sigmas are set to the 1/10 of the parameter intervals’ length.

acquire
(n, t=None)[source]¶ Acquire a batch of acquisition points.
Parameters:  n (int) – Number of acquisitions.
 t (int, optional) – Current iteration, (unused).
Returns: Coordinates of the yielded acquisition points.
Return type: array_like

evaluate
(theta_new, t=None)¶ Evaluate the acquisition function at the location theta_new.
Parameters:  theta_new (array_like) – Evaluation coordinates.
 t (int, optional) – Current iteration, (unused).
Returns: Variance of the approximate posterior.
Return type: array_like

evaluate_gradient
(theta_new, t=None)¶ Evaluate the acquisition function’s gradient at the location theta_new.
Parameters:  theta_new (array_like) – Evaluation coordinates.
 t (int, optional) – Current iteration, (unused).
Returns: Gradient of the variance of the approximate posterior
Return type: array_like

class
elfi.methods.bo.acquisition.
ExpIntVar
(quantile_eps=0.01, integration='grid', d_grid=0.2, n_samples_imp=100, iter_imp=2, sampler='nuts', n_samples=2000, sigma_proposals_metropolis=None, *args, **opts)[source]¶ The Expected Integrated Variance (ExpIntVar) acquisition method.
Essentially, we define a loss function that measures the overall uncertainty in the unnormalised ABC posterior over the parameter space. The value of the loss function depends on the next simulation and thus the next evaluation location theta^* is chosen to minimise the expected loss.
theta_{t+1} = arg min_{theta^* in Theta} L_{1:t}(theta^*), where
Theta is the parameter space, and L is the expected loss function approximated as follows:
 L_{1:t}(theta^*) approx 2 * sum_{i=1}^s (omega^i * p^2(theta^i)
 w_{1:t+1})(theta^i, theta^*), where
omega^i is an importance weight, p^2(theta^i) is the prior squared, and w_{1:t+1})(theta^i, theta^*) is the expected variance of the unnormalised ABC posterior at theta^i after running the simulation model with parameter theta^*
References
[1] arXiv:1704.00520 (Järvenpää et al., 2017)
Initialise ExpIntVar.
Parameters:  quantile_eps (int, optional) – Quantile of the observed discrepancies used in setting the discrepancy threshold.
 integration (str, optional) – Integration method. Options:  grid (points are taken uniformly): more accurate yet computationally expensive in high dimensions;  importance (points are taken based on the importance weight): less accurate though applicable in high dimensions.
 d_grid (float, optional) – Grid tightness.
 n_samples_imp (int, optional) – Number of importance samples.
 iter_imp (int, optional) – Gap between acquisition iterations in performing importance sampling.
 sampler (string, optional) – Sampler for generating random numbers from the proposal distribution for IS. (Options: metropolis, nuts.)
 n_samples (int, optional) – Chain length for the sampler that generates the random numbers from the proposal distribution for IS.
 sigma_proposals_metropolis (array_like, optional) – Standard deviation proposals for tuning the metropolis sampler.

acquire
(n, t)[source]¶ Acquire a batch of acquisition points.
Parameters:  n (int) – Number of acquisitions.
 t (int) – Current iteration.
Returns: Coordinates of the yielded acquisition points.
Return type: array_like

evaluate
(theta_new, t=None)[source]¶ Evaluate the acquisition function at the location theta_new.
Parameters:  theta_new (array_like) – Evaluation coordinates.
 t (int, optional) – Current iteration, (unused).
Returns: Expected loss’s term dependent on theta_new.
Return type: array_like

evaluate_gradient
(theta_new, t=None)¶ Evaluate the acquisition function’s gradient at the location theta_new.
Parameters:  theta_new (array_like) – Evaluation coordinates.
 t (int, optional) – Current iteration, (unused).
Returns: Gradient of the variance of the approximate posterior
Return type: array_like

class
elfi.methods.bo.acquisition.
UniformAcquisition
(model, prior=None, n_inits=10, max_opt_iters=1000, noise_var=None, exploration_rate=10, seed=None)[source]¶ Acquisition from uniform distribution.
Initialize AcquisitionBase.
Parameters:  model (an object with attributes) –
 input_dim : int
 bounds : tuple of length ‘input_dim’ of tuples (min, max)
 and methods
 evaluate(x) : function that returns model (mean, var, std)
 prior (scipylike distribution, optional) – By default uniform distribution within model bounds.
 n_inits (int, optional) – Number of initialization points in internal optimization.
 max_opt_iters (int, optional) – Max iterations to optimize when finding the next point.
 noise_var (float or np.array, optional) – Acquisition noise variance for adding noise to the points near the optimized location. If array, must be 1d specifying the variance for different dimensions. Default: no added noise.
 exploration_rate (float, optional) – Exploration rate of the acquisition function (if supported)
 seed (int, optional) – Seed for getting consistent acquisition results. Used in getting random starting locations in acquisition function optimization.

acquire
(n, t=None)[source]¶ Return random points from uniform distribution.
Parameters:  n (int) – Number of acquisition points to return.
 t (int, optional) – (unused)
Returns: x – The shape is (n, input_dim)
Return type: np.ndarray

evaluate
(x, t=None)¶ Evaluate the acquisition function at ‘x’.
Parameters:  x (numpy.array) –
 t (int) – current iteration (starting from 0)

evaluate_gradient
(x, t=None)¶ Evaluate the gradient of acquisition function at ‘x’.
Parameters:  x (numpy.array) –
 t (int) – Current iteration (starting from 0).
 model (an object with attributes) –
Model selection

elfi.
compare_models
(sample_objs, model_priors=None)[source]¶ Find posterior probabilities for different models.
The algorithm requires elfi.Sample objects from prerun inference methods. For example the output from elfi.Rejection.sample is valid. The portion of samples for each model in the top discrepancies are adjusted by each models acceptance ratio and prior probability.
The discrepancies (including summary statistics) must be comparable so that it is meaningful to sort them!
Parameters:  sample_objs (list of elfi.Sample) – Resulting Sample objects from prerun inference models. The objects must include a valid discrepancies attribute.
 model_priors (array_like, optional) – Prior probability of each model. Defaults to 1 / n_models.
Returns: Posterior probabilities for the considered models.
Return type: np.array
Other¶
Data pools

class
elfi.
OutputPool
(outputs=None, name=None, prefix=None)[source]¶ Store node outputs to dictionarylike stores.
The default store is a Python dictionary.
Notes
Saving the store requires that all the stores are pickleable.
Arbitrary objects that support simple array indexing can be used as stores by using the elfi.store.ArrayObjectStore class.
See the elfi.store.StoreBase interfaces if you wish to implement your own ELFI compatible store. Basically any object that fulfills the Pythons dictionary api will work as a store in the pool.
Initialize OutputPool.
Depending on the algorithm, some of these values may be reused after making some changes to ElfiModel thus speeding up the inference significantly. For instance, if all the simulations are stored in Rejection sampling, one can change the summaries and distances without having to rerun the simulator.
Parameters:  outputs (list, dict, optional) – List of node names which to store or a dictionary with existing stores. The stores are created on demand.
 name (str, optional) – Name of the pool. Used to open a saved pool from disk.
 prefix (str, optional) – Path to directory under which elfi.ArrayPool will place its folder. Default is a relative path ./pools.
Returns: instance
Return type: 
add_store
(node, store=None)[source]¶ Add a store object for the node.
Parameters:  node (str) –
 store (dict, StoreBase, optional) –

flush
()[source]¶ Flush all data from the stores.
If the store does not support flushing, do nothing.

get_batch
(batch_index, output_names=None)[source]¶ Return a batch from the stores of the pool.
Parameters:  batch_index (int) –
 output_names (list) – which outputs to include to the batch
Returns: batch
Return type: dict

has_context
¶ Check if current pool has context information.

classmethod
open
(name, prefix=None)[source]¶ Open a closed or saved ArrayPool from disk.
Parameters:  name (str) –
 prefix (str, optional) –
Returns: Return type:

output_names
¶ Return a list of stored names.

path
¶ Return the path to the pool.

class
elfi.
ArrayPool
(outputs=None, name=None, prefix=None)[source]¶ OutputPool that uses binary .npy files as default stores.
The default store medium for output data is a NumPy binary .npy file for NumPy array data. You can however also add other types of stores as well.
Notes
The default store is implemented in elfi.store.NpyStore that uses NpyArrays as stores. The NpyArray is a wrapper over NumPy .npy binary file for array data and supports appending the .npy file. It uses the .npy format 2.0 files.
Initialize OutputPool.
Depending on the algorithm, some of these values may be reused after making some changes to ElfiModel thus speeding up the inference significantly. For instance, if all the simulations are stored in Rejection sampling, one can change the summaries and distances without having to rerun the simulator.
Parameters:  outputs (list, dict, optional) – List of node names which to store or a dictionary with existing stores. The stores are created on demand.
 name (str, optional) – Name of the pool. Used to open a saved pool from disk.
 prefix (str, optional) – Path to directory under which elfi.ArrayPool will place its folder. Default is a relative path ./pools.
Returns: instance
Return type: 
add_batch
(batch, batch_index)¶ Add the outputs from the batch to their stores.

add_store
(node, store=None)¶ Add a store object for the node.
Parameters:  node (str) –
 store (dict, StoreBase, optional) –

clear
()¶ Remove all data from the stores.

close
()¶ Save and close the stores that support it.
The pool will not be usable afterwards.

delete
()¶ Remove all persisted data from disk.

flush
()¶ Flush all data from the stores.
If the store does not support flushing, do nothing.

get_batch
(batch_index, output_names=None)¶ Return a batch from the stores of the pool.
Parameters:  batch_index (int) –
 output_names (list) – which outputs to include to the batch
Returns: batch
Return type: dict

get_store
(node)¶ Return the store for node.

has_context
¶ Check if current pool has context information.

has_store
(node)¶ Check if node is in stores.

classmethod
open
(name, prefix=None)¶ Open a closed or saved ArrayPool from disk.
Parameters:  name (str) –
 prefix (str, optional) –
Returns: Return type:

output_names
¶ Return a list of stored names.

path
¶ Return the path to the pool.

remove_batch
(batch_index)¶ Remove the batch from all stores.

remove_store
(node)¶ Remove and return a store from the pool.
Parameters: node (str) – Returns: The removed store Return type: store

save
()¶ Save the pool to disk.
This will use pickle to store the pool under self.path.

set_context
(context)¶ Set the context of the pool.
The pool needs to know the batch_size and the seed.
Notes
Also sets the name of the pool if not set already.
Parameters: context (elfi.ComputationContext) –
Module functions

elfi.
set_client
(client=None, **kwargs)[source]¶ Set the current ELFI client instance.
Parameters: client (ClientBase or str) – Instance of a client from ClientBase, or a string from [‘native’, ‘multiprocessing’, ‘ipyparallel’]. If string, the respective constructor is called with kwargs.
Tools

tools.
vectorize
(constants=None, dtype=None)¶ Vectorize an operation.
Helper for cases when you have an operation that does not support vector arguments. This tool is still experimental and may not work in all cases.
Parameters:  operation (callable) – Operation to vectorize.
 constants (tuple, list, optional) – A mask for constants in inputs, e.g. (0, 2) would indicate that the first and third positional inputs are constants. The constants will be passed as they are to each operation call.
 dtype (np.dtype, bool[False], optional) – If None, numpy converts a list of outputs automatically. In some cases this produces non desired results. If you wish to keep the outputs as they are with no conversion, specify dtype=False. This results into a 1d object numpy array with outputs as they were returned.
Notes
This is a convenience method that uses a for loop internally for the vectorization. For best performance, one should aim to implement vectorized operations (by using e.g. numpy functions that are mostly vectorized) if at all possible.
Examples
# This form works in most cases vectorized_simulator = elfi.tools.vectorize(simulator) # Tell that the second and third argument to the simulator will be a constant vectorized_simulator = elfi.tools.vectorize(simulator, [1, 2]) elfi.Simulator(vectorized_simulator, prior, constant_1, constant_2) # Tell the vectorizer that it should not do any conversion to the outputs vectorized_simulator = elfi.tools.vectorize(simulator, dtype=False)

tools.
external_operation
(process_result=None, prepare_inputs=None, sep=' ', stdout=True, subprocess_kwargs=None)¶ Wrap an external command as a Python callable (function).
The external command can be e.g. a shell script, or an executable file.
Parameters:  command (str) – Command to execute. Arguments can be passed to the executable by using Python’s format strings, e.g. “myscript.sh {0} {batch_size} –seed {seed}”. The command is expected to write to stdout. Since random_state is python specific object, a seed keyword argument will be available to operations that use random_state.
 process_result (callable, np.dtype, str, optional) – Callable result handler with a signature output = callable(result, *inputs, **kwinputs). Here the result is either the stdout or subprocess.CompletedProcess depending on the stdout flag below. The inputs and kwinputs will come from ELFI. The default handler converts the stdout to numpy array with array = np.fromstring(stdout, sep=sep). If process_result is np.dtype or a string, then the stdout data is casted to that type with stdout = np.fromstring(stdout, sep=sep, dtype=process_result).
 prepare_inputs (callable, optional) – Callable with a signature inputs, kwinputs = callable(*inputs, **kwinputs). The inputs will come from elfi.
 sep (str, optional) – Separator to use with the default process_result handler. Default is a space ‘ ‘. If you specify your own callable to process_result this value has no effect.
 stdout (bool, optional) – Pass the process_result handler the stdout instead of the subprocess.CompletedProcess instance. Default is true.
 subprocess_kwargs (dict, optional) – Options for Python’s subprocess.run that is used to run the external command. Defaults are shell=True, check=True. See the subprocess documentation for more details.
Examples
>>> import elfi >>> op = elfi.tools.external_operation('echo 1 {0}', process_result='int8') >>> >>> constant = elfi.Constant(123) >>> simulator = elfi.Simulator(op, constant) >>> simulator.generate() array([ 1, 123], dtype=int8)
Returns: operation – ELFI compatible operation that can be used e.g. as a simulator. Return type: callable