Distance functions¶
Distance functions measure closeness of observed and sampled data. For custom distance functions, either pass a plain function to ABCSMC or subclass the DistanceFunction class if finer grained configuration is required.

class
pyabc.distance_functions.
AcceptAllDistance
(require_initialize: bool = True)¶ Bases:
pyabc.distance_functions.DistanceFunction
Just a mock distance function which always returns 1. So any sample should be accepted for any sane epsilon object.
Can be used for testing.

__call__
(t: int, x: dict, y: dict) → float¶ Evaluate, at time point t, the distance of the tentatively sampled particle to the measured data.
Abstract method. This method has to be overwritten by all concrete implementations.
Parameters:  t (int) – Time point at which to evaluate the distance.
 x (dict) – Summary statistics of the tentatively sampled parameter.
 x_0 (dict) – Summary statistics of the measured data.
Returns: distance – Attributes distance of the tentatively sampled particle from the measured data.
Return type: float


class
pyabc.distance_functions.
AdaptivePNormDistance
(p: float = 2, adaptive: bool = True, scale_type: int = 1)¶ Bases:
pyabc.distance_functions.PNormDistance
In the pnorm distance, adapt the weights for each generation, based on the previous simulations.
Parameters:  p (float) – p for pnorm. Required p >= 1, p = np.inf allowed (infinitynorm).
 adaptive (bool) – True: Adapt distance after each iteration. False: Adapt distance only once at the beginning in initialize(). This corresponds to a precalibration.
 scale_type (int) – What measure to use for deviation. Currently supports SCALE_TYPE_MAD for the median absolute deviation (might be more tolerant to outliers), and SCALE_TYPE_SD for the standard deviation.

configure_sampler
(sampler: pyabc.sampler.base.Sampler)¶ Make the sampler return also rejected summary statistics if required, because these are needed to get a better estimate of the summary statistic variabilities.
Parameters: sampler (Sampler) – The sampler employed.

initialize
(t: int, sample_from_prior: List[dict])¶ Initialize weights.

update
(t: int, all_sum_stats: List[dict])¶ Update weights based on all simulations.

class
pyabc.distance_functions.
DistanceFunction
(require_initialize: bool = True)¶ Bases:
abc.ABC
Abstract base class for distance functions.
Any other distance function should inherit from this class.

__call__
(t: int, x: dict, x_0: dict) → float¶ Evaluate, at time point t, the distance of the tentatively sampled particle to the measured data.
Abstract method. This method has to be overwritten by all concrete implementations.
Parameters:  t (int) – Time point at which to evaluate the distance.
 x (dict) – Summary statistics of the tentatively sampled parameter.
 x_0 (dict) – Summary statistics of the measured data.
Returns: distance – Attributes distance of the tentatively sampled particle from the measured data.
Return type: float

configure_sampler
(sampler: pyabc.sampler.base.Sampler)¶ This is called by the ABCSMC class and gives the distance function the opportunity to configure the sampler. For example, the distance function might request the sampler to also return rejected particles and their summary statistics in order to adapt the distance functions to the statistics of the sample.
The default is to do nothing.
Parameters: sampler (Sampler) – The Sampler used in ABCSMC.

get_config
() → dict¶ Return configuration of the distance function.
Returns: config – Dictionary describing the distance function. Return type: dict

initialize
(t: int, sample_from_prior: List[dict])¶ This method is called by the ABCSMC framework before the first use of the distance function (in
new
andload
) and can be used to calibrate it to the statistics of the samples.The default implementation is to do nothing.
This function is only called if require_initialize == True.
Parameters:  t (int) – Time point for which to initialize the distance function.
 sample_from_prior (List[dict]) – List of dictionaries containing the summary statistics.

to_json
() → str¶ Return JSON encoded configuration of the distance function.
Returns: json_str – JSON encoded string describing the distance function. The default implementation is to try to convert the dictionary returned my get_config
.Return type: str

update
(t: int, all_sum_stats: List[dict]) → bool¶ Update the distance function. Default: Do nothing.
Parameters:  t (int) – Time point for which to update/create the distance measure.
 all_sum_stats (List[dict]) – List of all summary statistics that should be used to update the distance (in particular also rejected ones).
Returns: is_updated – True: If distance function has changed compared to hitherto. False: If distance function has not changed (default).
Return type: bool


class
pyabc.distance_functions.
DistanceFunctionWithMeasureList
(measures_to_use='all')¶ Bases:
pyabc.distance_functions.DistanceFunction
Base class for distance functions with measure list. This class is not functional on its own.
Parameters: measures_to_use (Union[str, List[str]]) –  If set to “all”, all measures are used. This is the default.
 If a list is provided, the measures in the list are used.
 measures refers to the summary statistics.

get_config
()¶ Return configuration of the distance function.
Returns: config – Dictionary describing the distance function. Return type: dict

initialize
(t: int, sample_from_prior)¶ This method is called by the ABCSMC framework before the first use of the distance function (in
new
andload
) and can be used to calibrate it to the statistics of the samples.The default implementation is to do nothing.
This function is only called if require_initialize == True.
Parameters:  t (int) – Time point for which to initialize the distance function.
 sample_from_prior (List[dict]) – List of dictionaries containing the summary statistics.

measures_to_use
= None¶ The measures (summary statistics) to use for distance calculation.

class
pyabc.distance_functions.
IdentityFakeDistance
(require_initialize: bool = True)¶ Bases:
pyabc.distance_functions.DistanceFunction
A fake distance function, which just passes the summary statistics on. This class assumes that the model already returns the distance. This can be useful in cases where simulating can be stopped early, when during the simulation some condition is reached which makes it impossible to accept the particle.

__call__
(t: int, x: dict, y: dict)¶ Evaluate, at time point t, the distance of the tentatively sampled particle to the measured data.
Abstract method. This method has to be overwritten by all concrete implementations.
Parameters:  t (int) – Time point at which to evaluate the distance.
 x (dict) – Summary statistics of the tentatively sampled parameter.
 x_0 (dict) – Summary statistics of the measured data.
Returns: distance – Attributes distance of the tentatively sampled particle from the measured data.
Return type: float


class
pyabc.distance_functions.
MinMaxDistanceFunction
(measures_to_use='all')¶ Bases:
pyabc.distance_functions.RangeEstimatorDistanceFunction
Calculate upper and lower margins as max and min of the parameters. This works surprisingly well for normalization in simple cases

static
lower
(parameter_list)¶ Calculate the lower margin form a list of parameter values.
Parameters: parameter_list (List[float]) – List of values of a parameter. Returns: lower_margin – The lower margin of the range calculated from these parameters Return type: float

static
upper
(parameter_list)¶ Calculate the upper margin form a list of parameter values.
Parameters: parameter_list (List[float]) – List of values of a parameter. Returns: upper_margin – The upper margin of the range calculated from these parameters Return type: float

static

class
pyabc.distance_functions.
NoDistance
¶ Bases:
pyabc.distance_functions.DistanceFunction
Implements a kind of null object as distance function.
This can be used as a dummy distance function if e.g. integrated modeling is used.
Note
This distance function cannot be evaluated, so currently it is in particular not possible to use an epsilon threshold which requires initialization (i.e. eps.require_initialize==True is not possible).

__call__
(t: int, x: dict, x_0: dict) → float¶ Evaluate, at time point t, the distance of the tentatively sampled particle to the measured data.
Abstract method. This method has to be overwritten by all concrete implementations.
Parameters:  t (int) – Time point at which to evaluate the distance.
 x (dict) – Summary statistics of the tentatively sampled parameter.
 x_0 (dict) – Summary statistics of the measured data.
Returns: distance – Attributes distance of the tentatively sampled particle from the measured data.
Return type: float


class
pyabc.distance_functions.
PCADistanceFunction
(measures_to_use='all')¶ Bases:
pyabc.distance_functions.DistanceFunctionWithMeasureList
Calculate distance in whitened coordinates.
A whitening transformation \(X\) is calculated from an initial sample. The distance is measured as euclidean distance in the transformed space. I.e
\[d(x,y) = \ Wx  Wy \\]
__call__
(t: int, x: dict, y: dict) → float¶ Evaluate, at time point t, the distance of the tentatively sampled particle to the measured data.
Abstract method. This method has to be overwritten by all concrete implementations.
Parameters:  t (int) – Time point at which to evaluate the distance.
 x (dict) – Summary statistics of the tentatively sampled parameter.
 x_0 (dict) – Summary statistics of the measured data.
Returns: distance – Attributes distance of the tentatively sampled particle from the measured data.
Return type: float

initialize
(t: int, sample_from_prior)¶ This method is called by the ABCSMC framework before the first use of the distance function (in
new
andload
) and can be used to calibrate it to the statistics of the samples.The default implementation is to do nothing.
This function is only called if require_initialize == True.
Parameters:  t (int) – Time point for which to initialize the distance function.
 sample_from_prior (List[dict]) – List of dictionaries containing the summary statistics.


class
pyabc.distance_functions.
PNormDistance
(p: float = 2, w: dict = None)¶ Bases:
pyabc.distance_functions.DistanceFunction
Use weighted pnorm
\[d(x, y) = \left[\sum_{i} \left w_i x_iy_i \right^{p} \right]^{1/p}\]to compute distances between sets of summary statistics. E.g. set p=2 to get a Euclidean distance.
Parameters:  p (float) – p for pnorm. Required p >= 1, p = np.inf allowed (infinitynorm).
 w (dict) – Weights. Dictionary indexed by time points. Each entry contains a dictionary of numeric weights, indexed by summary statistics labels. If none is passed, a weight of 1 is considered for every summary statistic. If no entry is available in w for a given time point, the maximum available time point is selected.

__call__
(t: int, x: dict, y: dict) → float¶ Evaluate, at time point t, the distance of the tentatively sampled particle to the measured data.
Abstract method. This method has to be overwritten by all concrete implementations.
Parameters:  t (int) – Time point at which to evaluate the distance.
 x (dict) – Summary statistics of the tentatively sampled parameter.
 x_0 (dict) – Summary statistics of the measured data.
Returns: distance – Attributes distance of the tentatively sampled particle from the measured data.
Return type: float

get_config
() → dict¶ Return configuration of the distance function.
Returns: config – Dictionary describing the distance function. Return type: dict

class
pyabc.distance_functions.
PercentileDistanceFunction
(measures_to_use='all')¶ Bases:
pyabc.distance_functions.RangeEstimatorDistanceFunction
Calculate normalization 20% and 80% from percentiles as lower and upper margins

PERCENTILE
= 20¶ The percentiles

get_config
()¶ Return configuration of the distance function.
Returns: config – Dictionary describing the distance function. Return type: dict

static
lower
(parameter_list)¶ Calculate the lower margin form a list of parameter values.
Parameters: parameter_list (List[float]) – List of values of a parameter. Returns: lower_margin – The lower margin of the range calculated from these parameters Return type: float

static
upper
(parameter_list)¶ Calculate the upper margin form a list of parameter values.
Parameters: parameter_list (List[float]) – List of values of a parameter. Returns: upper_margin – The upper margin of the range calculated from these parameters Return type: float


class
pyabc.distance_functions.
RangeEstimatorDistanceFunction
(measures_to_use='all')¶ Bases:
pyabc.distance_functions.DistanceFunctionWithMeasureList
Abstract base class for distance functions which estimate is based on a range.
It defines the two template methods
lower
andupper
.Hence
\[d(x, y) = \sum_{i \in \text{measures}} \left  \frac{x_i  y_i}{u_i  l_i} \right \]where \(l_i\) and \(u_i\) are the lower and upper margin for measure \(i\).

__call__
(t: int, x: dict, y: dict) → float¶ Evaluate, at time point t, the distance of the tentatively sampled particle to the measured data.
Abstract method. This method has to be overwritten by all concrete implementations.
Parameters:  t (int) – Time point at which to evaluate the distance.
 x (dict) – Summary statistics of the tentatively sampled parameter.
 x_0 (dict) – Summary statistics of the measured data.
Returns: distance – Attributes distance of the tentatively sampled particle from the measured data.
Return type: float

get_config
()¶ Return configuration of the distance function.
Returns: config – Dictionary describing the distance function. Return type: dict

initialize
(t: int, sample_from_prior)¶ This method is called by the ABCSMC framework before the first use of the distance function (in
new
andload
) and can be used to calibrate it to the statistics of the samples.The default implementation is to do nothing.
This function is only called if require_initialize == True.
Parameters:  t (int) – Time point for which to initialize the distance function.
 sample_from_prior (List[dict]) – List of dictionaries containing the summary statistics.

static
lower
(parameter_list: List[float])¶ Calculate the lower margin form a list of parameter values.
Parameters: parameter_list (List[float]) – List of values of a parameter. Returns: lower_margin – The lower margin of the range calculated from these parameters Return type: float

static
upper
(parameter_list: List[float])¶ Calculate the upper margin form a list of parameter values.
Parameters: parameter_list (List[float]) – List of values of a parameter. Returns: upper_margin – The upper margin of the range calculated from these parameters Return type: float


class
pyabc.distance_functions.
SimpleFunctionDistance
(function)¶ Bases:
pyabc.distance_functions.DistanceFunction
This is a wrapper around a simple function which calculates the distance. If a function is passed to the ABCSMC class, then it is converted to an instance of the SimpleFunctionDistance class.
Parameters: function (Callable) – A Callable accepting two parameters, namely summary statistics x and y. 
__call__
(t: int, x: dict, y: dict) → float¶ Evaluate, at time point t, the distance of the tentatively sampled particle to the measured data.
Abstract method. This method has to be overwritten by all concrete implementations.
Parameters:  t (int) – Time point at which to evaluate the distance.
 x (dict) – Summary statistics of the tentatively sampled parameter.
 x_0 (dict) – Summary statistics of the measured data.
Returns: distance – Attributes distance of the tentatively sampled particle from the measured data.
Return type: float

get_config
()¶ Return configuration of the distance function.
Returns: config – Dictionary describing the distance function. Return type: dict


class
pyabc.distance_functions.
ZScoreDistanceFunction
(measures_to_use='all')¶ Bases:
pyabc.distance_functions.DistanceFunctionWithMeasureList
Calculate distance as sum of ZScore over the selected measures. The measured Data is the reference for the ZScore.
Hence
\[d(x, y) = \sum_{i \in \text{measures}} \left \frac{x_iy_i}{y_i} \right\]
__call__
(t: int, x: dict, y: dict) → float¶ Evaluate, at time point t, the distance of the tentatively sampled particle to the measured data.
Abstract method. This method has to be overwritten by all concrete implementations.
Parameters:  t (int) – Time point at which to evaluate the distance.
 x (dict) – Summary statistics of the tentatively sampled parameter.
 x_0 (dict) – Summary statistics of the measured data.
Returns: distance – Attributes distance of the tentatively sampled particle from the measured data.
Return type: float


pyabc.distance_functions.
median_absolute_deviation
(data: List)¶ Calculate the sample median absolute deviation (MAD), defined as median(abs(data  median(data)).
Parameters: data (List) – List of data points. Returns: mad – The median absolute deviation of the data. Return type: float

pyabc.distance_functions.
standard_deviation
(data: List)¶ Calculate the sample standard deviation (SD).
Parameters: data (List) – List of data points. Returns: sd – The standard deviation of the data points. Return type: float

pyabc.distance_functions.
to_distance
(maybe_distance_function)¶ Parameters:  maybe_distance_function (either a Callable, which takes two arguments, or) –
 DistanceFunction instance. (a) –