probabilistic_model.distributions.distributions

Classes

UnivariateDistribution	Abstract Base class for Univariate distributions.
ContinuousDistribution	Abstract base class for continuous distributions.
ContinuousDistributionWithFiniteSupport	Abstract base class for continuous distributions with finite support.
DiscreteDistribution	Abstract base class for univariate discrete distributions.
SymbolicDistribution	Class for symbolic (categorical) distributions.
IntegerDistribution	Abstract base class for integer distributions. Integer distributions also implement the methods of continuous
DiracDeltaDistribution	Class for Dirac delta distributions.

Module Contents

class probabilistic_model.distributions.distributions.UnivariateDistribution

Bases: probabilistic_model.probabilistic_model.ProbabilisticModel, random_events.variable.SubclassJSONSerializer, probabilistic_model.interfaces.drawio.drawio.DrawIOInterface

Abstract Base class for Univariate distributions.

variable: random_events.variable.Variable

property variables: typing_extensions.Tuple[random_events.variable.Variable, Ellipsis]

Returns:

The variables of the model.

property support: random_events.product_algebra.Event

Returns:

The support of the model.

property univariate_support: random_events.variable.AbstractCompositeSet

Abstractmethod:

Returns:

The univariate support of the distribution. This is not an Event.

log_mode() → typing_extensions.Tuple[random_events.product_algebra.Event, float]

Calculate the mode of the model.

Check the documentation of mode for more information.

Returns:

The mode and its log-likelihood.

abstract univariate_log_mode() → typing_extensions.Tuple[random_events.variable.AbstractCompositeSet, float]

Returns:

The univariate mode of the distribution and its log-likelihood. The mode is not an Event.

marginal(variables: typing_extensions.Iterable[random_events.variable.Variable]) → random_events.variable.Optional[typing_extensions.Self]

Calculate the marginal distribution of a set of variables.

Parameters:

variables – The variables to calculate the marginal distribution on.

Returns:

The marginal distribution over the variables.

__eq__(other: typing_extensions.Self)

to_json() → typing_extensions.Dict[str, typing_extensions.Any]

composite_set_from_event(event: random_events.product_algebra.Event) → random_events.variable.AbstractCompositeSet

Extract the composite set from the event that is relevant for this distribution. :param event: The event :return: The composite set

property abbreviated_symbol: str

property drawio_style: typing_extensions.Dict[str, typing_extensions.Any]

The style of the object.

class probabilistic_model.distributions.distributions.ContinuousDistribution

Bases: UnivariateDistribution

Abstract base class for continuous distributions.

variable: random_events.variable.Continuous

property univariate_support: random_events.variable.Interval

Abstractmethod:

Returns:

The univariate support of the distribution. This is not an Event.

abstract cdf(x: numpy.array) → numpy.array

Calculate the cumulative distribution function at x. :param x: The data :return: The cumulative distribution function at x

probability_of_simple_event(event: random_events.product_algebra.SimpleEvent) → float

Calculate the probability of a simple event.

The event belongs to the class of marginal queries.

Note

You can read more about queries of this class in Definition 11 in [CVVdB20] or watch the video tutorial. [US20]

Parameters:

event – The event.

Returns:

The probability of the event.

log_truncated(event: random_events.product_algebra.Event) → typing_extensions.Tuple[random_events.variable.Optional[typing_extensions.Self], float]

Calculate the truncated distribution P(*| event) and the probability of the event.

Check the documentation of truncated for more information.

Parameters:

event – The event to condition on.

Returns:

The truncated distribution and the log-probability of the event.

log_conditional(point: typing_extensions.Dict[random_events.variable.Variable, typing_extensions.Any]) → typing_extensions.Tuple[random_events.variable.Optional[typing_extensions.Union[probabilistic_model.probabilistic_model.ProbabilisticModel, typing_extensions.Self]], float]

Calculate the truncated distribution P(*| point) and the probability of the event. Check the documentation of conditional for more information.

Parameters:

point – A partial point to calculate the truncated distribution on.

Returns:

The truncated distribution and the log-probability of the point.

abstract log_conditional_from_simple_interval(interval: random_events.variable.SimpleInterval) → typing_extensions.Tuple[typing_extensions.Self, float]

Calculate the truncated distribution given a simple interval.

Parameters:

interval – The simple interval

Returns:

The truncated distribution and the log-probability of the interval.

abstract log_conditional_from_interval(interval) → typing_extensions.Tuple[typing_extensions.Self, float]

Calculate the truncated distribution given an interval with p(interval) > 0. :param interval: The simple interval :return: The truncated distribution and the log-probability of the interval.

class probabilistic_model.distributions.distributions.ContinuousDistributionWithFiniteSupport

Bases: ContinuousDistribution

Abstract base class for continuous distributions with finite support.

interval: random_events.variable.SimpleInterval

The interval of the distribution.

property lower: float

property upper: float

property univariate_support: random_events.variable.Interval

Returns:

The univariate support of the distribution. This is not an Event.

left_included_condition(x: numpy.array) → numpy.array

Check if x is included in the left bound of the interval. :param x: The data :return: A boolean array

right_included_condition(x: numpy.array) → numpy.array

Check if x is included in the right bound of the interval. :param x: The data :return: A boolean array

included_condition(x: numpy.array) → numpy.array

Check if x is included in interval. :param x: The data :return: A boolean array

log_likelihood(x: numpy.array) → numpy.array

Calculate the log-likelihood of an event.

Check the documentation of likelihood for more information.

Parameters:

events – The full evidence event with shape (#events, #variables)

Returns:

The log-likelihood of the event with shape (#events).

abstract log_likelihood_without_bounds_check(x: numpy.array) → numpy.array

Evaluate the logarithmic likelihood function at x without checking the inclusion into the interval. :param x: x where p(x) > 0 :return: log(p(x))

translate(translation: typing_extensions.Dict[random_events.variable.Variable, float])

Translate the model in-place. Translation is done by adding the translation to the variable location influencing values. The translation can be viewed as what happens when you shift the numeric variables of the model by a constant vector.

Parameters:

translation – The variable value pairs to translate the model by.

scale(scaling: typing_extensions.Dict[random_events.variable.Variable, float])

Scale the model in-place. Scaling is done by multiplying the variable location influencing values. The scaling can be viewed as what happens when you multiply the numeric variables of the model by a constant vector.

Parameters:

scaling – The variable value pairs to scale the model by.

class probabilistic_model.distributions.distributions.DiscreteDistribution(variable: typing_extensions.Union[random_events.variable.Symbolic, random_events.variable.Integer], probabilities: random_events.variable.Optional[probabilistic_model.utils.MissingDict[typing_extensions.Union[int, random_events.variable.SetElement], float]])

Bases: UnivariateDistribution

Abstract base class for univariate discrete distributions.

variable: typing_extensions.Union[random_events.variable.Symbolic, random_events.variable.Integer]

probabilities: probabilistic_model.utils.MissingDict[int, float]

A dict that maps from integers (hash(symbol) for symbols) to probabilities.

__eq__(other)

__hash__()

log_likelihood(events: numpy.array) → numpy.array

Calculate the log-likelihood of an event.

Check the documentation of likelihood for more information.

Parameters:

events – The full evidence event with shape (#events, #variables)

Returns:

The log-likelihood of the event with shape (#events).

fit(data: numpy.array) → typing_extensions.Self

Fit the distribution to the data.

The probabilities are set equal to the frequencies in the data. The data contains the indices of the domain elements (if symbolic) or the values (if integer).

Parameters:

data – The data.

Returns:

The fitted distribution

abstract probabilities_for_plotting() → typing_extensions.Dict[typing_extensions.Union[int, str], float]

Returns:

The probabilities as dict that can be plotted.

plot(**kwargs) → typing_extensions.List[plotly.graph_objects.Bar]

Plot the distribution.

to_json() → typing_extensions.Dict[str, typing_extensions.Any]

classmethod _from_json(data: typing_extensions.Dict[str, typing_extensions.Any]) → typing_extensions.Self

Create a variable from a json dict. This method is called from the from_json method after the correct subclass is determined and should be overwritten by the respective subclass.

Parameters:

data – The json dict

Returns:

The deserialized object

normalize()

Normalize the distribution.

log_truncated(event: random_events.product_algebra.Event) → typing_extensions.Tuple[random_events.variable.Optional[typing_extensions.Self], float]

Calculate the truncated distribution P(*| event) and the probability of the event.

Check the documentation of truncated for more information.

Parameters:

event – The event to condition on.

Returns:

The truncated distribution and the log-probability of the event.

log_conditional(point: typing_extensions.Dict[random_events.variable.Variable, typing_extensions.Any]) → typing_extensions.Tuple[random_events.variable.Optional[typing_extensions.Self], float]

Calculate the truncated distribution P(*| point) and the probability of the event. Check the documentation of conditional for more information.

Parameters:

point – A partial point to calculate the truncated distribution on.

Returns:

The truncated distribution and the log-probability of the point.

log_conditional_of_composite_set(event: random_events.variable.AbstractCompositeSet) → typing_extensions.Tuple[random_events.variable.Optional[typing_extensions.Self], float]

__copy__() → typing_extensions.Self

__deepcopy__(memo=None) → typing_extensions.Self

__repr__()

sample(amount: int) → numpy.array

Sample from the model.

Parameters:

amount – The number of samples to draw.

Returns:

The samples.

class probabilistic_model.distributions.distributions.SymbolicDistribution(variable: typing_extensions.Union[random_events.variable.Symbolic, random_events.variable.Integer], probabilities: random_events.variable.Optional[probabilistic_model.utils.MissingDict[typing_extensions.Union[int, random_events.variable.SetElement], float]])

Bases: DiscreteDistribution

Class for symbolic (categorical) distributions.

variable: random_events.variable.Symbolic

univariate_log_mode() → typing_extensions.Tuple[random_events.variable.Set, float]

Returns:

The univariate mode of the distribution and its log-likelihood. The mode is not an Event.

log_conditional_of_composite_set(event: random_events.variable.AbstractCompositeSet) → typing_extensions.Tuple[random_events.variable.Optional[typing_extensions.Self], float]

probabilities_for_plotting() → typing_extensions.Dict[typing_extensions.Union[int, str], float]

Returns:

The probabilities as dict that can be plotted.

property univariate_support: random_events.variable.Set

Returns:

The univariate support of the distribution. This is not an Event.

probability_of_simple_event(event: random_events.product_algebra.SimpleEvent) → float

Calculate the probability of a simple event.

The event belongs to the class of marginal queries.

Note

You can read more about queries of this class in Definition 11 in [CVVdB20] or watch the video tutorial. [US20]

Parameters:

event – The event.

Returns:

The probability of the event.

property representation

The symbol used to represent this distribution.

property drawio_label

The label of the object as a drawio compatible string.

property image

fit(data: numpy.array) → typing_extensions.Self

Fit the distribution to the data.

The probabilities are set equal to the frequencies in the data. The data contains the indices of the domain elements (if symbolic) or the values (if integer).

Parameters:

data – The data.

Returns:

The fitted distribution

fit_from_indices(data: numpy.array) → typing_extensions.Self

to_json() → typing_extensions.Dict[str, typing_extensions.Any]

classmethod _from_json(data: typing_extensions.Dict[str, typing_extensions.Any]) → typing_extensions.Self

Create a variable from a json dict. This method is called from the from_json method after the correct subclass is determined and should be overwritten by the respective subclass.

Parameters:

data – The json dict

Returns:

The deserialized object

class probabilistic_model.distributions.distributions.IntegerDistribution(variable: random_events.variable.Integer, probabilities: random_events.variable.Optional[probabilistic_model.utils.MissingDict[typing_extensions.Union[int, random_events.variable.SetElement], float]])

Bases: ContinuousDistribution, DiscreteDistribution

Abstract base class for integer distributions. Integer distributions also implement the methods of continuous distributions.

variable: random_events.variable.Integer

log_truncated(event: random_events.product_algebra.Event) → typing_extensions.Tuple[random_events.variable.Optional[typing_extensions.Self], float]

Calculate the truncated distribution P(*| event) and the probability of the event.

Check the documentation of truncated for more information.

Parameters:

event – The event to condition on.

Returns:

The truncated distribution and the log-probability of the event.

univariate_log_mode() → typing_extensions.Tuple[random_events.variable.AbstractCompositeSet, float]

Returns:

The univariate mode of the distribution and its log-likelihood. The mode is not an Event.

probabilities_for_plotting() → typing_extensions.Dict[typing_extensions.Union[int, str], float]

Returns:

The probabilities as dict that can be plotted.

property univariate_support: random_events.variable.Interval

Returns:

The univariate support of the distribution. This is not an Event.

cdf(x: numpy.array) → numpy.array

Calculate the cumulative distribution function at x. :param x: The data :return: The cumulative distribution function at x

probability_of_simple_event(event: random_events.product_algebra.SimpleEvent) → float

Calculate the probability of a simple event.

The event belongs to the class of marginal queries.

Note

You can read more about queries of this class in Definition 11 in [CVVdB20] or watch the video tutorial. [US20]

Parameters:

event – The event.

Returns:

The probability of the event.

property representation

The symbol used to represent this distribution.

moment(order: probabilistic_model.probabilistic_model.OrderType, center: probabilistic_model.probabilistic_model.CenterType) → probabilistic_model.probabilistic_model.MomentType

Calculate the (centralized) moment of the distribution.

\[\int_{-\infty}^{\infty} (x - center)^{order} pdf(x) dx\]

Note

You can read more about queries of this class in Definition 22 in :cite:p:`choi2020probabilistic`_. [US20]

Parameters:

• order – The orders of the moment as a variable map for every continuous and integer variable.

• center – The center of the moment as a variable map for every continuous and integer variable.

Returns:

The moments of the variables in order.

plot(**kwargs) → typing_extensions.List[plotly.graph_objects.Bar]

Generate traces that can be plotted with plotly.

Parameters:

• number_of_samples – The number of samples to draw.

• surface – If True, plot the model as a surface plot.

• mode – If True, plot the mode of the model.

Returns:

The traces.

translate(translation: typing_extensions.Dict[random_events.variable.Variable, int])

Translate the model in-place. Translation is done by adding the translation to the variable location influencing values. The translation can be viewed as what happens when you shift the numeric variables of the model by a constant vector.

Parameters:

translation – The variable value pairs to translate the model by.

scale(scaling: typing_extensions.Dict[random_events.variable.Variable, int])

Scale the model in-place. Scaling is done by multiplying the variable location influencing values. The scaling can be viewed as what happens when you multiply the numeric variables of the model by a constant vector.

Parameters:

scaling – The variable value pairs to scale the model by.

class probabilistic_model.distributions.distributions.DiracDeltaDistribution(variable: random_events.variable.Continuous, location: float, density_cap: float = np.inf, tolerance: float = 1e-06)

Bases: ContinuousDistribution

Class for Dirac delta distributions. The Dirac measure is used whenever evidence is given as a singleton instance.

https://en.wikipedia.org/wiki/Dirac_delta_function

variable: random_events.variable.Continuous

location: float

The location of the Dirac delta distribution.

density_cap: float

The density cap of the Dirac delta distribution. This value will be used to replace infinity in likelihood.

tolerance: float = 1e-06

The tolerance of deviations of the location of the Dirac delta distribution. This is used during calculations to take precision problems into account.

log_likelihood(events: numpy.array) → numpy.array

Calculate the log-likelihood of an event.

Check the documentation of likelihood for more information.

Parameters:

events – The full evidence event with shape (#events, #variables)

Returns:

The log-likelihood of the event with shape (#events).

cdf(x: numpy.array) → numpy.array

Calculate the cumulative distribution function at x. :param x: The data :return: The cumulative distribution function at x

property abbreviated_symbol: str

property univariate_support: random_events.variable.Interval

Returns:

The univariate support of the distribution. This is not an Event.

log_conditional_from_simple_interval(interval: random_events.variable.SimpleInterval) → typing_extensions.Tuple[typing_extensions.Self, float]

Calculate the truncated distribution given a simple interval.

Parameters:

interval – The simple interval

Returns:

The truncated distribution and the log-probability of the interval.

probability_of_simple_event(event: random_events.product_algebra.SimpleEvent) → float

Calculate the probability of a simple event.

The event belongs to the class of marginal queries.

Note

You can read more about queries of this class in Definition 11 in [CVVdB20] or watch the video tutorial. [US20]

Parameters:

event – The event.

Returns:

The probability of the event.

univariate_log_mode() → typing_extensions.Tuple[random_events.variable.AbstractCompositeSet, float]

Returns:

The univariate mode of the distribution and its log-likelihood. The mode is not an Event.

sample(amount: int) → numpy.array

Sample from the model.

Parameters:

amount – The number of samples to draw.

Returns:

The samples.

moment(order: probabilistic_model.probabilistic_model.OrderType, center: probabilistic_model.probabilistic_model.CenterType) → probabilistic_model.probabilistic_model.MomentType

Calculate the (centralized) moment of the distribution.

\[\int_{-\infty}^{\infty} (x - center)^{order} pdf(x) dx\]

Note

You can read more about queries of this class in Definition 22 in :cite:p:`choi2020probabilistic`_. [US20]

Parameters:

• order – The orders of the moment as a variable map for every continuous and integer variable.

• center – The center of the moment as a variable map for every continuous and integer variable.

Returns:

The moments of the variables in order.

__eq__(other)

__hash__()

property representation

The symbol used to represent this distribution.

__repr__()

__copy__()

__deepcopy__(memo=None)

to_json() → typing_extensions.Dict[str, typing_extensions.Any]

classmethod _from_json(data: typing_extensions.Dict[str, typing_extensions.Any]) → typing_extensions.Self

Create a variable from a json dict. This method is called from the from_json method after the correct subclass is determined and should be overwritten by the respective subclass.

Parameters:

data – The json dict

Returns:

The deserialized object

plot(**kwargs) → typing_extensions.List

Generate traces that can be plotted with plotly.

Parameters:

• number_of_samples – The number of samples to draw.

• surface – If True, plot the model as a surface plot.

• mode – If True, plot the mode of the model.

Returns:

The traces.

translate(translation: random_events.product_algebra.VariableMap[random_events.variable.Variable, float])

Translate the model in-place. Translation is done by adding the translation to the variable location influencing values. The translation can be viewed as what happens when you shift the numeric variables of the model by a constant vector.

Parameters:

translation – The variable value pairs to translate the model by.

scale(scaling: random_events.product_algebra.VariableMap[random_events.variable.Variable, float])

Scale the model in-place. Scaling is done by multiplying the variable location influencing values. The scaling can be viewed as what happens when you multiply the numeric variables of the model by a constant vector.

Parameters:

scaling – The variable value pairs to scale the model by.