Conditional Distribution

The Conditional distribution is used to model conditional dependencies between two random variables. This can be used for separate data types.

Assume we have observed \((x_i, y_i)\) where \(x_i\) has data type \(T_1\) and \(y_i\) has data type \(T_2\) The Conditional distribution is used to model conditional dependencies between two random variables. This can be used for separate data types.

Assume we have observed \((x_i, y_i)\) where \(x_i\) has data type \(T_1\) and \(y_i\) has data type \(T_2\). Choosing a compatible given distribution \(f(x_i \vert theta_1)\) for \(x_i\) and a distribution \(g(y_i \vert \theta_2)\), the conditional density is given by

\[f((x_i, y_i)) = g(y_i \vert x_i, \theta_2) h(x_i \vert \theta_1)).\]

Note that each value of \(x_i\) emits a distribution over the support of y values.

ConditionalDistribution

class dmx.stats.conditional.ConditionalDistribution(dmap, default_dist=NullDistribution(name=None), given_dist=NullDistribution(name=None), name=None, keys=None)

ConditionalDistribution object for data types x=Tuple[T0, T1].

dmap

Mapping from T0 to distributions.

Type:: Dict[T0, SequenceEncodableProbabilityDistribution]

default_dist

Default distribution if key not in dmap.

Type:: SequenceEncodableProbabilityDistribution

given_dist

Distribution for given variable.

Type:: SequenceEncodableProbabilityDistribution

has_default

True if default_dist is not NullDistribution.

Type:: bool

has_given

True if given_dist is not NullDistribution.

Type:: bool

name

Name assigned to object.

Type:: Optional[str]

keys

All ConditionalDistribution objects with same keys value are the same distribution.

Type:: Optional[str]

__init__(dmap, default_dist=NullDistribution(name=None), given_dist=NullDistribution(name=None), name=None, keys=None)

Initialize ConditionalDistribution.

Parameters:

dmap (Union[Dict[Any, SequenceEncodableProbabilityDistribution], List[SequenceEncodableProbabilityDistribution]]) – Used to create dictionary of distributions.
default_dist (Optional[SequenceEncodableProbabilityDistribution]) – Distribution for case where x[0] is not a key in dmap.
given_dist (Optional[SequenceEncodableProbabilityDistribution]) – Distribution for the given variable.
name (Optional[str], optional) – Name assigned to object.
keys (Optional[str], optional) – All ConditionalDistribution objects with same keys value are the same distribution.

density(x)

Evaluate density of ConditionalDistribution at Tuple x.

Parameters:: x (Tuple[T0, T1]) – T0 data type must match keys of dmap, T1 must match value of dmap distribution for key value.
Returns:: Density of ConditionalDistribution at Tuple x.
Return type:: float

dist_to_encoder()

Return a ConditionalDistributionDataEncoder for this distribution.

Returns:: Encoder object.
Return type:: ConditionalDistributionDataEncoder

estimator(pseudo_count=None)

Create ConditionalDistributionEstimator from sufficient statistics.

Parameters:: pseudo_count (Optional[float], optional) – Used to inflate the sufficient statistics.
Returns:: Estimator object.
Return type:: ConditionalDistributionEstimator

log_density(x)

Evaluate log-density of ConditionalDistribution at Tuple x.

Parameters:: x (Tuple[T0, T1]) – T0 data type must match keys of dmap, T1 must match value of dmap distribution for key value.
Returns:: Log-density of ConditionalDistribution at Tuple x.
Return type:: float

sampler(seed=None)

Create ConditionalDistributionSampler for sampling from this distribution.

Parameters:: seed (Optional[int], optional) – Seed for random number generator.
Returns:: Sampler object.
Return type:: ConditionalDistributionSampler

seq_log_density(x)

Vectorized log-density for encoded data.

Parameters:: x (ConditionalEncodedDataSequence) – Encoded data sequence.
Returns:: Log-density values.
Return type:: np.ndarray
Raises:: Exception – If input is not a ConditionalEncodedDataSequence.

ConditionalDistributionEstimator

class dmx.stats.conditional.ConditionalDistributionEstimator(estimator_map, default_estimator=<dmx.stats.null_dist.NullEstimator object>, given_estimator=<dmx.stats.null_dist.NullEstimator object>, name=None, keys=None)

Estimator for ConditionalDistribution.

estimator_map

Estimators for each conditional distribution.

Type:: Dict[T0, ParameterEstimator]

default_estimator

Estimator for default_distribution.

Type:: ParameterEstimator

given_estimator

Estimator for given_distribution.

Type:: ParameterEstimator

name

Name for object.

Type:: Optional[str]

keys

ConditionalDistributionEstimator with matching ‘keys’ will be aggregated.

Type:: Optional[str]

__init__(estimator_map, default_estimator=<dmx.stats.null_dist.NullEstimator object>, given_estimator=<dmx.stats.null_dist.NullEstimator object>, name=None, keys=None)

Initialize ConditionalDistributionEstimator.

Parameters:

estimator_map (Dict[T0, ParameterEstimator]) – Estimators for each conditional distribution.
default_estimator (Optional[ParameterEstimator]) – Estimator for default_distribution.
given_estimator (Optional[ParameterEstimator]) – Estimator for given_distribution.
name (Optional[str], optional) – Name for object.
keys (Optional[str], optional) – ConditionalDistributionEstimator with matching ‘keys’ will be aggregated.

Raises:

TypeError – If keys is not a string or None.

accumulator_factory()

Return a ConditionalDistributionAccumulatorFactory for this estimator.

Returns:: Factory object.
Return type:: ConditionalDistributionAccumulatorFactory

estimate(nobs, suff_stat)

Estimate a ConditionalDistribution from aggregated data.

Parameters:

nobs (Optional[float]) – Not used. Kept for consistency.
suff_stat (Tuple[Dict[T0, SS0], Optional[SS1], Optional[SS2]]) – Sufficient statistics.

Returns:

Estimated distribution.

Return type:

ConditionalDistribution

ConditionalDistributionSampler

class dmx.stats.conditional.ConditionalDistributionSampler(dist, seed=None)

Sampler for ConditionalDistribution.

dist

ConditionalDistribution object to draw samples from.

Type:: ConditionalDistribution

default_sampler

Sampler for default_dist.

Type:: DistributionSampler

has_default_sampler

True if default sampler is not NullDistribution.

Type:: bool

given_sampler

Sampler for given_dist.

Type:: DistributionSampler

has_given_sampler

True if given sampler is not NullDistribution.

Type:: bool

samplers

Dictionary of samplers for each key.

Type:: Dict[T0, DistributionSampler]

sample(size=None)

Sample independent samples from ConditionalDistribution.

Parameters:: size (Optional[int], optional) – Number of samples to draw. If None, returns a single sample.
Returns:: A tuple or list of tuples of (T0, T1).
Return type:: Union[Tuple[Any, Any], List[Tuple[Any, Any]]]

sample_given(x)

Sample from conditional distribution given value x.

Parameters:: x (T0) – Value of given/conditional variable.
Returns:: Single sample from the conditional distribution for x.
Return type:: Any

single_sample()

Generate a single sample from the ConditionalDistribution.

Returns:: (T0, T1) as defined from dmap and given_distribution types in dist.
Return type:: Tuple[Any, Any]