Learning from Continuous Data

All modules related to learning Bayesian Belief Networks BBNs from multivariate Gaussian data.

Data

The data.

class pysparkbbn.continuous.data.CondMvn(index_1: List[int], index_2: List[int], means: ndarray, cov: ndarray, zero=1e-06, cols_1: List[str] = None, cols_2: List[str] = None)

Bases: object

Conditional multivariate normal.

__init__(index_1: List[int], index_2: List[int], means: ndarray, cov: ndarray, zero=1e-06, cols_1: List[str] = None, cols_2: List[str] = None)

ctor

Parameters

index_1 – Index of dependent variables.
index_2 – Index oc conditioning variables.
means – Means.
cov – Covariance matrix.
zero – Threshold below which to consider a probability as zero.
cols_1 – Names corresponding to index_1.
cols_2 – Names corresponding to index_2.

equals(other: Any) → bool

Checks if this is equal to other.

Parameters: other – CondMvn.
Returns: Boolean.

log_proba(x: ndarray) → ndarray

Estimate the log conditional probability of the specified data point.

Parameters: x – Data point.
Returns: Log probability.

static partition_cov(cov: ndarray, index_1: List[int], index_2: List[int]) → Tuple[ndarray, ndarray, ndarray, ndarray]

Partitions the covariance matrix.

Parameters

cov – Covariance matrix.
index_1 – Index.
index_2 – Index.

Returns

Partitioned covariance matrix.

static partition_means(means: ndarray, index_1: List[int], index_2: List[int]) → Tuple[ndarray, ndarray]

Partitions the means.

Parameters

means – Means.
index_1 – Index.
index_2 – Index.

Returns

Partitoned mean.

static partition_x(x: ndarray, index_1: List[int], index_2: List[int]) → Tuple[ndarray, ndarray]

Partitions the data point.

Parameters

x – Data point.
index_1 – Index.
index_2 – Index.

Returns

Tuple of data point partitioned.

pdf(x: ndarray) → float

Estimate the conditional probability of the specified data point.

Parameters: x – Data point.
Returns: Probability.

class pysparkbbn.continuous.data.GaussianData(sdf: DataFrame, n_samples=6, spark=None)

Bases: object

Gaussian data.

__init__(sdf: DataFrame, n_samples=6, spark=None)

ctor

Parameters

sdf – Spark data frame.
n_samples – Number of samples.
spark – Spark object: Bug requirement.

drop(columns: List[str])

Drops specified columns.

Parameters: columns – List of columns.
Returns: Guassian data.

get_cmi_par(triplets: List[Triplet]) → List[Tuple[List[str], List[str], List[str], float]]

Computes conditional mutual information between triplets in parallel.

Parameters: triplets – List of triplets (of variables).
Returns: List of conditional mutual information.

get_covariance() → ndarray

Gets the covariance matrix.

Returns: Covariance matrix.

get_means() → ndarray

Get means.

Returns: List of means.

get_mi_par(pairs: List[Pair]) → List[Tuple[List[str], List[str], float]]

Computes mutual information between the pairs of variables in parallel.

Parameters: pairs – List of pairs (of variables).
Returns: List of mutual information.

get_min_max(columns: List[str]) → Dict[str, Dict[str, Union[int, float]]]

Get dictionary of min/max.

Parameters: columns – Variable names.
Returns: Dictionary of min/max associated with names.

get_min_max_for(column: str) → Dict[str, Union[int, float]]

Get min/max value for specified variable.

Parameters: column – Variable name.
Returns: Dictionary of min/max.

get_mvn(columns: List[str]) → Mvn

Gets a multivariate normal instance.

Parameters: columns – List of variable names.
Returns: Multivariate normal.

get_pair(x: List[str], y: List[str]) → Pair

Gets a pair.

Parameters

x – X variables.
y – Y variables.

Returns

Pair.

get_pairs(col_pairs: List[Tuple[List[str], List[str]]] = None) → List[Pair]

Gets list of pairs.

Parameters: col_pairs – List of column pairs.
Returns: List of pairs.

get_pairwise_columns() → Generator[Tuple[List[str], List[str]], None, None]

Gets pairs of columns.

Returns: List of pairs of columns. Each column is inside an array.

get_profile() → Dict[str, Dict[str, float]]

Gets profile of variables.

Returns: Dictionary; keys are variable names and values are summary stats.

get_score_par(cmvns: List[CondMvn]) → List[Tuple[List[str], List[str], float]]

Computes the scores.

Parameters: cmvns – List of conditional multivariate gaussian distributions.
Returns: List of scores.

get_triplet(x: List[str], y: List[str], z: List[str]) → Triplet

Gets a triplet.

Parameters

x – X variables.
y – Y variables.
z – Z variables.

Returns

Triplet.

get_triplets(col_triplets: List[Tuple[List[str], List[str], List[str]]])

Gets list of triplets.

Parameters: col_triplets – List of column triplets.
Returns: List of triplets.

slice_covariance(columns: List[str]) → ndarray

Slices covariance matrix according to variables.

Parameters: columns – List of variables.
Returns: Covariance matrix.

slice_means(columns: List[str]) → ndarray

Slices means vector according to variables.

Parameters: columns – List of variables.
Returns: List of means.

class pysparkbbn.continuous.data.Mvn(columns: List[str], means: ndarray, cov: ndarray, profile: Dict[str, Dict[str, float]], n_samples=10)

Bases: object

Multivariate normal distribution.

__init__(columns: List[str], means: ndarray, cov: ndarray, profile: Dict[str, Dict[str, float]], n_samples=10)

ctor

Parameters

columns – List of variable names.
means – Vector means.
cov – Covariance matrix.
profile – Dictionary of min/max for each variable.
n_samples – Number of samples.

get_values() → Generator[Tuple[float, ...], None, None]

Gets the sampled values.

Returns: Generator of values.

pdf(x: ndarray) → float

Estimate the probability of the specified data point.

Parameters: x – Data point.
Returns: Probability.

class pysparkbbn.continuous.data.Pair(X: Mvn, Y: Mvn, XY: Mvn)

Bases: object

Pair of variables.

__init__(X: Mvn, Y: Mvn, XY: Mvn)

ctor

Parameters

X – X variables.
Y – Y variables.
XY – XY variables.

get_mi() → float

Computes the mutual information.

Returns: Mutual information.

get_partial_mi(dp: ndarray) → float

Computes the partial mutual information.

Parameters: dp – Data point.
Returns: Partial mutual information.

get_values() → Generator[Tuple[float, ...], None, None]

Gets the XY values.

Returns: Generator of XY values.

class pysparkbbn.continuous.data.Triplet(x_cols: List[str], y_cols: List[str], z_cols: List[str], Z: Mvn, XZ: Mvn, YZ: Mvn, XYZ: Mvn)

Bases: object

Triplet variables.

__init__(x_cols: List[str], y_cols: List[str], z_cols: List[str], Z: Mvn, XZ: Mvn, YZ: Mvn, XYZ: Mvn)

ctor

Parameters

x_cols – X columns.
y_cols – Y columns.
z_cols – Z columns.
Z – Z variables.
XZ – XZ variables.
YZ – YZ variables.
XYZ – XYZ variables.

get_cmi() → float

Computes the conditional mutual information.

Returns: Conditional mutual information.

get_partial_mi(dp: ndarray) → float

Computes the partial mutual information.

Parameters: dp – Data point.
Returns: Partial mutual information.

get_values() → Generator[Tuple[float, ...], None, None]

Gets the XYZ values.

Returns: List of XYZ values.

Structure Learning

Constraint-Based

Constraint-based structure learning.

class pysparkbbn.continuous.scblearn.Ban(data: GaussianData, clazz: str, cmi_threshold=0.0001, method='pc')

Bases: BaseStructureLearner

Modified Bayesian network augmented naive bayes (BAN). See Bayesian Network Classifiers.

__init__(data: GaussianData, clazz: str, cmi_threshold=0.0001, method='pc')

ctor

Parameters

data – Data.
clazz – Class variable.
cmi_threshold – Threshold (equal to above which) to consider conditionally dependent.
method – Either pc or tpda (default=pc).

get_network() → DiGraph: Gets the network structure.

class pysparkbbn.continuous.scblearn.BaseStructureLearner(data: GaussianData)

Bases: object

Base structure learner.

__init__(data: GaussianData)

ctor

Parameters: data – Data.

get_network() → DiGraph: Gets the network structure.

class pysparkbbn.continuous.scblearn.Mwst(data: GaussianData, cmi_threshold=0.01)

Bases: BaseStructureLearner

Maximum weight spanning tree.

__init__(data: GaussianData, cmi_threshold=0.01)

ctor

Parameters: data – Data. :param cmi_threshold: Threshold (equal to above which) to consider conditionally dependent.

get_network() → DiGraph: Gets the network structure.

class pysparkbbn.continuous.scblearn.Naive(data: GaussianData, clazz: str)

Bases: BaseStructureLearner

Naive Bayesian network. The clazz variable/node is drawn with an arc to all other nodes.

__init__(data: GaussianData, clazz: str)

ctor.

Parameters

data – Data.
clazz – The clazz node.

get_network() → DiGraph: Gets the network structure.

class pysparkbbn.continuous.scblearn.Pc(data: GaussianData, cmi_threshold=0.0001)

Bases: BaseStructureLearner

PC algorithm. See A fast PC algorithm for high dimensional causal discovery with multi-core PCs.

__init__(data: GaussianData, cmi_threshold=0.0001)

ctor

Parameters

data – Data.
depth – Maximum depth.
cmi_threshold – Threshold (equal to above which) to consider conditionally dependent.

get_network() → DiGraph: Gets the network structure.

learn_undirected_graph() → Graph

Learns an undirected graph.

Returns: Undirected graph.

class pysparkbbn.continuous.scblearn.Tan(data: GaussianData, clazz: str, cmi_threshold=0.01)

Bases: Mwst

Tree-augmented network. See Comparing Bayesian Network Classifiers.

__init__(data: GaussianData, clazz: str, cmi_threshold=0.01)

ctor.

Parameters

data – Data.
clazz – The clazz node.
cmi_threshold – Threshold (equal to above which) to consider conditionally dependent.

get_network() → DiGraph: Gets the network structure.

class pysparkbbn.continuous.scblearn.Tpda(data: GaussianData, cmi_threshold=0.006)

Bases: Mwst

Three-phase dependency analysis (TPDA). See Learning Belief Networks from Data: An Information Theory Based Approach.

__init__(data: GaussianData, cmi_threshold=0.006)

ctor.

Parameters

data – Data.
cmi_threshold – Threshold (equal to above which) to consider conditionally dependent.

get_network() → DiGraph: Gets the network structure.

learn_undirected_graph() → Graph

Learns an undirected graph.

Returns: Undirected graph.

Search-and-Scoring

Search-and-scoring structure learning.

class pysparkbbn.continuous.ssslearn.Ga(data: GaussianData, sc: SparkContext, max_parents=4, mutation_rate=0.25, pop_size=100, crossover_prob=0.5, max_iters=20, convergence_threshold=3, ordering='mwst', ordering_params={'cmi_threshold': 0.0001}, seed=37)

Bases: object

Uses genetic algorithm to search-and-score candidate networks. The particular algorithm is actually a hybrid approach where the ordering of nodes is induced first by a constraint-based algorithm (MWST, PC or TPDA). The ordered nodes are then used to constrain the candidate parents of each node; later nodes cannot be parents of earlier ones. See Learning Bayesian Networks: Search Methods and Experimental results.

__init__(data: GaussianData, sc: SparkContext, max_parents=4, mutation_rate=0.25, pop_size=100, crossover_prob=0.5, max_iters=20, convergence_threshold=3, ordering='mwst', ordering_params={'cmi_threshold': 0.0001}, seed=37)

ctor

Parameters

data – Data.
sc – Spark context.
max_parents – Maximum number of parents (default=4).
mutation_rate – Mutation rate (default=0.25).
pop_size – Population size (default=100).
crossover_prob – Crossover probability (default=0.5).
max_iters – Maximum iterations (default=20).
convergence_threshold – Convergence threshold; terminate when no improvement is made after this many generations (default=3).
ordering – Ordering method: mwst, pc or tpda (default=mwst).
ordering_params – Ordering parameters to the ordering method.
seed – Seed for random number generation (default=37).

get_network() → DiGraph: Gets the network structure.