Trilearn package

Subpackages

• Distributions
  • Dirichlet
  • Discrete decomposable log linear
  • Graph intra-class
  • Graph inverse-Wishart
  • Gaussian graphical model
  • Junction tree clustering
  • Matrix multivariate normal
  • Multivariate students-t
  • Sequential junction tree distribution
  • Wishart distribution
• Graph
  • Decomposable graph
  • Empirical graph distribution
  • Undirected graph
  • Connect/disconnect cliques
  • Junction tree
  • Junction tree collapser
  • Junction tree expander
  • Subtree sampler
  • Graph trajectory

Auxiliary functions

trilearn.auxiliary_functions.gen_prec_mat(graph, a)

trilearn.auxiliary_functions.get_marg_counts(full_data, subset)

Returns a contingency table in dictionary form.

Parameters:

• data (np.array) – The data in n x p form.
• subset (list) – The subset of interest

trilearn.auxiliary_functions.group_trajectories_by_setting(trajlist)

trilearn.auxiliary_functions.is_pos_def(x)

trilearn.auxiliary_functions.l1_loss(m1, m2)

L1 loss.

Parameters:

• m1 (Numpy array) – A matrix
• m1 – A matrix

Returns:

float

trilearn.auxiliary_functions.l2_loss(m1, m2)

L2 loss between m1 and m2.

Parameters:

• m1 (Numpy array) – A matrix
• m1 – A matrix

Returns:

float

trilearn.auxiliary_functions.plot_graph_traj_statistics(graph_traj, write_to_file=False)

trilearn.auxiliary_functions.plot_heatmap(heatmap, cbar=False, annot=False, xticklabels=1, yticklabels=1)

trilearn.auxiliary_functions.plot_matrix(m, filename, extension, title='Adjmat')

Plots a 2-dim numpy array as heatmap. :param m: matrix to plot. :type m: numpy array

trilearn.auxiliary_functions.plot_multiple_traj_statistics(trajs, burnin_end, write_to_file=False, annot=False, output_directory='./', file_extension='eps')

trilearn.auxiliary_functions.random_element_from_coll(A)

trilearn.auxiliary_functions.random_subset(A)

Draws a random subset of elements in a list, inclding the empty set.

Parameters:A (list) – Returns:Subset of A. Return type:set

trilearn.auxiliary_functions.read_all_trajectories_in_dir(directory)

trilearn.auxiliary_functions.sample_classification_datasets(mus, covmats, n_samples_in_each_class)

trilearn.auxiliary_functions.spc1(true_graph, est_graph)

Takes 2 adjacency matrices.

trilearn.auxiliary_functions.tpr(true_graph, est_graph)

Calculates the True positive rate of an estimated adjacency matrix.

Graph predictive classification

A Bayesian graphical predictive classifier.

class trilearn.graph_predictive.GraphPredictive(n_particles=None, n_pgibbs_samples=None, prompt_burnin=False, only_map_graph=False, standard_bayes=False, cta_alpha=0.5, cta_beta=0.5, true_graphs=None, async=False)

Bases: sklearn.base.BaseEstimator

fit(x, y, hyper_mu=None, hyper_v=None, hyper_tau=None, hyper_alpha=None, same_graph_groups=None)

These parameters are set here in the constructor in order to avoid mismatch since the hyper parameters in classification has to be consistent with those in the structure learning procedure.

Parameters:

• x (Numpy matrix) – Matrix of training data
• y (Numpy array) – Array of class correspondence
• hyper_mu (Numpy array) – Array of mean hyper parameter for
• normal inverse Wishart density (the) –
• hyper_v (float) – Parameter in the covariace matrix in the normal inverse Wishart density
• hyper_tau (Numpy matrix) – Precision matrix in the normal inverse Wishart density
• hyper_alpha (float) – Degrees of freedom in the normal inverse Wishart density

gen_gibbs_chains(n_particles, n_pgibbs_samples, smc_radius=None, cta_alpha=0.5, cta_beta=0.5, async=True)

If same_graph is True, this generates one single Gibbs graph-trajectory for common for all classes. Otherwise, this generates Gibbs graph-trajectories for each class.

Parameters:smc_radius – radius for the SMC algorithm.

get_group(c)

gibbs_chains_from_json(gibbs_js)

Reads a Gibbs trajectory in json format.

Parameters:gibbs_js (dict) – Gibbs trajectory in json format.

gibbs_chains_to_json(title, optional={})

Returns the Gibbs trajectory in json format.

Parameters:

• title (string) – The json key for the attriute _id
• optional (dict) – Optional infor in json format to be included in the json object.

graph_dists_from_json(json_graph_dists)

graph_dists_to_json(dists_ids, optional={})

plot_class_heatmap(c)

plot_group_heatmap(group)

predict(x_new)

predict_likelihoods(x_new)

Model: x_i | M=m, R=r ~ Normal(m,r) R ~ Wishart(tau, alpha) M | R=r ~ Normal(mu, r*v) Args: x_new: row matrix with new observations for which we

the predictive density will be computed. Example 2-dim x. [[0.4, 0.5],

[0.2, 1.4]] x: row matrix with training data y: vector of classes mu: hyper parameter for M v: hyper parameter for M classes: unique class labels, eg. [0, 1, 2] graph_distribution: dictionary with graph distribution for each class.

predict_proba(X)

Estimate probability. :param X: Input data. :type X: array-like, shape (n_samples, n_features)

Returns:C – Estimated probabilities. Return type:array, shape (n_samples, n_classes)

predictive_pdf(x_new, x, mu, v, tau, alpha, graph_dist)

This is the predictive distribution of x_new. It is a multivatiate T-distributiona where the graph is marginalized out accordning to according to graph_dist.

score(x_test, y_test)

set_burnin(true_graphs=None, directory='.', title='')

Sets the burn-in period for the class-groups.

set_graph_dists(true_graphs=None, json_trajs=None, directory='.', title='', set_burnins=False)

set_hyper_parameters(hyper_mu, hyper_v, hyper_tau, hyper_alpha)

Parameters:

• hyper_mu (Numpy array) – Array of mean hyper parameter for the normal inverse wishart density
• hyper_v (float) – Parameter in the covariance matrix in the normal inverse wishart density
• hyper_tau (Numpy matrix) – Precision matrix in the normal inverse wishart density
• hyper_alpha (float) – Degrees of freedom in the normal inverse wishart density

P. Green & A. Thomas MH-sampler

trilearn.mh_greenthomas.sample_trajectories_ggm_parallel(dataframe, n_samples, randomize=[1000], D=None, delta=1.0, reps=1, output_directory='.', **args)

trilearn.mh_greenthomas.sample_trajectories_ggm_to_file(dataframe, n_samples, randomize=[1000], D=None, delta=1.0, reps=1, output_directory='.', **args)

trilearn.mh_greenthomas.sample_trajectories_loglin_parallel(dataframe, n_samples, randomize=[1000], pseudo_obs=[1.0], reps=1, output_directory='.', **args)

trilearn.mh_greenthomas.sample_trajectories_loglin_to_file(dataframe, n_samples, randomize=[1000], pseudo_obs=[1.0], reps=1, output_directory='.', **args)

trilearn.mh_greenthomas.sample_trajectory(n_samples, randomize, sd)

trilearn.mh_greenthomas.sample_trajectory_ggm(dataframe, n_samples, randomize=1000, D=None, delta=1.0, cache={}, **args)

trilearn.mh_greenthomas.sample_trajectory_loglin(dataframe, n_samples, pseudo_obs=1.0, randomize=1000, cache={}, **args)

trilearn.mh_greenthomas.sample_trajectory_uniform(n_samples, randomize=100, graph_size=5, cache={}, **args)

trilearn.mh_greenthomas.trajectory_to_file(n_samples, randomize, seqdist, dir='.', reseed=False)

Writes the trajectory of graphs generated by particle Gibbs to file.

Parameters:

• seq_dist (SequentialJTDistributions) – the distribution to be sampled from
• filename_prefix (string) – prefix to the filename

Returns:

Markov chain of underlying graphs of the junction trees sampled by pgibbs.

Return type:

Trajectory

trilearn.mh_greenthomas.trajectory_to_queue(n_samples, randomize, seqdist, queue, reseed=False)

Writes the trajectory of graphs generated by particle Gibbs to file.

Parameters:

• seq_dist (SequentialJTDistributions) – the distribution to be sampled from
• filename_prefix (string) – prefix to the filename

Returns:

Markov chain of underlying graphs of the junction trees sampled by pgibbs.

Return type:

Trajectory

Node-drive MH-sampler

Metropolis-Hastings sampler for junction tree distributions.

trilearn.mh_nodedriven.accept_proposal_prob(from_tree, reduced_tree, to_tree, moved_node, alpha, beta, seq_dist)

trilearn.mh_nodedriven.gen_ggm_trajectory(dataframe, n_samples, D=None, delta=1.0, cache={}, alpha=0.5, beta=0.5, **args)

trilearn.mh_nodedriven.log_post_ratio(from_tree, to_tree, seqdist)

trilearn.mh_nodedriven.log_prop_pdf(from_tree, reduced_tree, to_tree, moved_node, alpha, beta)

trilearn.mh_nodedriven.log_prop_ratio(from_tree, reduced_tree, to_tree, moved_node, alpha, beta)

trilearn.mh_nodedriven.mh(alpha, beta, traj_length, seq_dist, jt_traj=None, debug=False)

A Metropolis-Hastings implementation for approximating distributions over junction trees.

Parameters:

• traj_length (int) – Number of Gibbs iterations (samples)
• alpha (float) – sparsity parameter for the Christmas tree algorithm
• beta (float) – sparsity parameter for the Christmas tree algorithm
• seq_dist (SequentialJTDistributions) – the distribution to be sampled from

Returns:

Markov chain of teh underlying graphs of the junction trees sampled by M-H.

Return type:

Trajectory

trilearn.mh_nodedriven.proposal_sample(from_tree, alpha, beta, n_nodes, **args)

trilearn.mh_nodedriven.trans_sample(from_tree, alpha, beta, seq_dist, **args)

Particle Gibbs

trilearn.pgibbs.sample_trajectories_ggm(dataframe, n_particles, n_samples, D=None, delta=1.0, alphas=[0.5], betas=[0.5], radii=[None], reset_cache=True, reps=1, **args)

trilearn.pgibbs.sample_trajectories_ggm_parallel(dataframe, n_particles, n_samples, D=None, delta=1.0, alphas=[0.5], betas=[0.5], radii=[None], reset_cache=True, reps=1, **args)

trilearn.pgibbs.sample_trajectories_ggm_to_file(dataframe, n_particles, n_samples, D=None, delta=1.0, alphas=[0.5], betas=[0.5], radii=[None], reset_cache=True, reps=1, output_directory='.', output_filename='trajectory.json', **args)

trilearn.pgibbs.sample_trajectories_loglin(dataframe, n_particles, n_samples, pseudo_observations=[1.0], alphas=[0.5], betas=[0.5], radii=[None], reset_cache=True, reps=1, **args)

trilearn.pgibbs.sample_trajectories_loglin_parallel(dataframe, n_particles, n_samples, pseudo_observations=[1.0], alphas=[0.5], betas=[0.5], radii=[None], reset_cache=True, reps=1, output_directory='.', **args)

trilearn.pgibbs.sample_trajectories_loglin_to_file(dataframe, n_particles, n_samples, pseudo_observations=[1.0], alphas=[0.5], betas=[0.5], radii=[None], reset_cache=True, reps=1, output_directory='.', output_filename='trajectory.json', **args)

trilearn.pgibbs.sample_trajectory(smc_N, alpha, beta, radius, n_samples, seq_dist, jt_traj=None, debug=False, reset_cache=True)

A particle Gibbs implementation for approximating distributions over junction trees.

Parameters:

• smc_N (int) – Number of particles in SMC in each Gibbs iteration
• n_samples (int) – Number of Gibbs iterations (samples)
• alpha (float) – sparsity parameter for the Christmas tree algorithm
• beta (float) – sparsity parameter for the Christmas tree algorithm
• radius (float) – defines the radius within which ned nodes are selected
• seq_dist (SequentialJTDistributions) – the distribution to be sampled from

Returns:

Markov chain of the underlying graphs of the junction trees sampled by pgibbs.

Return type:

Trajectory

trilearn.pgibbs.sample_trajectory_ggm(dataframe, n_particles, n_samples, D=None, delta=1.0, alpha=0.5, beta=0.5, radius=None, reset_cache=True, **args)

Particle Gibbs for approximating distributions over Gaussian graphical models.

Parameters:

• n_particles (int) – Number of particles in SMC in each Gibbs iteration
• n_samples (int) – Number of Gibbs iterations (samples)
• alpha (float) – sparsity parameter for the Christmas tree algorithm
• beta (float) – sparsity parameter for the Christmas tree algorithm
• radius (float) – defines the radius within which ned nodes are selected
• dataframe (np.matrix) – row matrix of data
• D (np.matrix) – matrix parameter for the hyper inverse wishart prior
• delta (float) – degrees of freedom for the hyper inverse wishart prior
• cache (dict) – cache for clique likelihoods

Returns:

Markov chain of the underlying graphs of the junction trees sampled by pgibbs.

Return type:

Trajectory

trilearn.pgibbs.sample_trajectory_loglin(dataframe, n_particles, n_samples, pseudo_obs=1.0, alpha=0.5, beta=0.5, radius=None, reset_cache=True, **args)

trilearn.pgibbs.trajectory_to_file(n_particles, n_samples, alpha, beta, radius, seqdist, node_labels, reset_cache=True, dir='.', output_filename='trajectory.csv', reseed=False)

Writes the trajectory of graphs generated by particle Gibbs to file.

Parameters:

• n_particles (int) – Number of particles in SMC in each Gibbs iteration
• n_samples (int) – Number of Gibbs iterations (samples)
• alpha (float) – sparsity parameter for the Christmas tree algorithm
• beta (float) – sparsity parameter for the Christmas tree algorithm
• radius (float) – defines the radius within which ned nodes are selected
• seq_dist (SequentialJTDistributions) – the distribution to be sampled from
• filename_prefix (string) – prefix to the filename

Returns:

Markov chain of underlying graphs of the junction trees sampled by pgibbs.

Return type:

Trajectory

trilearn.pgibbs.trajectory_to_queue(n_particles, n_samples, alpha, beta, radius, seqdist, queue, reset_cache=True, reseed=False)

Writes the trajectory of graphs generated by particle Gibbs to file.

Parameters:

• n_particles (int) – Number of particles in SMC in each Gibbs iteration
• n_samples (int) – Number of Gibbs iterations (samples)
• alpha (float) – sparsity parameter for the Christmas tree algorithm
• beta (float) – sparsity parameter for the Christmas tree algorithm
• radius (float) – defines the radius within which ned nodes are selected
• seq_dist (SequentialJTDistributions) – the distribution to be sampled from
• filename_prefix (string) – prefix to the filename

Returns:

Markov chain of underlying graphs of the junction trees sampled by pgibbs.

Return type:

Trajectory

Stochastic set process

trilearn.set_process.backward_order_neigh_log_prob(from_order, to_order, radius, maxradius)

Probability of generating order from_order from the larger order to_order under the restriction that no hole greater than radius is created.

trilearn.set_process.backward_order_neigh_set(from_order, radius, maxradius)

Returns the list of nodes that can be removed from from_order (the greater order).

trilearn.set_process.backward_perm_traj_sample(p, radius)

Samples a permutation tajectory with maximum p indices.

trilearn.set_process.gen_backward_order_neigh(from_order, radius, maxradius)

Returns: A permutation wit one less element than fromm_order

trilearn.set_process.gen_order_neigh(from_order, radius, total_set)

Returns a list with one more element than from_order

such that the new element is within the radius and belongs to total_set.

Parameters:

• from_order (list) – list of elements
• radius (int) – specifies the radius within which the new element can be taken
• total_set (list) – the full set of elements

Returns:

numpy array

trilearn.set_process.order_neigh_log_prob(from_order, to_order, radius, total_set)

Since the perm trajectory is Markovian, the ratio becomes only the probability.

trilearn.set_process.order_neigh_set(current_order, radius, total_set)

The set of neighbors of current_order with maximal distance radius (of total_set current_order).

SMC

Sequential Monte Carlo sampler for junction tree distributions.

trilearn.smc.approximate(N, alpha, beta, radius, seq_dist, debug=False, neig_set_cache={})

Sequential Monte Carlo for junction trees using the christmas tree algorithm as proposal kernel.

Parameters:

• N (int) – number
• alpha (float) – sparsity parameter for the Christmas tree algorithm
• beta (float) – sparsity parameter for the Christmas tree algorithm
• radius (float) – defines the radius within which ned nodes are selected
• seqdist (SequentialJTDistributions) – the distribution to be sampled from

Returns:

(new_trees, log_w)

References:

trilearn.smc.approximate_cond(N, alpha, beta, radius, seq_dist, T_cond, perm_cond, debug=False, neig_set_cache={})

SMC an junction trees conditioned on the trajectories T_cond and perm_cond.

trilearn.smc.est_dec_max_clique_size(order, n_particles, alpha=0.5, beta=0.5, n_smc_estimates=1, debug=False)

trilearn.smc.est_log_norm_consts(order, n_particles, sequential_distribution, alpha=0.5, beta=0.5, n_smc_estimates=1, debug=False)

trilearn.smc.est_n_dec_graphs(order, n_particles, alpha=0.5, beta=0.5, n_smc_estimates=1, debug=False)

trilearn.smc.get_smc_trajs(Is)

This method is made for visualizing the collapsing in SMC.

trilearn.smc.get_traj(n, i, Is)

trilearn.smc.smc_approximate_ggm(N, alpha, beta, radius, X, D, delta)

trilearn.smc.smc_ggm_graphs(N, alpha, beta, radius, X, D, delta)

trilearn.smc.uniform_dec_maxl_clique_size_samples(order, n_particles, alpha=0.5, beta=0.5, debug=False)

trilearn.smc.uniform_dec_samples(order, n_particles, alpha=0.5, beta=0.5, debug=False)