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A Bayesian latent tree model of high-dimensional heterogeneous data
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Intended Use

TreeCat is an inference engine for machine learning and Bayesian inference. TreeCat is appropriate for analyzing medium-sized tabular data with categorical and ordinal values, possibly with missing observations.

TreeCat supports
Feature Types categorical, ordinal
# Rows (n) 1000-100K
# Features (p) 10-1000
# Cells (n × p) 10K-10M
# Categories 2-10ish
Max Ordinal 10ish
Missing obervations? yes
Repeated observations? yes
Sparse data? no, use something else
Unsupervised yes
Semisupervised yes
Supervised no, use something else


If you already have Numba installed, you should be able to simply

pip install pytreecat

If you're new to Numba, we recommend installing it using miniconda or Anaconda.

If you want to install TreeCat for development, then clone the source code and create a new conda env

git clone
cd treecat
conda env create -f environment.3.yml
source activate treecat3
pip install -e .

Quick Start

  1. Format your data as a data.csv file with a header row. It's fine to include extra columns that won't be used.

    Contents of data.csv:

    title genre decade rating
    vertigo thriller 1950s 5
    up family 2000s 3
    desk set comedy 1950s 4
    santapaws family 2010s
    ... ... ... ...
  2. Generate two schema files types.csv and values.csv using TreeCat's guess-schema command:

    $ treecat guess-schema data.csv types.csv values.csv

    Contents of types.csv:

    name type total unique singletons
    title 11 11 11
    genre categorical 11 7 4
    decade categorical 11 6 3
    rating ordinal 10 5 2

    Contents of values.csv:

    name value count
    genre drama 3
    genre family 2
    genre fantasy 2
    decade 1950s 3
    ... ... ...

    You can manually fix any incorrectly guessed feature types, or add/remove feature values. TreeCat ignores any feature with an empty type field.

  3. Import your csv files into treecat's internal format. We'll call our dataset dataset.pkz (a gzipped pickle file).

    $ treecat import-data data.csv types.csv values.csv '' dataset.pkz

    (the empty argument '' is an optional structural prior that we ignore).

  4. Train an ensemble model on your dataset. This typically takes ~15minutes for a 1M cell dataset.

    $ treecat train dataset.pkz model.pkz
  5. Load your trained model into a server

    from treecat.serving import serve_model
    server = serve_model('dataset.pkz', 'model.pkz')
  6. Run queries against the server. For example we can compute expecations

    samples = server.sample(100, evidence={'genre': 'drama'})
    print(np.mean([s['rating'] for s in samples]))

    or explore feature structure through the latent correlation matrix


Tuning Hyperparameters

TreeCat requires tuning of two parameters: learning_init_epochs (like the number of iterations) and model_num_clusters (the number of latent classes above each feature). The easiest way to tune these is to do grid search using the treecat.validate module with a csv file of example parameters.

Contents of tuning.csv:

model_num_clusters learning_init_epochs
2 2
2 3
4 2
... ...
# This reads parameters from tuning.csv and dumps results to tuning.pkz
$ treecat.validate tune-csv dataset.pkz tuning.csv tuning.pkz

The tune-csv command prints its results, but if you want to seem them later, you can

$ treecat.format cat tuning.pkz

The Server Interface

TreeCat's server interface supports primitives for Bayesian inference and tools to inspect latent structure:

  • server.sample(N, evidence=None) draws N samples from the joint posterior distribution over observable data, optionally conditioned on evidence.

  • server.logprob(rows, evidence=None) computes posterior log probability of data, optionally conditioned on evidence.

  • server.median(evidence) computes L1-loss-minimizing estimates, conditioned on evidence.

  • server.observed_perplexity() computes the perplexity (a soft measure of cardinality) of each observed feature.

  • server.latent_perplexity() computes the perplexity of the latent class behind each observed feature.

  • server.latent_correlation() computes the latent-latent correlation between each pair of latent variables.

  • server.estimate_tree() computes a maximum a posteriori estimate of the latent tree structure.

  • server.sample_tree(N) draws N samples from posterior distribution over the latent tree structures.

The Model

TreeCat's generative model is closest to Zhang and Poon's Latent Tree Analysis [1], with the notable difference that TreeCat fixes exactly one latent node per observed node. TreeCat is historically a descendent of Mansinghka et al.'s CrossCat, a model in which latent nodes ("views" or "kinds") are completely independent. TreeCat addresses the same kind of high-dimensional categorical distribution that Dunson and Xing's mixture-of-product-multinomial models [3] addresses. While TreeCat currently supports only categorical and ordinal feature types, it is straight-forward to generalize to other feature types with conjugate priors such as real (normal-inverse-chi-squared), integer (gamma-Poisson), and angular (von-Mises). This generalization places it in the class of models high-dimensional heterogeneous data with Valera et al. [4].

Let V be a set of vertices (one vertex per feature).
Let C[v] be the dimension of the vth feature.
Let N be the number of datapoints.
Let K[n,v] be the number of observations of feature v in row n (e.g. 1 for a categorical variable, 0 for missing data, or k for an ordinal value with minimum 0 and maximum k).

TreeCat is the following generative model:

E ~ UniformSpanningTree(V)    # An undirected tree.
for v in V:
    Pv[v] ~ Dirichlet(size = [M], alpha = 1/2)
for (u,v) in E:
    Pe[u,v] ~ Dirichlet(size = [M,M], alpha = 1/(2*M))
    assume(Pv[u] == sum(Pe[u,v], axis = 1))
    assume(Pv[v] == sum(Pe[u,v], axis = 0))
for v in V:
    for i in 1:M:
        Q[v,i] ~ Dirichlet(size = [C[v]])
for n in 1:N:
    for v in V:
        X[n,v] ~ Categorical(Pv[v])
    for (u,v) in E:
        (X[n,u],X[n,v]) ~ Categorical(Pe[u,v])
    for v in V:
        Z[n,v] ~ Multinomial(Q[v,X[n,v]], count = K[n,v])

where we've avoided adding an arbitrary root to the tree, and instead presented the model as a manifold with overlapping variables and constraints.

The Inference Algorithm

This package implements fully Bayesian MCMC inference using subsample-annealed collapsed Gibbs sampling. There are two pieces of latent state that are sampled:

  • Latent class assignments for each row for each vertex (feature). These are sampled by single-site collapsed Gibbs sampler with a linear subsample-annealing schedule.

  • The latent tree structure is sampled by randomly removing an edge and replacing it. Since removing an edge splits the graph into two connected components, the only replacement locations that are feasible are those that re-connect the graph.

The single-site Gibbs sampler uses dynamic programming to simultaneously sample the complete latent assignment vector for each row. A dynamic programming program is created each time the tree structure changes. This program is interpreted by various virtual machines for different purposes (training the model, sampling from the posterior, computing log probability of the posterior). The virtual machine for training is jit-compiled using numba.


  1. Nevin L. Zhang, Leonard K. M. Poon (2016)
    Latent Tree Analysis
  2. Vikash Mansinghka, Patrick Shafto, Eric Jonas, Cap Petschulat, Max Gasner, Joshua B. Tenenbaum (2015)
    CrossCat: A Fully Bayesian Nonparametric Method for Analyzing Heterogeneous, High Dimensional Data
  3. David B. Dunson, Chuanhua Xing (2012)
    Nonparametric Bayes Modeling of Multivariate Categorical Data
  4. Isabel Valera, Melanie F Pradier, Zoubin Ghahramani (2017)
    General Latent Feature Modeling for Data Exploration Tasks.


Copyright (c) 2017 Fritz Obermeyer.
TreeCat is licensed under the Apache 2.0 License.

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