🌲 torch-treecrf

A PyTorch implementation of Tree-structured Conditional Random Fields.

🗺️ Overview

Conditional Random Fields (CRF) are a family of discriminative graphical learning models that can be used to model the dependencies between variables. The most common form of CRFs are Linear-chain CRF, where a prediction depends on an observed variable, as well as the prediction before and after it (the context). Linear-chain CRFs are widely used in Natural Language Processing.

$$ P(Y | X) = \frac{1}{Z(X)} \prod_{i=1}^n{ \Psi_i(y_i, x_i) } \prod_{i=2}^n{ \Psi_{i-1,i}(y_{i-1}, y_i)} $$

In 2006, Tang et al.[1] introduced Tree-structured CRFs to model hierarchical relationships between predicted variables, allowing dependencies between a prediction variable and its parents and children.

$$ P(Y | X) = \frac{1}{Z(X)} \prod_{i=1}^{n}{ \Psi_i(y_i, x_i) } \prod_{j \in \mathcal{N}(i)}{ \Psi_{j,i}(y_j, y_i)} $$

This package implements a generic Tree-structured CRF layer in PyTorch. The layer can be stacked on top of a linear layer to implement a proper Tree-structured CRF, or on any other kind of model producing emission scores in log-space for every class of each label. Computation of marginals is implemented using Belief Propagation[2], allowing for exact inference on trees[3]:

$$ \begin{aligned} P(y_i | X) & = \frac{1}{Z(X)} \Psi_i(y_i, x_i) & \underbrace{\prod_{j \in \mathcal{C}(i)}{\mu_{j \to i}(y_i)}} & & \underbrace{\prod_{j \in \mathcal{P}(i)}{\mu_{j \to i}(y_i)}} \\ & = \frac1Z \Psi_i(y_i, x_i) & \alpha_i(y_i) & & \beta_i(y_i) \\ \end{aligned} $$

where for every node $i$, the message from the parents $\mathcal{P}(i)$ and the children $\mathcal{C}(i)$ is computed recursively with the sum-product algorithm[4]:

$$ \begin{aligned} \forall j \in \mathcal{C}(i), \mu_{j \to i}(y_i) = \sum_{y_j}{ \Psi_{i,j}(y_i, y_j) \Psi_j(y_j, x_j) \prod_{k \in \mathcal{C}(j)}{\mu_{k \to j}(y_j)} } \\ \forall j \in \mathcal{P}(i), \mu_{j \to i}(y_i) = \sum_{y_j}{ \Psi_{i,j}(y_i, y_j) \Psi_j(y_j, x_j) \prod_{k \in \mathcal{P}(j)}{\mu_{k \to j}(y_j)} } \\ \end{aligned} $$

The implementation should be generic enough that any kind of Directed acyclic graph can be used as a label hierarchy, not just trees.

🔧 Installing

Install the torch-treecrf package directly from PyPi which hosts universal wheels that can be installed with pip:

$ pip install torch-treecrf

📋 Features

• Encoding of directed graphs in an adjacency matrix, with $\mathcal{O}(1)$ retrieval of children and parents for any node, and $\mathcal{O}(N+E)$ storage.
• Support for any acyclic hierarchy representable as a Directed Acyclic Graph and not just directed trees, allowing prediction of classes such as the Gene Ontology.
• Multiclass output, provided all the target labels have the same number of classes: $Y \in \left\{ 0, .., C \right\}^L$.
• Minibatch support, with vectorized computation of the messages $\alpha_i(y_i)$ and $\beta_i(y_i)$.

💡 Example

To create a Tree-structured CRF, you must first define the tree encoding the relationships between variables. Let's build a simple CRF for a root variable with two children:

First, define an adjacency matrix $M$ representing the hierarchy, such that $M_{i,j}$ is $1$ if $j$ is a parent of $i$:

adjacency = torch.tensor([
    [0, 0, 0],
    [1, 0, 0],
    [1, 0, 0]
])

Then, create the a CRF with the right number of features, depending on your feature space, like you would for a torch.nn.Linear module, to obtain a Torch model:

crf = torch_treecrf.TreeCRF(n_features=30, hierarchy=hierarchy)

If you wish to use the CRF layer only, use the TreeCRFLayer module, which expects and outputs an emission tensor of shape $(\star, C, L)$, where $\star$ is the minibatch size, $L$ the number of labels and $C$ the number of class per label.

💭 Feedback

⚠️ Issue Tracker

Found a bug ? Have an enhancement request ? Head over to the GitHub issue tracker if you need to report or ask something. If you are filing in on a bug, please include as much information as you can about the issue, and try to recreate the same bug in a simple, easily reproducible situation.

🏗️ Contributing

Contributions are more than welcome! See CONTRIBUTING.md for more details.

⚖️ License

This library is provided under the MIT License.

This library was developed by Martin Larralde during his PhD project at the European Molecular Biology Laboratory in the Zeller team.

📚 References

• [1] Tang, Jie, Mingcai Hong, Juanzi Li, and Bangyong Liang. ‘Tree-Structured Conditional Random Fields for Semantic Annotation’. In The Semantic Web - ISWC 2006, edited by Isabel Cruz, Stefan Decker, Dean Allemang, Chris Preist, Daniel Schwabe, Peter Mika, Mike Uschold, and Lora M. Aroyo, 640–53. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer, 2006. doi:10.1007/11926078_46.
• [2] Pearl, Judea. ‘Reverend Bayes on Inference Engines: A Distributed Hierarchical Approach’. In Proceedings of the Second AAAI Conference on Artificial Intelligence, 133–136. AAAI’82. Pittsburgh, Pennsylvania: AAAI Press, 1982.
• [3] Bach, Francis, and Guillaume Obozinski. ‘Sum Product Algorithm and Hidden Markov Model’, ENS Course Material, 2016. http://imagine.enpc.fr/%7Eobozinsg/teaching/mva_gm/lecture_notes/lecture7.pdf.
• [4] Kschischang, Frank R., Brendan J. Frey, and Hans-Andrea Loeliger. ‘Factor Graphs and the Sum-Product Algorithm’. IEEE Transactions on Information Theory 47, no. 2 (February 2001): 498–519. doi:10.1109/18.910572.