🌲 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.