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Loopy Belief Propagation

The project contains an implementation of Loopy Belief Propagation, a popular message passing algorithm for performing inference in probabilistic graphical models. It provides exact inference for graphical models without loops. While inference for graphical models with loops is approximate, in practice it is shown to work well. Our implementation is generic and operates on factor graph representation of graphical models. It handles factors of any order, and variable domains of any size. In addition, we provide specialized implementation for pairwise factors. The algorithm is implemented with Apache Spark GraphX, and thus can scale to large scale models. Further, it supports computations in log scale for numerical stability.


Clone and build with Maven:

git clone
mvn package

The library will appear in the target folder. By default it is compiled against Scala 2.11.8 and Spark 1.6.1. If you need a different Scala/Spark versions, please modify pom.xml.

BP for Factor Graph

We use factor graph format derived from libDAI with small modification (example):

# number of factors in the file

# factor id preceded with 3 hashes (unique, must not intersect with variable name/id)
### 5
# number of vars
# name of vars
# number of values of vars
# number of non-zero entries in factor table
# non-zero factor table entries
0  1
1  1

Data parallel loading requires the factors to be partitioned across multiple files.


import sparkle.graph._
// Load graph from the input path with factor files
val graph = Utils.loadLibDAIToFactorGraph(sc, inputPath)
// Run Belief Propagation on the graph with maximum iterations "maxIterations" and epsilon "epsilon"
val beliefs = BP(graph, maxIterations, epsilon)

Command line

./spark-submit --master spark://MASTER:PORT --jars belief-propagation.jar --class sparkle.graph.BP INPUT_PATH OUTPUT_PATH N_ITERATIONS EPSILON

BP for pairwise factors

We use two file format. Each line of the first file contains variable id and its prior delimited with space (example):

1 1.0 1.0
2 1.0 0.0

The second file contains pairwise factors with first variable id, second variable id, and the factor in column-major format delimited with space (example):

1 2 1.0 0.9 0.9 1.0 
2 3 0.1 1.0 1.0 0.1 

No additional effort is required for enabling data parallel loading since each variable and factor are stored on separate lines and can automatically be processed by Spark in parallel.


import sparkle.graph._
// Load graph from two input files
val graph = PairwiseBP.loadPairwiseGraph(sc, variableFile, factorFile)
// Run Belief Propagation on the graph with maximum iterations "maxIterations" and epsilon "epsilon"
val beliefs = PairwiseBP(graph, maxIterations, epsilon)

Command line

./spark-submit --master spark://MASTER:PORT --jars belief-propagation.jar --class sparkle.graph.PairwiseBP VARIABLES_FILE FACTORS_FILE OUTPUT_PATH N_ITERATIONS EPSILON


  1. Belief propagation algorithm
  2. Yedidia, J.S.; Freeman, W.T.; Weiss, Y., "Understanding Belief Propagation and Its Generalizations" in Exploring Artificial Intelligence in the New Millennium, Lakemeyer, G. and Nebel, B., Eds., ISBN: 1-55860-811-7, chapter 8, pp. 239-236, Morgan Kaufmann Publishers, January 2003. (pdf) [An excellent description of BP]
  3. LibDAI file format is used with explicit factor ids: example.
  4. Talk by the project authors: Alexander Ulanov, Manish Marwah "Malicious site detection with large scale belief propagation", Strata+Hadoop, March 2017 (slides)
  5. [BigData 2017] Alexander Ulanov, Manish Marwah, Mijung Kim, Roshan Dathathri, Carlos Zubieta, and Jun Li. Sandpiper: Scaling Probabilistic Inferencing to Large Scale Graphical Models, In IEEE Big Data , Boston, MA, Dec. 2017.

How to contribute

Contributors are required to sign the Corporate Contributor License Agreement


Implementation of the Loopy Belief Propagation algorithm for Apache Spark







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