Summary of the Pascal approximate inference competition
See www.cs.huji.ac.il/project/PASCAL for more information about the competition
1 - Winner of the marginal and partition function categories
|Title:||Structured Propagation-based and Sampling-based Algorithms for Graphical Models|
|Speaker:||Vibhah Gogate, University of Texas|
|Team:||Vibhav Gogate, The University of Texas at Dallas; Pedro Domingos, University of Washington; Rina Dechter, University of California, Irvine.|
Approximate probabilistic inference algorithms can be classified into two broad types: propagation-based and sampling-based. Propagation-based algorithms such as Belief propagation operate by iteratively running message-passing equations that yield exact answers on a junction tree on a cluster graph. Sampling-based algorithms operate by generating a set of samples and then estimating the quantity of interest by computing a statistic over the samples. Both types of algorithms can be improved in a numbers of ways and only a few of them have been explored to date. In particular, the most dominant line of research in the UAI community is exploiting the structure of the directed or the undirected graph associated with the probabilistic model. In this talk, I'll show how we can move beyond graph structure and exploit other structures such as context-specific independence (CSI), determinism and similar probability values by leveraging the work done in the satisfiability (SAT), constraint programming (CP) and verification communities; the SAT and CP communities provide us with tools such as constraint propagation (e.g., unit propagation and arc consistency) and efficient SAT solvers (e.g., minisat) while the verification community provides us with tools such as binary decision diagrams (BDDs) and algebraic decision diagrams (ADDs). I'll show, both theoretically and empirically, that both sampling-based and propagation-based algorithms that exploit the aforementioned structures are more accurate and scalable than the ones that do not. If time permits, I'll describe the structured message passing (SMP) framework, which can help us combine structure-aware sampling-based and propagation-based algorithms in a principled way. It also presents several new bias versus variance tradeoffs that can be used to improve the quality of inference.
2 - Winner of the MAP category
|Title:||DAOOPT: Improving AND/OR Branch-and-Bound for Graphical Models|
|Speaker:||Lars Otten, UCI|
|Team:||Lars Otten, Alexander Ihler, Kalev Kask, Rina Dechter, UCI|
Our winning entry for the MPE task implements Breadth-Rotating AND/OR Branch and Bound, a new Branch-and-Bound scheme over AND/OR search spaces for graphical models, with subproblem decomposition, full caching, and subproblem rotation for improved anytime performance. It is combined with MPLP preprocessing on a join graph of the problem, which yields tighter bounds for pruning through the mini-bucket heuristic. We also integrate recent results for highly optimized variable ordering schemes and one pass of initial stochastic local search.
3 - Runner up in the marginal and partition function categories
|Title:||Efficient generalized belief propagation estimates|
|Speaker:||Alex Ihler, UCI|
|Team:||Alex Ihler, UCI|
Our entry for the Pascal2 partition function and marginalization categories implemented an efficient hypertree reparameterization variant of generalized belief propagation. To perform region selection under memory constraints, we used a mini-bucket elimination procedure with stochastic greedy search over variable orderings. At higher time limits, we combined the GBP estimates with variable conditioning search.
4 - Runner up in the MAP category
|Title:||Combining exact WCSP techniques and VNS search for solving MPE|
|Team:||D. Allouche, A. Favier, S. de Givry, T. Schiex, M. Zytnicki, INRA. M. Fontaine, J-P Métivier,GREYC-CNRS, UMR 6072. M. Sanchez (Spain), K. L. Leung (China)|
We used VNS/LDS+CP for the 2012 challenge. Our solver combines the Variable Neighborhood Search (VNS) approach with the exact Cost Function Network (CFN) solver toulbar2 to tackle MPE problems in graphical models. Using a -log() transform, MPE can be directly reduced to a pure CFN optimization problem. VNS/LDS+CP is a local search method which uses neighbourhoods of variable sizes. These neighborhoods are obtained by unfixing a subpart of the current solution. Then the exploration of the subproblem related to the unfixed part of the current solution is performed using toulbar2 (based on branch and bound with soft local consistencies derived bounds and limited discrepancy search). The solution found is then returned to the VNS solver. This combination finished close to the best solver in categories 20 minutes and 1 hour.