Scaling Up AND/OR Abstraction Sampling

Abstraction Sampling (AS) is a recently introduced enhancement of Importance Sampling that exploits stratification by using a notion of abstractions: groupings of similar nodes into abstract states. It was previously shown that AS performs particularly well when sampling over an AND/OR search space; however, existing schemes were limited to “proper” abstractions in order to ensure unbiasedness, severely hindering scalability. In this paper, we introduce AOAS, a new Abstraction Sampling scheme on AND/OR search spaces that allow more flexible use of abstractions by circumventing the properness requirement. We analyze the properties of this new algorithm and, in an extensive empirical evaluation on five benchmarks, over 480 problems, and comparing against other state of the art algorithms, illustrate AOAS’s properties and show that it provides a far more powerful and competitive Abstraction Sampling framework.

[1]  John W. Fisher,et al.  Probabilistic Variational Bounds for Graphical Models , 2015, NIPS.

[2]  Rina Dechter,et al.  Dynamic Importance Sampling for Anytime Bounds of the Partition Function , 2017, NIPS.

[3]  Vibhav Gogate,et al.  SampleSearch: Importance sampling in presence of determinism , 2011, Artif. Intell..

[4]  Rina Dechter,et al.  Interleave Variational Optimization with Monte Carlo Sampling: A Tale of Two Approximate Inference Paradigms , 2019, AAAI.

[5]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[6]  Qiang Liu,et al.  Bounding the Partition Function using Holder's Inequality , 2011, ICML.

[7]  Rina Dechter,et al.  Mini-buckets: A general scheme for bounded inference , 2003, JACM.

[8]  Dirk P. Kroese,et al.  Simulation and the Monte Carlo Method (Wiley Series in Probability and Statistics) , 1981 .

[9]  Rina Dechter,et al.  AND/OR Cutset Conditioning , 2005, IJCAI.

[10]  Adnan Darwiche,et al.  Modeling and Reasoning with Bayesian Networks , 2009 .

[11]  Pang C. Chen.  Heuristic Sampling: A Method for Predicting the Performance of Tree Searching Programs , 1992, SIAM J. Comput..

[12]  Rina Dechter,et al.  AND/OR search spaces for graphical models , 2007, Artif. Intell..

[13]  Filjor Broka.  Abstraction Sampling in Graphical Models , 2018, UAI.

[14]  Rina Dechter.  Reasoning with Probabilistic and Deterministic Graphical Models: Exact Algorithms , 2013, Reasoning with Probabilistic and Deterministic Graphical Models: Exact Algorithms.

[15]  E. Slud.  Statistical Computing with R , 2009 .