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Bucket Elimination

The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform

Rina Dechter – 1st expert on this subject based on the ideXlab platform

  • A general scheme for automatic generation of search heuristics from specification dependencies☆☆Preliminary versions of this paper were presented in [15,16,18]. This work was supported in part by NSF grant IIS-0086529 and by MURI ONR award N00014-00-
    Artificial Intelligence, 2020
    Co-Authors: Kalev Kask, Rina Dechter

    Abstract:

    AbstractThe paper presents and evaluates the power of a new scheme that generates search heuristics mechanically for problems expressed using a set of functions or relations over a finite set of variables. The heuristics are extracted from a parameterized approximation scheme called Mini-Bucket Elimination that allows controlled trade-off between computation and accuracy. The heuristics are used to guide Branch-and-Bound and Best-First search. Their performance is compared on two optimization tasks: the Max-CSP task defined on deterministic databases and the Most Probable Explanation task defined on probabilistic databases. Benchmarks were random data sets as well as applications to coding and medical diagnosis problems. Our results demonstrate that the heuristics generated are effective for both search schemes, permitting controlled trade-off between preprocessing (for heuristic generation) and search

  • ISAIM – Evaluating Partition Strategies for Mini-Bucket Elimination
    , 2020
    Co-Authors: Emma Rollón, Rina Dechter

    Abstract:

    Mini-Bucket Elimination(MBE) is a well-known approximation algorithm for graphical models. It relies on a procedure to partition a set of funtions, called Bucket, into smaller subsets, called mini-Buckets. The impact of the partition process on the quality of the bound computed has never been investigated before. We take first steps to address this issue by presenting a framework within which partition strategies can be described, analyzed and compared. We derive a new class of partition heuristics from first-principles and demonstrate its impact on a number of benchmarks for probabilistic reasoning.

  • SOCS – Beyond Static Mini-Bucket: Towards Integrating with Iterative Cost-Shifting Based Dynamic Heuristics
    , 2014
    Co-Authors: Kalev Kask, Rina Dechter, Alexander T Ihler

    Abstract:

    We explore the use of iterative cost-shifting as a dynamic heuristic generator for solving MPE in graphical models via Branch and Bound. When mini-Bucket Elimination is limited by its memory budget, it may not provide good heuristics. This can happen often when the graphical model has a very high induced width with large variable domain sizes. In addition, we explore a hybrid setup where both MBE and the iterative cost-shifting bound are used in a combined heuristic. We compare these approaches with the most advanced statically generated heuristics.

Javier Larrosa – 2nd expert on this subject based on the ideXlab platform

  • ToolBar: a state-of-the-art platform for WCSP
    , 2020
    Co-Authors: S. Bouveret, Javier Larrosa, Federico Heras, Martí Sánchez, Thomas Schiex

    Abstract:

    A lot of work has been done recently around soft constraints. Following the work on algebraic structures (valued, semiring CSP), the class of weighted networks is now identified as one of the most important class: it is among the most difficult one and many practical problems (satellite scheduling, frequency assignment, computer aided musical composition, pedigree analysis, Max-SAT – useful in electronic design – or maximum probability explanation in Bayesian nets for examples) are actually instances or can easily reduce to weighted CSP. Several algorithms have been proposed for WCSP resolution, making the comparison of all these algorithms difficult to establish. We have started the collaborative CVS based development of ToolBar, a C experimental platform that integrates WCSP algorithms and benchmarks in an efficient implementation. ToolBar includes several recently published algorithms maintaining some form of local consistency for solving WCSP and Max-SAT [2, 1]. Currently node, arc, directional arc and full directional arc consistencies are available. Algorithms such as tree decomposition, Bucket Elimination, dominance testing, singleton arc consistency are currently being integrated. ToolBar also offers two languages to describe problems: one is a very basic language (called wcsp), in the spirit of MPS for linear programming, and the other is a higher macro language that makes problem description much easier and which expands in the first language. On the Max-SAT side, ToolBar is also able to read classical propositional CNF files. Bayesian net (ERGO) and weighted CNF files are being developed. The wcsp format is also readable by other solvers for WCSP including Incop (a local search engine for WCSP), Lvcsp (a lisp library of soft constraint algorithms) and Vcsp (a C++ library for VCSP with simplification techniques). Several benchmarks and random problem generators in these formats are available on the SoftCSP collaborative WIKI based web site. The benchmarks, for a current total of 1606 instances, are either locally generated problems or instances of known problems (DIMACS, JNH, CELAR, SPOT5) in the community. For most problems, a known upper bound is also provided.

  • IJCAI – Semiring-based mini-Bucket partitioning schemes
    , 2013
    Co-Authors: Emma Rollón, Javier Larrosa, Rina Dechter

    Abstract:

    Graphical models are one of the most prominent frameworks to model complex systems and efficiently query them. Their underlying algebraic properties are captured by a valuation structure that, most usually, is a semiring. Depending on the semiring of choice, we can capture probabilistic models, constraint networks, cost networks, etc. In this paper we address the partitioning problem which occurs in many approximation techniques such as mini-Bucket Elimination and joingraph propagation algorithms. Roghly speaking, subject to complexity bounds, the algorithm needs to find a partition of a set of factors such that best approximates the whole set. While this problem has been addressed in the past in a particular case, we present here a general description. Furthermore, we also propose a general partitioning scheme. Our proposal is general in the sense that it is presented in terms of a generic semiring with the only additional requirements of a division operation and a refinement of its order. The proposed algorithm instantiates to the particular task of computing the probability of evidence, but also applies directly to other important reasoning tasks. We demonstrate its good empirical behaviour on the problem of computing the most probable explanation.

  • CP – On mini-Buckets and the min-fill Elimination ordering
    Principles and Practice of Constraint Programming – CP 2011, 2011
    Co-Authors: Emma Rollón, Javier Larrosa

    Abstract:

    Mini-Bucket Elimination (MBE) is a well-known approximation of Bucket Elimination (BE), deriving bounds on quantities of interest over graphical models. Both algorithms are based on the sequential transformation of the original problem by eliminating variables, one at a time. The order in which variables are eliminated is usually computed using the greedy min-fill heuristic. In the BE case, this heuristic has a clear intuition, because it faithfully represents the structure of the sequence of sub-problems that BE generates and orders the variables using a greedy criteria based on such structure. However, MBE produces a sequence of sub-problems with a different structure. Therefore, using the min-fill heuristic with MBE means that decisions are made using the structure of the sub-problems that BE would produce, which is clearly meaningless. In this paper we propose a modification of the min-fill ordering heuristic that takes into account this fact. Our experiments on a number of benchmarks over two important tasks (i.e., computing the probability of evidence and optimization) show that MBE using the new ordering is often far more accurate than using the standard one.

Kalev Kask – 3rd expert on this subject based on the ideXlab platform

  • CP – New Search Heuristics for Max-CSP
    Principles and Practice of Constraint Programming – CP 2000, 2020
    Co-Authors: Kalev Kask

    Abstract:

    This paper evaluates the power of a new scheme that generates search heuristics mechanically. This approach was presented and evaluated first in the context of optimization in belief networks. In this paper we extend this work to Max-CSP. The approach involves extracting heuristics from a parameterized approximation scheme called Mini-Bucket Elimination that allows controlled trade-off between computation and accuracy. The heuristics are used to guide Branch-and-Bound and Best-First search, whose performance are compared on a number of constraint problems. Our results demonstrate that both search schemes exploit the heuristics effectively, permitting controlled trade-off between preprocessing (for heuristic generation) and search. These algorithms are compared with a state of the art complete algorithm as well as with the stochastic local search anytime approach, demonstrating superiority in some problem cases.

  • A general scheme for automatic generation of search heuristics from specification dependencies☆☆Preliminary versions of this paper were presented in [15,16,18]. This work was supported in part by NSF grant IIS-0086529 and by MURI ONR award N00014-00-
    Artificial Intelligence, 2020
    Co-Authors: Kalev Kask, Rina Dechter

    Abstract:

    AbstractThe paper presents and evaluates the power of a new scheme that generates search heuristics mechanically for problems expressed using a set of functions or relations over a finite set of variables. The heuristics are extracted from a parameterized approximation scheme called Mini-Bucket Elimination that allows controlled trade-off between computation and accuracy. The heuristics are used to guide Branch-and-Bound and Best-First search. Their performance is compared on two optimization tasks: the Max-CSP task defined on deterministic databases and the Most Probable Explanation task defined on probabilistic databases. Benchmarks were random data sets as well as applications to coding and medical diagnosis problems. Our results demonstrate that the heuristics generated are effective for both search schemes, permitting controlled trade-off between preprocessing (for heuristic generation) and search

  • SOCS – Beyond Static Mini-Bucket: Towards Integrating with Iterative Cost-Shifting Based Dynamic Heuristics
    , 2014
    Co-Authors: Kalev Kask, Rina Dechter, Alexander T Ihler

    Abstract:

    We explore the use of iterative cost-shifting as a dynamic heuristic generator for solving MPE in graphical models via Branch and Bound. When mini-Bucket Elimination is limited by its memory budget, it may not provide good heuristics. This can happen often when the graphical model has a very high induced width with large variable domain sizes. In addition, we explore a hybrid setup where both MBE and the iterative cost-shifting bound are used in a combined heuristic. We compare these approaches with the most advanced statically generated heuristics.