Rina Dechter

• University of California, Irvine

This paper focuses on the computational complexity of computing empirical plug-in estimates for causal effect queries. Given a causal graph and observational data, any identifiable causal query can be estimated from an expression over the observed variables, called the estimand. The estimand can then be evaluated by plugging in probabilities comput...

The standard approach to answering an identifiable causal-effect query (e.g., P(Y|do(X)) given a causal diagram and observational data is to first generate an estimand, or probabilistic expression over the observable variables, which is then evaluated using the observational data. In this paper, we propose an alternative paradigm for answering caus...

The standard approach to answering an identifiable causal-effect query (e.g., $P(Y|do(X)$) when given a causal diagram and observational data is to first generate an estimand, or probabilistic expression over the observable variables, which is then evaluated using the observational data. In this paper, we propose an alternative paradigm for answeri...

Weighted search was explored significantly in recent years for path-finding problems, but until now was barely considered for optimization tasks such as MPE/MAP and Weighted CSPs. An important virtue of weighted search schemes, especially in the context of anytime search, is that they are w-optimal, i.e. when terminated, they return a weight w, and...

In empirical studies we observed that caching can have very little impact in reducing the search effort in Branch and Bound search over context-minimal OR spaces. For example, in one of the problem domains used in our experiments we reduce only by 1% the number of nodes expanded when using caching in context-minimal OR spaces. By contrast, we reduc...

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 a...

The paper explores the potential of look-ahead methods within the context of AND/OR search in graphical models using the Mini-Bucket heuristic for combinatorial optimization tasks (e.g., weighted CSPS or MAP inference). We study how these methods can be used to compensate for the approximation error of the initially generated Mini-Bucket heuristics...

An influence diagram is a graphical representation of sequential decision-making under uncertainty, defining a structured decision problem by conditional probability functions and additive utility functions over discrete state and action variables. The task of finding the maximum expected utility of influence diagrams is closely related to the cost...

One popular and efficient scheme for solving exactly combinatorial optimization problems over graphical models is depth-first Branch and Bound. However, when the algorithm exploits problem decomposition using AND/OR search spaces, its anytime behavior breaks down. This paper 1) analyzes and demonstrates this inherent conflict between effective expl...

Bucket Elimination (BE) is a universal inference scheme that can solve most tasks over probabilistic and deterministic graphical models exactly. However, it often requires exponentially high levels of memory (in the induced-width) preventing its execution. In the spirit of exploiting Deep Learning for inference tasks, in this paper, we will use neu...

Influence diagrams (IDs) are graphical models for representing and reasoning with sequential decision-making problems under uncertainty. Limited memory influence diagrams (LIMIDs) model a decision-maker (DM) who forgets the history in the course of making a sequence of decisions. The standard inference task in IDs and LIMIDs is to compute the maxim...

Influence diagrams provide a modeling and inference framework for sequential decision problems, representing the probabilistic knowledge by a Bayesian network and the preferences of an agent by utility functions over the random variables and decision variables. Computing the maximum expected utility (MEU) and the optimizing policy is exponential in...

We report the PASCAL2 benchmark for DAOOPT and GUROBI on MPE task with 330 optimally solved instances from 8 benchmark domains. DAOOPT out-performed GUROBI in 3 domains, while GUROBI was faster than DAOOPT in the rest of the 5 domains. We show that DAOOPT performed well in domains where it could have high quality initial solutions for pruning the A...

In this position paper, we present our current progress in applying marginal MAP algorithms for solving the conformant planning problems. Conformant planning problem is formulated as probabilistic inference in graphi-cal models compiled from relational PPDDL domains. The translation from PPDDL into Dynamic Bayesian Network is developed by mapping t...

Probabilistic conformant planning problems can be solved by probabilistic inference algorithms after translating their PPDDL specifications into graphical models. We present two translation schemes that convert probabilistic conformant planning problems as graphical models. The first encoding is based on the probabilistic extension of the serial en...

We introduce a new decomposition method for bounding the maximum expected utility of influence diagrams. While most current schemes use reductions to the Marginal Map task over a Bayesian Network, our approach is direct, aiming to avoid the large explosion in the model size that often results by such reductions. In this paper, we extend to influenc...

Influence diagrams provide a modeling and inference framework for sequential decision problems , representing the probabilistic knowledge by a Bayesian network and the preferences of an agent by utility functions over the random variables and decision variables. The time and space complexity of computing the maximum expected utility (MEU) and its m...

Influence diagrams (IDs) are graphical models for representing and reasoning with sequential decision-making problems under uncertainty. Limited memory influence diagrams (LIMIDs) model a decision-maker (DM) who forgets the history in the course of making a sequence of decisions. The standard inference task in IDs and LIMIDs is to compute the maxim...

This paper explores the anytime performance of search-based algorithms for solving the Marginal MAP task over graphical models. The current state-of-the-art for solving this challenging task is based on best-first search exploring the AND/OR graph with the guidance of heuristics based on mini-bucket and variational cost-shifting principles. Yet, th...

We introduce new anytime search algorithms that combine best-first with depth-first search into hybrid schemes for Marginal MAP inference in graphical models. The main goal is to facilitate the generation of upper bounds (via the best-first part) alongside the lower bounds of solutions (via the depth-first part) in an anytime fashion. We compare ag...

We address an AND/OR search for solving influence diagrams with heuristics derived from graphical model decomposition bounds. Then, we present how the heuristics guide AND/OR branch and bound search and show its potential for solving influence diagrams on a preliminary experiment.

ion 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'' abst...

Marginal MAP is a difficult mixed inference task for graphical models. Existing state-of-the-art solvers for this task are based on a hybrid best-first and depth-first search scheme that allows them to compute upper and lower bounds on the optimal solution value in an anytime fashion. These methods however are memory intensive schemes (via the best...

Computing the partition function of a graphical model is a fundamental task in probabilistic inference. Variational bounds and Monte Carlo methods, two important approximate paradigms for this task, each has its respective strengths for solving different types of problems, but it is often nontrivial to decide which one to apply to a particular prob...

Graphical models (e.g., Bayesian and constraint networks, influence diagrams, and Markov decision processes) have become a central paradigm for knowledge representation and reasoning in both artificial intelligence and computer science in general. These models are used to perform many reasoning tasks, such as scheduling, planning and learning, diag...

The Marginal MAP inference task is known to be extremely hard particularly because the evaluation of each complete MAP assignment involves an exact likelihood computation (a combinatorial sum). For this reason, most recent state-of-the-art solvers that focus on computing anytime upper and lower bounds on the optimal value are limited to solving ins...

Marginal MAP is a key task in Bayesian inference and decision-making. It is known to be very difficult in general, particularly because the evaluation of each MAP assignment requires solving an internal summation problem. In this paper, we propose a best-first search algorithm that provides anytime upper bounds for marginal MAP in graphical models....

Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including Weighted Constraint Programs (WCSPs), Distributed Constraint Optimization (DCOP), as well as optimization in stochastic variants such as the tasks of finding the most...

Mixed inference such as the marginal MAP query (some variables marginalized by summation and others by maximization) is key to many prediction and decision models. It is known to be extremely hard; the problem is NP PP-complete while the decision problem for MAP is only NP-complete and the summation problem is #P-complete. Consequently, approximati...

Best-first search can be regarded as anytime scheme for producing lower bounds on the optimal solution, a characteristic that is mostly overlooked. We explore this topic in the context of AND/OR best-first search, guided by the MBE heuristic, when solving graphical models. In that context, the impact of the secondary heuristic for subproblem orderi...

We introduce the concept of local bucket error for the mini-bucket heuristics and show how it can be used to improve the power of AND/OR search for combinatorial optimization tasks in graphical models (e.g. MAP/MPE or weighted CSPs). The local bucket error illuminates how the heuristic errors are distributed in the search space, guided by the mini-...

We present a parallel AND/OR Branch-and-Bound scheme that uses the power of a computational grid to push the boundaries of feasibility for combinatorial optimization. Two variants of the scheme are described, one of which aims to use machine learning techniques for parallel load balancing. In-depth analysis identifies two inherent sources of parall...

Weighted heuristic search (best-first or depth-first) refers to search with a heuristic function multiplied by a constant w [31]. The paper shows, for the first time, that for optimization queries in graphical models the weighted heuristic best-first and weighted heuristic depth-first branch and bound search schemes are competitive energy-minimizat...

Bounding the partition function is a key inference task in many graphical models. In this paper, we develop an anytime anyspace search algorithm taking advantage of AND/OR tree structure and optimized variational heuristics to tighten deterministic bounds on the partition function. We study how our priority-driven best-first search scheme can impro...

We introduce new anytime search algorithms that combine best-first with depth-first search into hybrid schemes for Marginal MAP inference in graphical models. The main goal is to facilitate the generation of upper bounds (via the best-first part) alongside the lower bounds of solutions (via the depth-first part) in an anytime fashion. We compare ag...

We present SGDPLL(T), an algorithm that solves (among many other problems) probabilistic inference modulo theories, that is, inference problems over probabilistic models defined via a logic theory provided as a parameter (currently, propositional, equalities on discrete sorts, and inequalities, more specifically difference arithmetic, on bounded in...

The paper focuses on finding the m best solutions to combinatorial optimization problems using best-first or depth-first branch and bound search. Specifically, we present a new algorithm m-A∗, extending the well-known A∗ to the m-best task, and for the first time prove that all its desirable properties, including soundness, completeness and optimal...

This paper explores the anytime performance of search-based algorithms for solving the Marginal MAP task over graphical models. The current state of the art for solving this challenging task is based on best-first search exploring the AND/OR graph with the guidance of heuristics based on mini-bucket and variational cost-shifting principles. Yet, th...

The paper investigates the potential of look-ahead in the con-text of AND/OR search in graphical models using the Mini-Bucket heuristic for combinatorial optimization tasks (e.g., MAP/MPE or weighted CSPs). We present and analyze the complexity of computing the residual (a.k.a Bellman update) of the Mini-Bucket heuristic and show how this can be us...

We address the problem of predicting the size of the search tree explored by Depth-First Branch and Bound (DFBnB) while solving optimization problems over graphical models. Building upon methodology introduced by Knuth and his student Chen, this paper presents a memory-efficient scheme called Retentive Stratified Sampling (RSS). Through empirical e...

Marginal MAP problems are known to be very difficult tasks for graphical models and are so far solved exactly by systematic search guided by a join-tree upper bound. In this paper, we develop new AND/OR branch and bound algorithms for marginal MAP that use heuristics extracted from weighted mini-buckets enhanced with messagepassing updates. We demo...

Graphical models (e.g., Bayesian and constraint networks, influence diagrams, and Markov decision processes) have become a central paradigm for knowledge representation and reasoning in both artificial intelligence and computer science in general. These models are used to perform many reasoning tasks, such as scheduling, planning and learning, diag...

This paper provides algorithms for predicting the size of the Expanded Search Tree (EST) of Depth-first Branch and Bound algorithms (DFBnB) for optimization tasks. The prediction algorithm is implemented and evaluated in the context of solving combinatorial optimization problems over graphical models such as Bayesian and Markov networks. Our method...

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...

Motivation: The use of dense single nucleotide polymorphism (SNP) data in genetic linkage analysis of large pedigrees is impeded by significant technical, methodological and computational challenges. Here we describe Superlink-Online SNP, a new powerful online system that streamlines the linkage analysis of SNP data. It features a fully integrated...

Probabilistic inference algorithms for finding the most probable explanation, the maximum aposteriori hypothesis, and the maximum expected utility and for updating belief are reformulated as an elimination--type algorithm called bucket elimination. This emphasizes the principle common to many of the algorithms appearing in that literature and clari...

Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by parameters such as tree width and cycle-cut set size. In this paper we initiate a study to determine the poten...

We show that the d -separation criterion constitutes a valid test for conditional independence relationships that are induced by feedback systems involving discrete variables.

This paper describes a class of probabilistic approximation algorithms based on bucket elimination which offer adjustable levels of accuracy and efficiency. We analyze the approximation for several tasks: finding the most probable explanation, belief updating and finding the maximum a posteriori hypothesis. We identify regions of completeness and p...

It was recently shown that the problem of decoding messages transmitted through a noisy channel can be formulated as a belief updating task over a probabilistic network [McEliece]. Moreover, it was observed that iterative application of the (linear time) Pearl's belief propagation algorithm designed for polytrees outperformed state of the art decod...

The paper is a second in a series of two papers evaluating the power of a new scheme that generates search heuristics mechanically. The heuristics are extracted from an approximation scheme called mini-bucket elimination that was recently introduced. The first paper introduced the idea and evaluated it within Branch-and-Bound search. In the current...

This paper explores algorithms for processing probabilistic and deterministic information when the former is represented as a belief network and the latter as a set of boolean clauses. The motivating tasks are 1. evaluating beliefs networks having a large number of deterministic relationships and2. evaluating probabilities of complex boolean querie...

The paper presents an iterative version of join-tree clustering that applies the message passing of join-tree clustering algorithm to join-graphs rather than to join-trees, iteratively. It is inspired by the success of Pearl's belief propagation algorithm as an iterative approximation scheme on one hand, and by a recently introduced mini-clustering...

Motivation: The use of dense single nucleotide polymorphism (SNP) data in genetic linkage analysis of large pedigrees is impeded by significant technical, methodological and computational challenges. Here we describe Superlink-Online SNP, a new powerful online system that streamlines the linkage analysis of SNP data. It features a fully integrated...

The paper studies empirically the time-space trade-off between sampling and inference in a sl cutset sampling algorithm. The algorithm samples over a subset of nodes in a Bayesian network and applies exact inference over the rest. Consequently, while the size of the sampling space decreases, requiring less samples for convergence, the time for gene...

In Non - ergodic belief networks the posterior belief OF many queries given evidence may become zero.The paper shows that WHEN belief propagation IS applied iteratively OVER arbitrary networks(the so called, iterative OR loopy belief propagation(IBP)) it IS identical TO an arc - consistency algorithm relative TO zero - belief queries(namely assessi...

The paper continues the study of partitioning based inference of heuristics for search in the context of solving the Most Probable Explanation task in Bayesian Networks. We compare two systematic Branch and Bound search algorithms, BBBT (for which the heuristic information is constructed during search and allows dynamic variable/value ordering) and...

We develop several algorithms taking advantage of two common approaches for bounding MPE queries in graphical models: minibucket elimination and message-passing updates for linear programming relaxations. Both methods are quite similar, and offer useful perspectives for the other; our hybrid approaches attempt to balance the advantages of each. We...

We study the problem of complexity estimation in the context of parallelizing an advanced Branch and Bound-type algorithm over graphical models. The algorithm's pruning power makes load balancing, one crucial element of every distributed system, very challenging. We propose using a statistical regression model to identify and tackle disproportional...

This is the Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence, which was held in Cambridge, MA, July 13 - 16 2006.

In this paper, we present a Branch and Bound algorithm called QuickBB for computing the treewidth of an undirected graph. This algorithm performs a search in the space of perfect elimination ordering of vertices of the graph. The algorithm uses novel pruning and propagation techniques which are derived from the theory of graph minors and graph isom...

The paper introduces mixed networks, a new framework for expressing and reasoning with probabilistic and deterministic information. The framework combines belief networks with constraint networks, defining the semantics and graphical representation. We also introduce the AND/OR search space for graphical models, and develop a new linear space searc...

The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity where instantiated variables are removed. If the assigned variables constitute a cycle-cutset, the rest of th...

This paper describes a general framework called Hybrid Dynamic Mixed Networks (HDMNs) which are Hybrid Dynamic Bayesian Networks that allow representation of discrete deterministic information in the form of constraints. We propose approximate inference algorithms that integrate and adjust well known algorithmic principles such as Generalized Belie...

In this paper, we consider Hybrid Mixed Networks (HMN) which are Hybrid Bayesian Networks that allow discrete deterministic information to be modeled explicitly in the form of constraints. We present two approximate inference algorithms for HMNs that integrate and adjust well known algorithmic principles such as Generalized Belief Propagation, Rao-...

In this paper we compare search and inference in graphical models through the new framework of AND/OR search spaces. Specifically, we com- pare Variable Elimination (VE) and memory- intensive AND/OR Search (AO) and place al- gorithms such as graph-based backjumping and no-good learning, as well as Recursive Condi- tioning (7) and Value Elimination...

The paper analyzes theoretically and empirically the performance of likelihood weighting (LW) on a subset of nodes in Bayesian networks. The proposed scheme requires fewer samples to converge due to reduction in sampling variance. The method exploits the structure of the network to bound the complexity of exact inference used to compute sampling di...

Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on probability of evidence but does not have any guarantees in terms of relative or absolute error. Our proposed approxima...

Compiling graphical models has recently been under intense investigation, especially for probabilistic modeling and processing. We present here a novel data structure for compiling weighted graphical models (in particular, probabilistic models), called AND/OR Multi-Valued Decision Diagram (AOMDD). This is a generalization of our previous work on co...

The paper evaluates the power of best-first search over AND/OR search spaces for solving the Most Probable Explanation (MPE) task in Bayesian networks. The main virtue of the AND/OR representation of the search space is its sensitivity to the structure of the problem, which can translate into significant time savings. In recent years depth-first AN...

This paper develops a measure for bounding the performance of AND/OR search algorithms for solving a variety of queries over graphical models. We show how drawing a connection to the recent notion of hypertree decompositions allows to exploit determinism in the problem specification and produce tighter bounds. We demonstrate on a variety of practic...

The paper introduces AND/OR importance sampling for probabilistic graphical models. In contrast to importance sampling, AND/OR importance sampling caches samples in the AND/OR space and then extracts a new sample mean from the stored samples. We prove that AND/OR importance sampling may have lower variance than importance sampling; thereby providin...

The paper introduces a family of approximate schemes that extend the process of computing sample mean in importance sampling from the conventional OR space to the AND/OR search space for graphical models. All the sample means are defined on the same set of samples and trade time with variance. At one end is the AND/OR sample tree mean which has the...

In the context of distributed Branch and Bound Search for Graphical Models, effective load balancing is crucial yet hard to achieve due to early pruning of search branches. This paper proposes learning a regression model over structural as well as cost function-based features to more accurately predict subproblem complexity ahead of time, thereby e...

The paper present a formalization of the m-best task within the unifying framework of semirings. As a consequence, known inference algorithms are defined and their correctness and completeness for the m-best task are immediately implied. We also describe and analyze a Bucket Elimination algorithm for solving the m-best task, elim-m-opt, presented i...

We investigate a hybrid of two styles of algorithms for deriving bounds for op-timization tasks over graphical models: non-iterative message-passing schemes exploiting variable duplication to reduce cluster sizes (e.g. MBE) and iterative methods that re-parameterize the problem's functions aiming to produce good bounds even if functions are process...

In his seminal paper, Pearl [1986] introduced the notion of Bayesian networks and the first processing algorithm, Belief Propagation (BP), that computes posterior marginals, called beliefs, for each variable when the network is singly connected. The paper provided the foundation for the whole area of Bayesian networks. It was the first in a series...

A major limitation of exact inference algorithms for probabilistic graphical models is their extensive memory usage, which often puts real-world problems out of their reach. In this paper we show how we can extend inference algorithms, particularly Bucket Elimination, a special case of cluster (join) tree decomposition, to utilize disk memory. We p...

The paper focuses on finding the m best solutions to com-binatorial optimization problems using Best-First or Branch-and-Bound search. Specifically, we present m-A*, extend-ing the well-known A* to the m-best task, and prove that all its desirable properties, including soundness, completeness and optimal efficiency, are maintained. Since Best-First...

We describe a distributed version of an advanced branch and bound algorithm over graphical models. The crucial issue of load balancing is addressed by estimating subproblem complexity through learning, yielding impressive speedups on various hard problems using hundreds of parallel CPUs.

The paper presents a new sampling methodology for Bayesian networks that samples only a subset of variables and applies exact inference to the rest. Cutset sampling is a network structure-exploiting application of the Rao-Blackwellisation principle to sampling in Bayesian networks. It improves convergence by exploiting memory-based inference algori...

Many algorithms for performing inference in graphical models have complexity that is exponential in the treewidth — a parameter of the underlying graph structure. Computing the (minimal) treewidth is NPcomplete, so stochastic algorithms are sometimes used to find low width tree decompositions. A common approach for finding good decompositions is it...

We study iterative randomized greedy algorithms for generating (elimination) orderings with small induced width and state space size — two parameters known to bound the complexity of inference in graphical models. We propose and implement the Iterative Greedy Variable Ordering (IGVO) algorithm, a new variant within this algorithm class. An empirica...

The paper focuses on the task of generating the first m best solutions for a combinatorial optimization problem defined over a graphical model (e.g., the m most probable explanations for a Bayesian network). We show that the m-best task can be expressed within the unifying framework of semirings making known inference algorithms defined and their c...

The paper introduces AND/OR importance sampling for probabilistic graphical models. In contrast to importance sampling, AND/OR importance sampling caches samples in the AND/OR space and then extracts a new sample mean from the stored samples. We prove that AND/OR importance sampling may have lower variance than importance sampling; thereby providin...

Itiswellknownthatcomputingrelativeapproximationsofweightedcountingqueries such as the probability of evidence in a Bayesian network, the partition function of a Markov network, and the number of solutions of a constraint satisfaction problem is NP-hard. In this paper, we settle therefore on an easier problem of computing highconfidence lower bounds...

One popular and efficient scheme for solving exactly combinatorial optimization problems over graphical models is depth-first Branch and Bound. However, when the algorithm exploits problem decomposition using AND/OR search spaces, its anytime behavior breaks down. This paper 1) analyzes and demonstrates this inherent conflict between effective expl...

Many algorithms for performing inference in graphical models have complexity that is exponential in the treewidth- a parameter of the underlying graph structure. Computing the (minimal) treewidth is NPcomplete, so stochastic algorithms are sometimes used to find low width tree decompositions. A common approach for finding good decompositions is ite...

We study iterative randomized greedy algorithms for generating (elimination) orderings with small induced width and state space size- two parameters known to bound the complexity of inference in graphical models. We propose and implement the Iterative Greedy Variable Ordering (IGVO) algorithm, a new variant within this algorithm class. An empirical...

General pedigrees can be encoded as Bayesian networks, where the common MPE query corresponds to finding the most likely haplotype configuration. Based on this, a strategy for grid parallelization of a state-of-the-art Branch and Bound algorithm for MPE is introduced: independent worker nodes concurrently solve subproblems, managed by a Branch and...

The paper presents a scheme for computing lower and upper bounds on the posterior marginals in Bayesian networks with discrete variables. Its power lies in its ability to use any available scheme that bounds the probability of evidence or posterior marginals and enhance its performance in an anytime manner. The scheme uses the cutset conditioning p...

Mini-Bucket Elimination (MBE) is a well-known approximation algorithm deriving lower and upper bounds on quantities of interest over graphical models. It relies on a procedure that partitions a set of functions, called bucket, into smaller subsets, called mini-buckets. The method has been used with a single partitioning heuristic throughout, so the...

The paper investigates parameterized approximate message-passing schemes that are based on bounded inference and are inspired by Pearl's belief propagation algorithm (BP). We start with the bounded inference mini-clustering algorithm and then move to the iterative scheme called Iterative Join-Graph Propagation (IJGP), that combines both iteration a...

AND/OR search spaces accommodate advanced algorithmic schemes for graphical models which can exploit the structure of the model. We extend and evaluate the depth-first and best-first AND/OR search algorithms to solving 0-1 Integer Linear Programs (0-1 ILP) within this framework. We also include a class of dynamic variable ordering heuristics while...

In this paper, we consider two variance reduction schemes that exploit the structure of the primal graph of the graphical model: Rao-Blackwellised w-cutset sampling and AND/OR sampling. We show that the two schemes are orthogonal and can be combined to further reduce the variance. Our combination yields a new family of estima- tors which trade time...

Mini-Bucket Elimination(MBE) is a well-known approxima- tion algorithm for graphical models. It relies on a procedure to partition a set of funtions, called bucket, into smaller sub- sets, called mini-buckets. The impact of the partition process on the quality of the bound computed has never been inves- tigated before. We take first steps to addres...

We introduce a strategy for parallelizing a state-of-the-art se- quential search algorithm for optimization on a grid of com- puters. Based on the AND/OR graph search framework, the procedure exploits the structure of the underlying problem graph. Worker nodes concurrently solve subproblems that are generated by a single master process. Subproblem...

Mini-Bucket Elimination (MBE) is a well-known approximation algorithm deriving lower and upper bounds on quantities of interest over graphical models. It relies on a procedure that partitions a set of functions, called bucket, into smaller subsets, called mini-buckets. The method has been used with a single partitioning heuristic throughout, so the...