Results 1  10
of
11
Taming the curse of dimensionality: Discrete integration by hashing and optimization
 In ICML (To appear
, 2013
"... Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constantfactor approximation of a general discrete integral defined over an exponentially large s ..."
Abstract

Cited by 15 (5 self)
 Add to MetaCart
(Show Context)
Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constantfactor approximation of a general discrete integral defined over an exponentially large set. This algorithm relies on solving only a small number of instances of a discrete combinatorial optimization problem subject to randomly generated parity constraints used as a hash function. As an application, we demonstrate that with a small number of MAP queries we can efficiently approximate the partition function of discrete graphical models, which can in turn be used, for instance, for marginal computation or model selection. 1.
Embed and Project: Discrete Sampling with Universal Hashing
"... We consider the problem of sampling from a probability distribution defined over a highdimensional discrete set, specified for instance by a graphical model. We propose a sampling algorithm, called PAWS, based on embedding the set into a higherdimensional space which is then randomly projected usi ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
We consider the problem of sampling from a probability distribution defined over a highdimensional discrete set, specified for instance by a graphical model. We propose a sampling algorithm, called PAWS, based on embedding the set into a higherdimensional space which is then randomly projected using universal hash functions to a lowerdimensional subspace and explored using combinatorial search methods. Our scheme can leverage fast combinatorial optimization tools as a blackbox and, unlike MCMC methods, samples produced are guaranteed to be within an (arbitrarily small) constant factor of the true probability distribution. We demonstrate that by using stateoftheart combinatorial search tools, PAWS can efficiently sample from Ising grids with strong interactions and from software verification instances, while MCMC and variational methods fail in both cases. 1
Rational deployment of CSP heuristics
 In IJCAI
, 2011
"... Heuristics are crucial tools in decreasing search effort in varied fields of AI. In order to be effective, a heuristic must be efficient to compute, as well as provide useful information to the search algorithm. However, some wellknown heuristics which do well in reducing backtracking are so heavy ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Heuristics are crucial tools in decreasing search effort in varied fields of AI. In order to be effective, a heuristic must be efficient to compute, as well as provide useful information to the search algorithm. However, some wellknown heuristics which do well in reducing backtracking are so heavy that the gain of deploying them in a search algorithm might be outweighed by their overhead. We propose a rational metareasoning approach to decide when to deploy heuristics, using CSP backtracking search as a case study. In particular, a value of information approach is taken to adaptive deployment of solutioncount estimation heuristics for value ordering. Empirical results show that indeed the proposed mechanism successfully balances the tradeoff between decreasing backtracking and heuristic computational overhead, resulting in a significant overall search time reduction. 1
Exploiting Problem Structure for Solution Counting
"... Abstract. This paper deals with the challenging problem of counting the number of solutions of a CSP, denoted #CSP. Recent progress have been made using search methods, such as BTD [15], which exploit the constraint graph structure in order to solve CSPs. We propose to adapt BTD for solving the #CSP ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Abstract. This paper deals with the challenging problem of counting the number of solutions of a CSP, denoted #CSP. Recent progress have been made using search methods, such as BTD [15], which exploit the constraint graph structure in order to solve CSPs. We propose to adapt BTD for solving the #CSP problem. The resulting exact counting method has a worstcase time complexity exponential in a specific graph parameter, called treewidth. For problems with sparse constraint graphs but large treewidth, we propose an iterative method which approximates the number of solutions by solving a partition of the set of constraints into a collection of partial chordal subgraphs. Its time complexity is exponential in the maximum clique size the clique number of the original problem, which can be much smaller than its treewidth. Experiments on CSP and SAT benchmarks shows the practical efficiency of our proposed approaches. 1
Random Stimulus Generation using Entropy and XOR Constraints
"... Despite the growing research effort in formal verification, constraintbased random simulation remains an integral part of design validation, especially for large design components where formal techniques do not scale. However, stimulating important aspects of a design to uncover bugs often requires ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Despite the growing research effort in formal verification, constraintbased random simulation remains an integral part of design validation, especially for large design components where formal techniques do not scale. However, stimulating important aspects of a design to uncover bugs often requires the construction of complex constraints to guide stimulus generation. We propose Toggle, a stimulus generation engine, which features (1) an entropybased coverage analysis to efficiently find portions of the design inadequately sensitized by simulation and (2) a novel strategy to automatically stimulate these portions through a specialized SAT algorithm that uses small randomized XOR constraints. As our experimental results demonstrate, Toggle requires minimal input from the verification engineer, and significantly improves the coverage qualities of the generated stimuli when compared to plain random simulation. 1
Synthesis and Verification of Digital Circuits using Functional Simulation and Boolean Satisfiability
, 2008
"... for inspiring me to consider various fields of research and providing feedback on my projects and papers. I also want to thank my defense committee for their comments and insights: Professor John Hayes, Professor Karem Sakallah, and Professor Dennis Sylvester. I would like to thank Professor David K ..."
Abstract
 Add to MetaCart
(Show Context)
for inspiring me to consider various fields of research and providing feedback on my projects and papers. I also want to thank my defense committee for their comments and insights: Professor John Hayes, Professor Karem Sakallah, and Professor Dennis Sylvester. I would like to thank Professor David Kieras for enhancing my knowledge and appreciation for computer programming and providing invaluable advice. Over the years, I have been fortunate to know and work with several wonderful students. I have collaborated extensively with Kaihui Chang and Smita Krishnaswamy and have enjoyed numerous research discussions with them and have benefited from their insights. I would like to thank Ian Kountanis and Zaher Andraus for our many fun discussions on parallel SAT. I also appreciate the time spent collaborating with Kypros Constantinides and Jason Blome. Although I have not formally collaborated with Ilya Wagner, I have enjoyed numerous discussions with him during my doctoral studies. I also thank my office mates Jarrod Roy, Jin Hu, and Hector Garcia. Without my family and friends I would never have come this far. I would like to thank Geoff Blake and Smita Krishnaswamy, who have been both good friends and colleagues
Proceedings of the TwentySecond International Joint Conference on Artificial Intelligence Rational Deployment of CSP Heuristics
"... Heuristics are crucial tools in decreasing search effort in varied fields of AI. In order to be effective, a heuristic must be efficient to compute, as well as provide useful information to the search algorithm. However, some wellknown heuristics which do well in reducing backtracking are so heavy ..."
Abstract
 Add to MetaCart
Heuristics are crucial tools in decreasing search effort in varied fields of AI. In order to be effective, a heuristic must be efficient to compute, as well as provide useful information to the search algorithm. However, some wellknown heuristics which do well in reducing backtracking are so heavy that the gain of deploying them in a search algorithm might be outweighed by their overhead. We propose a rational metareasoning approach to decide when to deploy heuristics, using CSP backtracking search as a case study. In particular, a value of information approach is taken to adaptive deployment of solutioncount estimation heuristics for value ordering. Empirical results show that indeed the proposed mechanism successfully balances the tradeoff between decreasing backtracking and heuristic computational overhead, resulting in a significant overall search time reduction. 1
Importance Sampling over Sets: A New Probabilistic Inference Scheme
"... Computing expectations in highdimensional spaces is a key challenge in probabilistic inference and machine learning. Monte Carlo sampling, and importance sampling in particular, is one of the leading approaches. We propose a generalized importance sampling scheme based on randomly selecting (expo ..."
Abstract
 Add to MetaCart
Computing expectations in highdimensional spaces is a key challenge in probabilistic inference and machine learning. Monte Carlo sampling, and importance sampling in particular, is one of the leading approaches. We propose a generalized importance sampling scheme based on randomly selecting (exponentially large) subsets of states rather than individual ones. By collecting a small number of extreme states in the sampled sets, we obtain estimates of statistics of interest, such as the partition function of an undirected graphical model. We incorporate this idea into a novel maximum likelihood learning algorithm based on cutting planes. We demonstrate empirically that our scheme provides accurate answers and scales to problems with up to a million variables. 1
Annals of Operations Research manuscript No. (will be inserted by the editor) Leveraging Belief Propagation, Backtrack Search, and Statistics for Model Counting
"... Abstract We consider the problem of estimating the model count (number of solutions) of Boolean formulas, and present two techniques that compute estimates of these counts, as well as either lower or upper bounds with different tradeoffs between efficiency, bound quality, and correctness guarantee. ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract We consider the problem of estimating the model count (number of solutions) of Boolean formulas, and present two techniques that compute estimates of these counts, as well as either lower or upper bounds with different tradeoffs between efficiency, bound quality, and correctness guarantee. For lower bounds, we use a recent framework for probabilistic correctness guarantees, and exploit message passing techniques for marginal probability estimation, namely, variations of the Belief Propagation (BP) algorithm. Our results suggest that BP provides useful information even on structured, loopy formulas. For upper bounds, we perform multiple runs of the MiniSat SAT solver with a minor modification, and obtain statistical bounds on the model count based on the observation that the distribution of a certain quantity of interest is often very close to the normal distribution. Our experiments demonstrate that our model counters based on these two ideas, BPCount and MiniCount, can provide very good bounds in time significantly less than alternative approaches.
Lowlatency SAT Solving on Multicore Processors with Priority Scheduling and XOR Partitioning
"... As multicore processors become prevalent, computational methodologies for decisionmaking, combinatorial optimization, optimal design, and formal verification must adapt to better utilize available CPU resources. We propose new techniques to exploit the power offered by upcoming sharedmemory multic ..."
Abstract
 Add to MetaCart
(Show Context)
As multicore processors become prevalent, computational methodologies for decisionmaking, combinatorial optimization, optimal design, and formal verification must adapt to better utilize available CPU resources. We propose new techniques to exploit the power offered by upcoming sharedmemory multicore/multiCPU architectures to boost the performance of solvers for fundamental NPhard problems, such as Boolean and PseudoBoolean SAT. We develop an algorithmic paradigm for parallel solvers centered on 1) a scheduling strategy to reduce the average latency for solving batches of instances of varying complexity, and 2) a novel, balanced decomposition of a SAT instance’s search space among multiple threads. These techniques are implemented in a software library that provides parallelsolving services to user applications. Evaluation on an eightcore workstation shows significantly reduced latency for solving multiple SAT instances in parallel, as well as greater CPU utilization. 1.