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Approximating PseudoBoolean Functions on NonUniform Domains ∗
"... In Machine Learning (ML) and Evolutionary Computation (EC), it is often beneficial to approximate a complicated function by a simpler one, such as a linear or quadratic function, for computational efficiency or feasibility reasons (cf. [Jin, 2005]). A complicated function (the target function in ML ..."
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or the fitness function in EC) may require an exponential amount of computation to learn/evaluate, and thus approximations by simpler functions are needed. We consider the problem of approximating pseudoBoolean functions by simpler (e.g., linear) functions when the instance space is associated with a
Translating pseudoboolean constraints into SAT
 Journal on Satisfiability, Boolean Modeling and Computation
, 2006
"... In this paper, we describe and evaluate three different techniques for translating pseudoboolean constraints (linear constraints over boolean variables) into clauses that can be handled by a standard SATsolver. We show that by applying a proper mix of translation techniques, a SATsolver can perfor ..."
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Cited by 181 (2 self)
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perform on a par with the best existing native pseudoboolean solvers. This is particularly valuable in those cases where the constraint problem of interest is naturally expressed as a SAT problem, except for a handful of constraints. Translating those constraints to get a pure clausal problem will take
Submodularization for Quadratic PseudoBoolean Optimization
 In ArXiv
"... Many computer vision problems require optimization of binary nonsubmodular energies. We propose a general optimization framework based on local submodular approximations (LSA). Unlike standard LP relaxation methods that linearize the whole energy globally, our approach iteratively approximates t ..."
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Cited by 1 (1 self)
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the energies locally. On the other hand, unlike standard local optimization methods (e.g. gradient descent or projection techniques) we use nonlinear submodular approximations and optimize them without leaving the domain of integer solutions. We discuss two specific LSA algorithms based on trust region
PseudoBoolean Optimization
 DISCRETE APPLIED MATHEMATICS
, 2001
"... This survey examines the state of the art of a variety of problems related to pseudoBoolean optimization, i.e. to the optimization of set functions represented by closed algebraic expressions. The main parts of the survey examine general pseudoBoolean optimization, the specially important case of ..."
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Cited by 183 (5 self)
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This survey examines the state of the art of a variety of problems related to pseudoBoolean optimization, i.e. to the optimization of set functions represented by closed algebraic expressions. The main parts of the survey examine general pseudoBoolean optimization, the specially important case
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
Learning pseudoBoolean kDNF and submodular functions
, 2013
"... We prove that any submodular function f: {0, 1} n → {0, 1,..., k} can be represented as a pseudoBoolean 2kDNF formula. PseudoBoolean DNFs are a natural generalization of DNF representation for functions with integer range. Each term in such a formula has an associated integral constant. We show t ..."
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Cited by 6 (2 self)
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We prove that any submodular function f: {0, 1} n → {0, 1,..., k} can be represented as a pseudoBoolean 2kDNF formula. PseudoBoolean DNFs are a natural generalization of DNF representation for functions with integer range. Each term in such a formula has an associated integral constant. We show
Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a
Greedy Function Approximation: A Gradient Boosting Machine
 Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 951 (12 self)
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Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query
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