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888
Learning structured prediction models: a large margin approach
, 2004
"... We consider large margin estimation in a broad range of prediction models where inference involves solving combinatorial optimization problems, for example, weighted graphcuts or matchings. Our goal is to learn parameters such that inference using the model reproduces correct answers on the training ..."
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Cited by 225 (8 self)
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We consider large margin estimation in a broad range of prediction models where inference involves solving combinatorial optimization problems, for example, weighted graphcuts or matchings. Our goal is to learn parameters such that inference using the model reproduces correct answers on the training data. Our method relies on the expressive power of convex optimization problems to compactly capture inference or solution optimality in structured prediction models. Directly embedding this structure within the learning formulation produces concise convex problems for efficient estimation of very complex and diverse models. We describe experimental results on a matching task, disulfide connectivity prediction, showing significant improvements over stateoftheart methods. 1.
MAP estimation via agreement on trees: Messagepassing and linear programming
, 2002
"... We develop and analyze methods for computing provably optimal maximum a posteriori (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex combination of treestructured distributions, we obtain an upper bound ..."
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Cited by 196 (10 self)
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We develop and analyze methods for computing provably optimal maximum a posteriori (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex combination of treestructured distributions, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in terms of the combined optimal values of the tree problems. We prove that this upper bound is tight if and only if all the tree distributions share an optimal configuration in common. An important implication is that any such shared configuration must also be a MAP configuration for the original distribution. Next we develop two approaches to attempting to obtain tight upper bounds: (a) a treerelaxed linear program (LP), which is derived from the Lagrangian dual of the upper bounds; and (b) a treereweighted maxproduct messagepassing algorithm that is related to but distinct from the maxproduct algorithm. In this way, we establish a connection between a certain LP relaxation of the modefinding problem, and a reweighted form of the maxproduct (minsum) messagepassing algorithm.
Optimal Approximation for the Submodular Welfare Problem in the value oracle model
 STOC'08
, 2008
"... In the Submodular Welfare Problem, m items are to be distributed among n players with utility functions wi: 2 [m] → R+. The utility functions are assumed to be monotone and submodular. Assuming that player i receives a set of items Si, we wish to maximize the total utility Pn i=1 wi(Si). In this pap ..."
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Cited by 122 (11 self)
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In the Submodular Welfare Problem, m items are to be distributed among n players with utility functions wi: 2 [m] → R+. The utility functions are assumed to be monotone and submodular. Assuming that player i receives a set of items Si, we wish to maximize the total utility Pn i=1 wi(Si). In this paper, we work in the value oracle model where the only access to the utility functions is through a black box returning wi(S) for a given set S. Submodular Welfare is in fact a special case of the more general problem of submodular maximization subject to a matroid constraint: max{f(S) : S ∈ I}, where f is monotone submodular and I is the collection of independent sets in some matroid. For both problems, a greedy algorithm is known to yield a 1/2approximation [21, 16]. In special cases where the matroid is uniform (I = {S: S  ≤ k}) [20] or the submodular function is of a special type [4, 2], a (1 − 1/e)approximation has been achieved and this is optimal for these problems in the value oracle model [22, 6, 15]. A (1 − 1/e)approximation for the general Submodular Welfare Problem has been known only in a stronger demand oracle model [4], where in fact 1 − 1/e can be improved [9]. In this paper, we develop a randomized continuous greedy algorithm which achieves a (1 − 1/e)approximation for the Submodular Welfare Problem in the value oracle model. We also show that the special case of n equal players is approximation resistant, in the sense that the optimal (1 − 1/e)approximation is achieved by a uniformly random solution. Using the pipage rounding technique [1, 2], we obtain a (1 − 1/e)approximation for submodular maximization subject to any matroid constraint. The continuous greedy algorithm has a potential of wider applicability, which we demonstrate on the examples of the Generalized Assignment Problem and the AdWords Assignment Problem.
Maximizing a Submodular Set Function subject to a Matroid Constraint (Extended Abstract)
 PROC. OF 12 TH IPCO
, 2007
"... Let f: 2 N → R + be a nondecreasing submodular set function, and let (N, I) be a matroid. We consider the problem maxS∈I f(S). It is known that the greedy algorithm yields a 1/2approximation [9] for this problem. It is also known, via a reduction from the maxkcover problem, that there is no (1 ..."
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Cited by 114 (12 self)
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Let f: 2 N → R + be a nondecreasing submodular set function, and let (N, I) be a matroid. We consider the problem maxS∈I f(S). It is known that the greedy algorithm yields a 1/2approximation [9] for this problem. It is also known, via a reduction from the maxkcover problem, that there is no (1 − 1/e + ɛ)approximation for any constant ɛ> 0, unless P = NP [6]. In this paper, we improve the 1/2approximation to a (1−1/e)approximation, when f is a sum of weighted rank functions of matroids. This class of functions captures a number of interesting problems including set coverage type problems. Our main tools are the pipage rounding technique of Ageev and Sviridenko [1] and a probabilistic lemma on monotone submodular functions that might be of independent interest. We show that the generalized assignment problem (GAP) is a special case of our problem; although the reduction requires N  to be exponential in the original problem size, we are able to interpret the recent (1 − 1/e)approximation for GAP by Fleischer et al. [10] in our framework. This enables us to obtain a (1 − 1/e)approximation for variants of GAP with more complex constraints.
Scheduling Strategies for MasterSlave Tasking on Heterogeneous Processor Grids
, 2002
"... In this paper, we consider the problem of allocating a large number of independent, equalsized tasks to a heterogeneous "grid" computing platform. We use a nonoriented graph to model a grid, where resources can have different speeds of computation and communication, as well as different ..."
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Cited by 102 (33 self)
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In this paper, we consider the problem of allocating a large number of independent, equalsized tasks to a heterogeneous "grid" computing platform. We use a nonoriented graph to model a grid, where resources can have different speeds of computation and communication, as well as different overlap capabilities. We show how to determine the optimal steadystate scheduling strategy for each processor (the fraction of time spent computing and the fraction of time spent communicating with each neighbor). This result holds for a quite general framework, allowing for cycles and multiple paths in the interconnection graph, and allowing for several masters. Because
A discriminative matching approach to word alignment
 In Proceedings of HLTEMNLP
, 2005
"... We present a discriminative, largemargin approach to featurebased matching for word alignment. In this framework, pairs of word tokens receive a matching score, which is based on features of that pair, including measures of association between the words, distortion between their positions, similari ..."
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Cited by 98 (7 self)
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We present a discriminative, largemargin approach to featurebased matching for word alignment. In this framework, pairs of word tokens receive a matching score, which is based on features of that pair, including measures of association between the words, distortion between their positions, similarity of the orthographic form, and so on. Even with only 100 labeled training examples and simple features which incorporate counts from a large unlabeled corpus, we achieve AER performance close to IBM Model 4, in much less time. Including Model 4 predictions as features, we achieve a relative AER reduction of 22 % in over intersected Model 4 alignments. 1
Pyramid codes: Flexible schemes to trade space for access efficiency in reliable data storage systems
 In Proceedings of the IEEE International Symposium on Network Computing and Applications. IEEE, Los Alamitos
"... We design flexible schemes to explore the tradeoffs between storage space and access efficiency in reliable data storage systems. Aiming at this goal, two new classes of erasureresilient codes are introduced – Basic Pyramid Codes (BPC) and Generalized Pyramid Codes (GPC). Both schemes require sligh ..."
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Cited by 78 (8 self)
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We design flexible schemes to explore the tradeoffs between storage space and access efficiency in reliable data storage systems. Aiming at this goal, two new classes of erasureresilient codes are introduced – Basic Pyramid Codes (BPC) and Generalized Pyramid Codes (GPC). Both schemes require slightly more storage space than conventional schemes, but significantly improve the critical performance of read during failures and unavailability. As a byproduct, we establish a necessary matching condition to characterize the limit of failure recovery, that is, unless the matching condition is satisfied, a failure case is impossible to recover. In addition, we define a maximally recoverable (MR) property. For all ERC schemes holding the MR property, the matching condition becomes sufficient, that is, all failure cases satisfying the matching condition are indeed recoverable. We show that GPC is the first class of nonMDS schemes holding the MR property.