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21
Euclidean embedding of cooccurrence data
 Advances in Neural Information Processing Systems 17
, 2005
"... Abstract Embedding algorithms search for low dimensional structure in complexdata, but most algorithms only handle objects of a single type for which pairwise distances are specified. This paper describes a method for embedding objects of different types, such as images and text, into a single comm ..."
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Cited by 36 (2 self)
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Abstract Embedding algorithms search for low dimensional structure in complexdata, but most algorithms only handle objects of a single type for which pairwise distances are specified. This paper describes a method for embedding objects of different types, such as images and text, into a single common Euclidean space based on their cooccurrence statistics. Thejoint distributions are modeled as exponentials of Euclidean distances in the lowdimensional embedding space, which links the problem to convex optimization over positive semidefinite matrices. The local structure of our embedding corresponds to the statistical correlations via random walks in the Euclidean space. We quantify the performance of our method on two text datasets, and show that it consistently and significantly outperforms standard methods of statistical correspondence modeling, such as multidimensional scaling and correspondence analysis. 1 Introduction Embeddings of objects in a lowdimensional space are an important tool in unsupervisedlearning and in preprocessing data for supervised learning algorithms. They are especially valuable for exploratory data analysis and visualization by providing easily interpretablerepresentations of the relationships among objects. Most current embedding techniques build low dimensional mappings that preserve certain relationships among objects and differ in the relationships they choose to preserve, which range from pairwise distances in multidimensional scaling (MDS) [4] to neighborhood structure in locally linear embedding[12]. All these methods operate on objects of a single type endowed with a measure of similarity or dissimilarity. However, realworld data often involve objects of several very different types without anatural measure of similarity. For example, typical web pages or scientific papers contain
Theory and applications of Robust Optimization
, 2007
"... In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most pr ..."
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Cited by 23 (5 self)
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In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most prominent theoretical results of RO over the past decade, we will also present some recent results linking RO to adaptable models for multistage decisionmaking problems. Finally, we will highlight successful applications of RO across a wide spectrum of domains, including, but not limited to, finance, statistics, learning, and engineering.
Markov approximation for combinatorial network optimization,” CUHK Technical Report, 2009, available at http://www.ie.cuhk.edu/∼mhchen/ma.tr.pdf
"... Abstract—Many important network design problems can be formulated as a combinatorial optimization problem. A large number of such problems, however, cannot readily be tackled by distributed algorithms. The Markov approximation framework studied in this paper is a general technique for synthesizing d ..."
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Cited by 17 (11 self)
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Abstract—Many important network design problems can be formulated as a combinatorial optimization problem. A large number of such problems, however, cannot readily be tackled by distributed algorithms. The Markov approximation framework studied in this paper is a general technique for synthesizing distributed algorithms. We show that when using the logsumexp function to approximate the optimal value of any combinatorial problem, we end up with a solution that can be interpreted as the stationary probability distribution of a class of timereversible Markov chains. Certain carefully designed Markov chains among this class yield distributed algorithms that solve the logsumexp approximated combinatorial network optimization problem. By three case studies, we illustrate that Markov approximation technique not only can provide fresh perspective to existing distributed solutions, but also can help us generate new distributed algorithms in various domains with provable performance. We believe the Markov approximation framework will find applications in many network optimization problems, and this paper serves as a call for participation. I.
MIMO relaying with linear processing for multiuser transmission in fixed relay networks
 IEEE TRANS. SIGNAL PROCESSING
, 2006
"... In this paper, a novel relaying strategy that uses multiple input multiple output (MIMO) fixed relays with linear processing to support multiuser transmission in cellular networks is proposed. The fixed relay processes the received signal with linear operations and forwards the processed signal to m ..."
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Cited by 14 (1 self)
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In this paper, a novel relaying strategy that uses multiple input multiple output (MIMO) fixed relays with linear processing to support multiuser transmission in cellular networks is proposed. The fixed relay processes the received signal with linear operations and forwards the processed signal to multiple users creating a multiuser MIMO relay. This paper proposes upper and lower bounds on the achievable sum rate for this architecture assuming zero forcing dirty paper coding at the base station, neglecting the direct links from the base station to the users, and with certain structure in the relay. These bounds are used to motivate an implementable multiuser precoding strategy that combines TomlinsonHarashima precoding at the base station and linear signal processing at the relay, adaptive stream selection, and QAM modulation. Reduced complexity algorithms based on the sum rate lower bounds are used to select a subset of users. Simulations compare the upper bounds, lower bounds, and the throughput with TomlinsonHarashima precoding without coding. These results show that the sum rates achieved by the proposed system architecture and algorithms are close to the sum rate upper bound and the sum rate achieved by the decodeandforward relaying though decoding at the relay is not required.
Convergent propagation algorithms via oriented trees
 In UAI. 2007
"... Inference problems in graphical models are often approximated by casting them as constrained optimization problems. Message passing algorithms, such as belief propagation, have previously been suggested as methods for solving these optimization problems. However, there are few convergence guarantees ..."
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Cited by 12 (3 self)
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Inference problems in graphical models are often approximated by casting them as constrained optimization problems. Message passing algorithms, such as belief propagation, have previously been suggested as methods for solving these optimization problems. However, there are few convergence guarantees for such algorithms, and the algorithms are therefore not guaranteed to solve the corresponding optimization problem. Here we present an oriented tree decomposition algorithm that is guaranteed to converge to the global optimum of the TreeReweighted (TRW) variational problem. Our algorithm performs local updates in the convex dual of the TRW problem – an unconstrained generalized geometric program. Primal updates, also local, correspond to oriented reparametrization operations that leave the distribution intact. 1
Approximate inference using conditional entropy decompositions
"... We introduce a novel method for estimating the partition function and marginals of distributions defined using graphical models. The method uses the entropy chain rule to obtain an upper bound on the entropy of a distribution given marginal distributions of variable subsets. The structure of the b ..."
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Cited by 9 (2 self)
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We introduce a novel method for estimating the partition function and marginals of distributions defined using graphical models. The method uses the entropy chain rule to obtain an upper bound on the entropy of a distribution given marginal distributions of variable subsets. The structure of the bound is determined by a permutation, or elimination order, of the model variables. Optimizing this bound results in an upper bound on the log partition function, and also yields an approximation to the model marginals. The optimization problem is convex, and is in fact a dual of a geometric program. We evaluate the method on a 2D Ising model with a wide range of parameters, and show that it compares favorably with previous methods in terms of both partition function bound, and accuracy of marginals.
Solutions and optimality criteria to box constrained nonconvex minimization problems
 J. Industrial and Management Optimization
"... (Communicated by K.L. Teo) Abstract. This paper presents a canonical duality theory for solving nonconvex polynomial programming problems subjected to box constraints. It is proved that under certain conditions, the constrained nonconvex problems can be converted to the socalled canonical (perfect) ..."
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Cited by 3 (2 self)
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(Communicated by K.L. Teo) Abstract. This paper presents a canonical duality theory for solving nonconvex polynomial programming problems subjected to box constraints. It is proved that under certain conditions, the constrained nonconvex problems can be converted to the socalled canonical (perfect) dual problems, which can be solved by deterministic methods. Both global and local extrema of the primal problems can be identified by a triality theory proposed by the author. Applications to nonconvex integer programming and Boolean least squares problems are discussed. Examples are illustrated. A conjecture on NPhard problems is proposed. 1. Primal problem and its dual form. The box constrained nonconvex minimization problem is proposed as a primal problem (P) given below: (P) : min {P (x) = Q(x) + W (x)} (1) x∈Xa where Xa = {x ∈ R n  ℓ l ≤ x ≤ ℓ u} is a feasible space, Q(x) = 1 2 xT Ax − c T x is a quadratic function, A = A T ∈ R n×n is a given symmetric matrix, ℓ l, ℓ u, and c are three given vectors in R n, W (x) is a nonconvex function. In this paper, we simply assume that W (x) is a socalled doublewell fourth order polynomial function defined by W (x) = 1 1 2 2 Bx2 �2 − α, (2) where B ∈ Rm×n is a given matrix and α> 0 is a given parameter. The notation x  used in this paper denotes the Euclidean norm of x. Problems of the form (1) appear frequently in many applications, such as semilinear nonconvex partial differential equations [15], structural limit analysis, discretized optimal control problems with distributed parameters, information theory, and network communication. Particularly, if W (x) = 0, the problem (P) is directly related to certain successive quadratic programming methods ([9, 10, 18]).
Distributed power control for cognitive user access based on primary link control feedback
 In IEEE Infocom. IEEE
, 2010
"... Abstract—We venture beyond the “listenbeforetalk ” strategy that is common in many traditional cognitive radio access schemes. We exploit the bidirectional nature of most primary communication systems. By intelligently choosing their transmission parameters based on the observation of primary use ..."
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Cited by 3 (2 self)
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Abstract—We venture beyond the “listenbeforetalk ” strategy that is common in many traditional cognitive radio access schemes. We exploit the bidirectional nature of most primary communication systems. By intelligently choosing their transmission parameters based on the observation of primary user (PU) communications, secondary users (SUs) in a cognitive network can achieve higher spectrum usage while limiting their interference to the PU. Specifically, we propose that the SUs listen to the PU’s feedback channel to assess their interference on the primary receiver (PURx), and adjust radio power accordingly to satisfy the PU’s interference constraint. We investigate both centralized and distributed power control algorithms without active PU cooperation. We show that the PU feedback information inherent in many twoway primary systems can be used as important coordination signal among multiple SUs to distributively achieve a joint performance guarantee on the primary receiver’s quality of service. data link control information is available in many practical systems, e.g., power control feedback in CDMA cellular systems [6], channel quality indicator (CQI) feedback in HSDPA [6], and ACK/NACK feedback in cellular and WiFi networks [6], [7]. Such feedback information from the PU receiver can serve as a good indicator of the actual (often aggregated) impact of the SU interference on the reception quality of the PU communication link. SURx PUTx
On achievable sum rates of a multiuser MIMO relay channel
 in Proceedings of IEEE Int. Symp. Inform. Theory
, 2006
"... Abstract — In this paper, we investigate a multiple input multiple output (MIMO) multiuser relay channel, where a source with multiple antennas sends data to multiple users via a relay with multiple antennas. The relay applies linear processing to the received signal and forwards the processed signa ..."
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Cited by 2 (0 self)
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Abstract — In this paper, we investigate a multiple input multiple output (MIMO) multiuser relay channel, where a source with multiple antennas sends data to multiple users via a relay with multiple antennas. The relay applies linear processing to the received signal and forwards the processed signal to multiple users. In our system model, the direct links from the source to the users are neglected. We propose algorithms to compute achievable sum rates of this system based on dirty paper coding. An achievable sum rate defines a sum rate that can be achieved in the MIMO multiuser relay channel with zero error probability for any user, hence it is also a lower bound of the capacity of this channel. These algorithms also produce coefficients of the precoder at the source node and the coefficients of the linear processing unit at the relay. Simulations show that the proposed system architecture and algorithms achieve sum rate performance that is close to the derived performance upper bound. I.
Decentralized Cognitive Radio Control based on Inference from Primary Link Control Information 1
"... This work on cognitive radio access ventures beyond the more traditional “listenbeforetalk ” paradigm that underlies many cognitive radio access proposals. We exploit the bidirectional interaction of most primary communication links. By intelligently controlling their access parameters based on t ..."
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Cited by 2 (0 self)
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This work on cognitive radio access ventures beyond the more traditional “listenbeforetalk ” paradigm that underlies many cognitive radio access proposals. We exploit the bidirectional interaction of most primary communication links. By intelligently controlling their access parameters based on the inference from observed link control signals of primary user (PU) communications, cognitive secondary users (SUs) can achieve higher spectrum efficiency while limiting their interference to the PU network. In one specific implementation, we let the SUs listen to the PU’s feedback channel to assess their own interference on the primary receiver (PURx), and adjust radio power accordingly to satisfy the PU’s interference constraint. We propose a discounted distributed power control algorithm to achieve nonintrusive secondary spectrum access without a centralized controller or active PU cooperation, and study analytically its convergence property. We show that the link control feedback information inherent in many twoway primary systems can be used as important reference signal among multiple SU pairs to distributively achieve a joint performance assurance for primary receiver’s quality of service. Index Terms Wireless communications, inference for opportunistic spectrum access, dynamic spectrum access control, distributed algorithm, cognitive radio networks. I.