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Convergence of the Huber Regression M-Estimate in the Presence of Dense Outliers ; ; et al in IEEE Signal Processing Letters (2014), 21(11), 1211-1214 We consider the problem of estimating a deterministic unknown vector which depends linearly on noisy measurements, additionally contaminated with (possibly unbounded) additive outliers. The measurement ... [more ▼] We consider the problem of estimating a deterministic unknown vector which depends linearly on noisy measurements, additionally contaminated with (possibly unbounded) additive outliers. The measurement matrix of the model (i.e., the matrix involved in the linear transformation of the sought vector) is assumed known, and comprised of standard Gaussian i.i.d. entries. The outlier variables are assumed independent of the measurement matrix, deterministic or random with possibly unknown distribution. Under these assumptions we provide a simple proof that the minimizer of the Huber penalty function of the residuals converges to the true parameter vector with a root n-rate, even when outliers are dense, in the sense that there is a constant linear fraction of contaminated measurements which can be arbitrarily close to one. The constants influencing the rate of convergence are shown to explicitly depend on the outlier contamination level. [less ▲] Detailed reference viewed: 177 (0 UL)Maximum likelihood based sparse and distributed conjoint analysis ; ; et al in Statistical Signal Processing Workshop (SSP), 2012 IEEE (2012) A new statistical model for choice-based conjoint analysis is proposed. The model uses auxiliary variables to account for outliers and to detect the salient features that influence decisions. Unlike ... [more ▼] A new statistical model for choice-based conjoint analysis is proposed. The model uses auxiliary variables to account for outliers and to detect the salient features that influence decisions. Unlike recent classification-based approaches to choice-based conjoint analysis, a sparsity-aware maximum likelihood (ML) formulation is proposed to estimate the model parameters. The proposed approach is conceptually appealing, mathematically tractable, and is also well-suited for distributed implementation. Its performance is tested and compared to the prior state-of-art using synthetic as well as real data coming from a conjoint choice experiment for coffee makers, with very promising results. [less ▲] Detailed reference viewed: 170 (0 UL)Semidefinite Relaxations of Robust Binary Least Squares under Ellipsoidal Uncertainty Sets ; ; Ottersten, Björn in IEEE Transactions on Signal Processing (2011), 59(11), 5169-5180 The problem of finding the least squares solution s to a system of equations Hs = y is considered, when s is a vector of binary variables and the coefficient matrix H is unknown but of bounded uncertainty ... [more ▼] The problem of finding the least squares solution s to a system of equations Hs = y is considered, when s is a vector of binary variables and the coefficient matrix H is unknown but of bounded uncertainty. Similar to previous approaches to robust binary least squares, we explore the potential of a min-max design with the aim to provide solutions that are less sensitive to the uncertainty in H. We concentrate on the important case of ellipsoidal uncertainty, i.e., the matrix H is assumed to be a deterministic unknown quantity which lies in a given uncertainty ellipsoid. The resulting problem is NP-hard, yet amenable to convex approximation techniques: Starting from a convenient reformulation of the original problem, we propose an approximation algorithm based on semidefinite relaxation that explicitly accounts for the ellipsoidal uncertainty in the coefficient matrix. Next, we show that it is possible to construct a tighter relaxation by suitably changing the description of the feasible region of the problem, and formulate an approximation algorithm that performs better in practice. Interestingly, both relaxations are derived as Lagrange bidual problems corresponding to the two equivalent problem reformulations. The strength of the proposed tightened relaxation is demonstrated by pertinent simulations. [less ▲] Detailed reference viewed: 180 (2 UL)Robust binary least squares: Relaxations and algorithms ; ; Ottersten, Björn in Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on (2011) Finding the least squares (LS) solution s to a system of linear equations Hs = y where H, y are given and s is a vector of binary variables, is a well known NP-hard problem. In this paper, we consider ... [more ▼] Finding the least squares (LS) solution s to a system of linear equations Hs = y where H, y are given and s is a vector of binary variables, is a well known NP-hard problem. In this paper, we consider binary LS problems under the assumption that the coefficient matrix H is also unknown, and lies in a given uncertainty ellipsoid. We show that the corresponding worst-case robust optimization problem, although NP-hard, is still amenable to semidefinite relaxation (SDR)-based approximations. However, the relaxation step is not obvious, and requires a certain problem reformulation to be efficient. The proposed relaxation is motivated using Lagrangian duality and simulations suggest that it performs well, offering a robust alternative over the traditional SDR approaches for binary LS problems. [less ▲] Detailed reference viewed: 185 (0 UL)The Error Probability of the Fixed-Complexity Sphere Decoder ; ; Ottersten, Björn et al in IEEE Transactions on Signal Processing (2009), 57(7), 2711-2720 Download Citation Email Print Request Permissions Save to Project The fixed-complexity sphere decoder (FSD) has been previously proposed for multiple-input multiple-output (MIMO) detection in order to ... [more ▼] Download Citation Email Print Request Permissions Save to Project The fixed-complexity sphere decoder (FSD) has been previously proposed for multiple-input multiple-output (MIMO) detection in order to overcome the two main drawbacks of the sphere decoder (SD), namely its variable complexity and its sequential structure. Although the FSD has shown remarkable quasi-maximum-likelihood (ML) performance and has resulted in a highly optimized real-time implementation, no analytical study of its performance existed for an arbitrary MIMO system. Herein, the error probability of the FSD is analyzed, proving that it achieves the same diversity as the maximum-likelihood detector (MLD) independent of the constellation used. In addition, it can also asymptotically yield ML performance in the high-signal-to-noise ratio (SNR) regime. Those two results, together with its fixed complexity, make the FSD a very promising algorithm for uncoded MIMO detection. [less ▲] Detailed reference viewed: 172 (0 UL)Detection Based on Relaxation in MIMO Systems ; Ottersten, Björn in Handbook on Advancements in Smart Antenna Technologies for Wireless Networks (2009) Detailed reference viewed: 154 (1 UL)The Diversity Order of the Semidefinite Relaxation Detector ; Ottersten, Björn in IEEE Transactions on Information Theory (2008), 54(4), 14061422 Detailed reference viewed: 67 (0 UL)On the Maximal Diversity Order of Spatial Multiplexing With Transmit Antenna Selection ; Ottersten, Björn in IEEE Transactions on Information Theory (2007), 53(11), 42734276 Detailed reference viewed: 43 (0 UL)Full Diversity Detection in MIMO Systems with a Fixed-Complexity Sphere Decoder ; ; Ottersten, Björn et al in Proceedings IEEE International Conference on Acoustics, Speech, and Signal Processing (2007) Detailed reference viewed: 50 (0 UL)Realization of a Spatially Multiplexed MIMO System ; ; et al in EURASIP Journal on Applied Signal Processing (2006), 2006 Detailed reference viewed: 47 (0 UL)On the Complexity of Sphere Decoding in Digital Communications ; Ottersten, Björn in IEEE Transactions on Signal Processing (2005), 53 Detailed reference viewed: 63 (0 UL)Semidefinite Programming for Detection in Linear Systems - Optimality Conditions and Space-Time Decoding ; ; Ottersten, Björn in IEEE International Conference on Acoustics Speech and Signal Processing (2003) Optimal maximum likelihood detection of finite alphabet symbols in general requires time consuming exhaustive search methods. The computational complexity of such techniques is exponential in the size of ... [more ▼] Optimal maximum likelihood detection of finite alphabet symbols in general requires time consuming exhaustive search methods. The computational complexity of such techniques is exponential in the size of the problem and for large problems sub-optimal algorithms are required. In this paper, to find a solution in polynomial time, a semidefinite programming approach is taken to estimate binary symbols in a general linear system. A condition under which the proposed method provides optimal solutions is derived. As an application, the proposed algorithm is used as a decoder for a linear space-time block coding system and the results are illustrated with numerical examples. [less ▲] Detailed reference viewed: 47 (0 UL) |
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