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17
Sharp thresholds for highdimensional and noisy sparsity recovery using l1constrained quadratic programmming (Lasso)
, 2006
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Learning graphical models for stationary time series
 IEEE Transactions on Signal Processing, 52(8):2189 – 2199
, 2004
"... Probabilistic graphical models can be extended to time series by considering probabilistic dependencies between entire time series. For stationary Gaussian time series, the graphical model semantics can be expressed naturally in the frequency domain, leading to interesting families of structured tim ..."
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Cited by 18 (0 self)
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Probabilistic graphical models can be extended to time series by considering probabilistic dependencies between entire time series. For stationary Gaussian time series, the graphical model semantics can be expressed naturally in the frequency domain, leading to interesting families of structured time series models that are complementary to families defined in the time domain. In this paper, we present an algorithm to learn the structure from data for directed graphical models for stationary Gaussian time series. We describe an algorithm for efficient forecasting for stationary Gaussian time series whose spectral densities factorize in a graphical model. We also explore the relationships between graphical model structure and sparsity, comparing and contrasting the notions of sparsity in the time domain and the frequency domain. Finally, we show how to make use of Mercer kernels in this setting, allowing our ideas to be extended to nonlinear models. 1
A minimax classification approach with application to robust speech recognition
 IEEE Trans. Speech Audio Processing
, 1993
"... Abstruct A minimax approach for robust classification of parametric information sources is studied and applied to isolatedword speech recognition based on hidden Markov modeling. The goal is to reduce the sensitivity of speech recognition systems to a possible mismatch between the training and test ..."
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Cited by 17 (8 self)
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Abstruct A minimax approach for robust classification of parametric information sources is studied and applied to isolatedword speech recognition based on hidden Markov modeling. The goal is to reduce the sensitivity of speech recognition systems to a possible mismatch between the training and testing conditions. To this end, a generalized likelihood ratio test is developed and shown to be optimal in the sense of achieving the highest asymptotic exponential rate of decay of the error probability for the worstcase mismatch situation. The proposed approach is compared to the standard approach, where no mismatch is assumed, in recognition of noisy speech and in other realistic mismatch situations. I.
PROOFS A.: Beyond hard negative mining: Efficient detector learning via blockcirculant decomposition
 In Computer Vision (ICCV), 2013 IEEE
, 2013
"... Competitive sliding window detectors require vast training sets. Since a pool of natural images provides a nearly endless supply of negative samples, in the form of patches at different scales and locations, training with all the available data is considered impractical. A staple of current appro ..."
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Cited by 14 (3 self)
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Competitive sliding window detectors require vast training sets. Since a pool of natural images provides a nearly endless supply of negative samples, in the form of patches at different scales and locations, training with all the available data is considered impractical. A staple of current approaches is hard negative mining, a method of selecting relevant samples, which is nevertheless expensive. Given that samples at slightly different locations have overlapping support, there seems to be an enormous amount of duplicated work. It is natural, then, to ask whether these redundancies can be eliminated. In this paper, we show that the Gram matrix describing such data is blockcirculant. We derive a transformation based on the Fourier transform that blockdiagonalizes the Gram matrix, at once eliminating redundancies and partitioning the learning problem. This decomposition is valid for any dense features and several learning algorithms, and takes full advantage of modern parallel architectures. Surprisingly, it allows training with all the potential samples in sets of thousands of images. By considering the full set, we generate in a single shot the optimal solution, which is usually obtained only after several rounds of hard negative mining. We report speed gains on Caltech Pedestrians and INRIA Pedestrians of over an order of magnitude, allowing training on a desktop computer in a couple of minutes. 1.
Conditioning and Preconditioning of the Variational Data Assimilation Problem by S.A. Haben, A.S. Lawless, N.K. NicholsConditioning and Preconditioning of the Variational Data Assimilation Problem
, 2010
"... Numerical weather prediction (NWP) centres use numerical models of the atmospheric flow to forecast future weather states from an estimate of the current state. Variational data assimilation (VAR) is used commonly to determine an optimal state estimate that miminizes the errors between observations ..."
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Cited by 8 (1 self)
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Numerical weather prediction (NWP) centres use numerical models of the atmospheric flow to forecast future weather states from an estimate of the current state. Variational data assimilation (VAR) is used commonly to determine an optimal state estimate that miminizes the errors between observations of the dynamical system and model predictions of the flow. The rate of convergence of the VAR scheme and the sensitivity of the solution to errors are dependent on the condition number of the Hessian of the variational leastsquares objective function. The traditional formulation of VAR is illconditioned and hence leads to slow convergence and an inaccurate solution. In practice, operational NWP centres precondition the system via a control variable transform to reduce the condition number of the Hessian. In this paper we investigate the conditioning of VAR for a single, periodic, spatiallydistributed state variable. We present theoretical bounds on the condition number of the original and preconditioned Hessians and hence establish the improvement produced by the preconditioning. We also investigate theoretically the effect of observation position and error variance on the preconditioned system and show that the problem becomes more illconditioned with increasingly dense and accurate observations. Finally, we confirm the theoretical results in an operational setting by giving experimental results from the Met Office variational system.
Spectral Efficiency of CDMA Downlink Cellular Networks with Matched Filter
, 2006
"... In this contribution, the performance of a downlink code division multiple access (CDMA) system with orthogonal spreading and multicell interference is analyzed. A useful framework is provided in order to determine the optimal base station coverage for wireless frequency selective channels with dens ..."
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Cited by 7 (2 self)
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In this contribution, the performance of a downlink code division multiple access (CDMA) system with orthogonal spreading and multicell interference is analyzed. A useful framework is provided in order to determine the optimal base station coverage for wireless frequency selective channels with dense networks where each user is equipped with a matched filter. Using asymptotic arguments, explicit expressions of the spectral efficiency are obtained and provide a simple expression of the network spectral efficiency based only on a few meaningful parameters. Contrarily to a common misconception which asserts that to increase spectral efficiency in a CDMA network, one has to increase the number of cells, we show that, depending on the path loss and the fading channel statistics, the code orthogonal gain (due to the synchronization of all the users at the base station) can compensate and even compete in some cases with the drawbacks due to intercell interference. The results are especially realistic and useful for the design of dense networks.
Principles of MIMOOFDM Wireless Systems
"... The use of multiple antennas at both ends of a wireless link (MIMO technology) holds the potential to drastically improve the spectral efficiency and link reliability in future wireless communications systems. A particularly promising candidate for nextgeneration fixed and mobile wireless systems i ..."
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Cited by 7 (0 self)
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The use of multiple antennas at both ends of a wireless link (MIMO technology) holds the potential to drastically improve the spectral efficiency and link reliability in future wireless communications systems. A particularly promising candidate for nextgeneration fixed and mobile wireless systems is the combination of MIMO technology with Orthogonal Frequency Division Multiplexing (OFDM). This chapter provides an overview of the basic principles of MIMOOFDM.
Adaptive estimation of Stationary Gaussian fields
 ANNALS OF STATISTICS
, 2010
"... We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a regular lattice. In the time series setting, some procedures like AIC are proved to achieve optimal model selection among autoregressive models. However, there exists no such equivalent results of adaptiv ..."
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Cited by 6 (0 self)
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We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a regular lattice. In the time series setting, some procedures like AIC are proved to achieve optimal model selection among autoregressive models. However, there exists no such equivalent results of adaptivity in a spatial setting. By considering collections of Gaussian Markov random fields (GMRF) as approximation sets for the distribution of X, we introduce a novel model selection procedure for spatial fields. For all neighborhoods m in a given collection M, this procedure first amounts to computing a covariance estimator of X within the GMRFs of neighborhood m. Then it selects a neighborhood ̂m by applying a penalization strategy. The sodefined method satisfies a nonasymptotic oracletype inequality. If X is a GMRF, the procedure is also minimax adaptive to the sparsity of its neighborhood. More generally, the procedure is adaptive to the rate of approximation of the true distribution by GMRFs with growing neighborhoods.
Recent advancements in speech enhancement
, 2006
"... Speech enhancement is a long standing problem with numerous applications ranging from hearing aids, to coding and automatic recognition of speech signals. In this survey paper we focus on enhancement from a single microphone, and assume that the noise is additive and statistically independent of the ..."
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Cited by 5 (1 self)
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Speech enhancement is a long standing problem with numerous applications ranging from hearing aids, to coding and automatic recognition of speech signals. In this survey paper we focus on enhancement from a single microphone, and assume that the noise is additive and statistically independent of the signal. We present the principles that guide researchers working in this area, and provide a detailed design example. The example focuses on minimum mean square error estimation of the clean signal’s logspectral magnitude. This approach has attracted significant attention in the past twenty years. We also describe the principles of a MonteCarlo simulation approach for speech enhancement. 1
AntiHadamard Matrices
, 1984
"... An antiHadamard matrix may be loosely defined as a real (0,1) matrix which is invertible, but only just. Let A be an invertible (0,1) matrix with eigenvalues l i , singular values s i , and inverse B = (b ij ). We are interested in the four closely related problems of finding l(n) = A , i min ï ..."
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Cited by 4 (0 self)
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An antiHadamard matrix may be loosely defined as a real (0,1) matrix which is invertible, but only just. Let A be an invertible (0,1) matrix with eigenvalues l i , singular values s i , and inverse B = (b ij ). We are interested in the four closely related problems of finding l(n) = A , i min ï l i ï , s(n) = A , i min s i , c(n) = A , i , j max ï b ij ï , and µ(n) = A max i , j S b ij 2 . Then A is an antiHadamard matrix if it attains µ(n). We show that l(n), s(n) are between (2n)  1 (n /4)  n/2 and cÖ"n (2.274)  n , where c is a constant, c (2.274) n c(n) 2(n /4) n/2 , and c (5.172) n µ(n) 4n 2 (n /4) n . We also consider these problems when A is restricted to be a Toeplitz, triangular, circulant or ( + 1 ,  1) matrix. Besides the obvious application, to finding the most illconditioned (0,1) matrices, there are connections with weighing designs, number theory and geometry. _______________ * This paper appeared in "Linear Algebra and Its...