Search

This paper proposes a novel algorithm to determine the optimal orientation of sensing axes of redundant inertial sensors such as accelerometers and gyroscopes (gyros) for increasing the sensing accuracy. In this paper, we have proposed a novel iterative algorithm to find the optimal sensor configuration. The proposed algorithm utilizes the majorization-minimization (MM) algorithm and the duality principle to find the optimal configuration. Unlike the state-of-the-art approaches which are mainly geometrical in nature and restricted to sensors’ noise being uncorrelated, the proposed algorithm gives the exact orientations of the sensors and can easily deal with the cases of correlated noise. The proposed algorithm has been implemented and tested via numerical simulation in the MATLAB. The simulation results show that the algorithm converges to the optimal configurations and shows the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a new framework for the design of transmit and receive beamformers for interference alignment (IA) without symbol extensions in multi-antenna cellular networks. We consider IA in a G cell network with K users/cell, N antennas at each base station (BS) and M antennas at each user. The proposed framework is developed by recasting the conditions for IA as two sets of rank constraints, one on the rank of interference matrices, and the other on the transmit beamformers in the uplink. The interference matrix consists of all the interfering vectors received at a BS from the out-of-cell users in the uplink. Using these conditions and the crucial observation that the rank of interference matrices under alignment can be determined beforehand, this paper develops two sets of algorithms for IA. The first part of this paper develops rank minimization algorithms for IA by iteratively minimizing a weighted matrix norm of the interference matrix. Different choices of matrix norms lead to reweighted nuclear norm minimization (RNNM) or reweighted Frobenius norm minimization (RFNM) algorithms with significantly different per-iteration complexities. Alternately, the second part of this paper devises an alternating minimization (AM) algorithm where the rank-deficient interference matrices are expressed as a product of two lower-dimensional matrices that are then alternately optimized. Simulation results indicate that RNNM, which has a per-iteration complexity of a semidefinite program, is effective in designing aligned beamformers for proper-feasible systems with or without redundant antennas, while RFNM and AM, which have a per-iteration complexity of a quadratic program, are better suited for systems with redundant antennas. [ABSTRACT FROM PUBLISHER]

The problem of range estimation based on noisy measurements with phase ambiguity can be solved using signals across multiple frequencies by existing algorithms based on either the Chinese Remainder Theorem or lattice theory. The performances of these algorithms are constrained by the trade-off between SNR of measurements and required estimation accuracy. In this paper, we firstly propose an algorithm to find a set of wavelengths satisfying the conditions to apply the closed-form lattice algorithm from a given interval. Then we propose an enhanced lattice algorithm for range estimation based on existing lattice approaches. In the conventional lattice algorithm, the selection of an integer vector by the estimator often fails to be the ground truth because of noise. As a result, the true value can be a neighbouring lattice point of the estimated point where neighbours are defined in terms of a distance depending on the noise characteristics. In this paper, all neighbouring lattice points of the estimated point obtained by a conventional lattice algorithm are regarded as candidates for the new estimate. Then an efficient estimator is presented to choose one of those candidates to be the new estimate. The performance of the proposed algorithm, i.e. the successful probability of reconstruction, is derived mathematically. Additionally, a computation-reduced algorithm is presented to reduce the overhead of computation. The calculated probability and simulation results demonstrate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a decentralized algorithm for solving a consensus optimization problem defined in a static networked multi-agent system, where the local objective functions have the smooth+nonsmooth composite form. Examples of such problems include decentralized constrained quadratic programming and compressed sensing problems, as well as many regularization problems arising in inverse problems, signal processing, and machine learning, which have decentralized applications. This paper addresses the need for efficient decentralized algorithms that take advantages of proximal operations for the nonsmooth terms. We propose a proximal gradient exact first-order algorithm (PG-EXTRA) that utilizes the composite structure and has the best known convergence rate. It is a nontrivial extension to the recent algorithm EXTRA. At each iteration, each agent locally computes a gradient of the smooth part of its objective and a proximal map of the nonsmooth part, as well as exchanges information with its neighbors. The algorithm is “exact” in the sense that an exact consensus minimizer can be obtained with a fixed step size, whereas most previous methods must use diminishing step sizes. When the smooth part has Lipschitz gradients, PG-EXTRA has an ergodic convergence rate of O\left(1\over k\right) in terms of the first-order optimality residual. When the smooth part vanishes, PG-EXTRA reduces to P-EXTRA, an algorithm without the gradients (so no “G” in the name), which has a slightly improved convergence rate at o\left(1\over k\right) in a standard (non-ergodic) sense. Numerical experiments demonstrate effectiveness of PG-EXTRA and validate our convergence results [ABSTRACT FROM PUBLISHER]

The Unlimited Sensing Framework (USF) was recently introduced to overcome the sensor saturation bottleneck in conventional digital acquisition systems. At its core, the USF converts a continuous-time high-dynamic-range (HDR) signal into folded, low-dynamic-range, modulo samples and allows the recovery of the HDR signal via algorithmic unfolding. In hardware, however, implementing ideal modulo folding requires careful calibration, analog design and high precision. At the interface of theory and practice, this paper explores a computational sampling strategy that relaxes strict hardware requirements via a novel, mathematically guaranteed reconstruction. We start with a generalized model for USF with two new parameters modeling hysteresis and folding transients in addition to the modulo threshold. Hysteresis accounts for mismatches between the reset threshold and the amplitude displacement at the folding time and the folding transient is a continuous transition period in the implementation of a reset. Both these effects are motivated by our hardware experiments and also occur in previous, domain-specific applications. We show that hysteresis is beneficial for USF and leverage it to derive the first recovery guarantees in the context of our generalized USF model for a certain sampling rate regime. Additionally, we show how the sampling rate requirement can be greatly reduced via a direct generalization of the proposed recovery. Our theoretical work is corroborated by hardware experiments with a hysteresis enabled, modulo ADC testbed comprising off-the-shelf electronic components. Thus, by capitalizing on a collaboration between hardware and algorithms, our paper enables an end-to-end pipeline for HDR sampling allowing more flexible hardware implementations. [ABSTRACT FROM AUTHOR]

In this paper, we propose to extend the standard Convolutional Dictionary Learning problem to a tensor representation where the activations are constrained to be “low-rank” through a Canonical Polyadic decomposition. We show that this additional constraint increases the robustness of the CDL with respect to noise and improve the interpretability of the final results. In addition, we discuss in detail the advantages of this representation and introduce two algorithms, based on ADMM or FISTA, that efficiently solve this problem. We show that by exploiting the low rank property of activations, they achieve lower complexity than the main CDL algorithms. Finally, we evaluate our approach on a wide range of experiments, highlighting the modularity and the advantages of this tensorial low-rank formulation. [ABSTRACT FROM AUTHOR]

This paper proposes a low complexity n-dimensional (nD) FastICA algorithm and architecture by introducing the concept of coordinate rotation where n\geq 2. The proposed algorithm can merge the two key steps of conventional FastICA—preprocessing and update and is therefore capable of reducing the hardware complexity of the conventional FastICA significantly as demonstrated in this paper. Hardware implementation can further be simplified due to the recursive nature of the proposed algorithm where the same 2D hardware module can be used as the fundamental core to implement nD architecture. Together with the algorithm formulation, its functionality is also validated and hardware complexity is analyzed and compared with the conventional nD FastICA. [ABSTRACT FROM PUBLISHER]

This paper studies the convergence properties of the well-known message-passing algorithm for convex optimisation. Under the assumption of pairwise separability and scaled diagonal dominance, asymptotic convergence is established and a simple bound for the convergence rate is provided for message-passing. In comparison with previous results, our results do not require the given convex program to have known convex pairwise components and that our bound for the convergence rate is tighter and simpler. When specialised to quadratic optimisation, we generalise known results by providing a very simple bound for the convergence rate. [ABSTRACT FROM AUTHOR]

We consider the problem of minimizing the $\ell _1$ norm of a linear map over the sphere, which arises in various machine learning applications such as orthogonal dictionary learning (ODL) and robust subspace recovery (RSR). The problem is numerically challenging due to its nonsmooth objective and nonconvex constraint, and its algorithmic aspects have not been well explored. In this paper, we show how the manifold structure of the sphere can be exploited to design fast algorithms with provable guarantees for tackling this problem. Specifically, our contribution is fourfold. First, we present a manifold proximal point algorithm (ManPPA) for the problem and show that it converges at a global sublinear rate. Furthermore, we show that ManPPA can achieve a local quadratic convergence rate when applied to sharp instances of the problem. Second, we develop a semismooth Newton-based inexact augmented Lagrangian method for computing the search direction in each iteration of ManPPA and show that it has an asymptotic superlinear convergence rate. Third, we propose a stochastic variant of ManPPA called StManPPA, which is well suited for large-scale computation, and establish its sublinear convergence rate. Both ManPPA and StManPPA have provably faster convergence rates than existing subgradient-type methods. Fourth, using ManPPA as a building block, we propose a new heuristic method for solving a matrix analog of the problem, in which the sphere is replaced by the Stiefel manifold. The results from our extensive numerical experiments on the ODL and RSR problems demonstrate the efficiency and efficacy of our proposed methods. [ABSTRACT FROM AUTHOR]

The paper derives the stability bound of the initial mean-square deviation of an adaptive filtering algorithm based on minimizing the 2Lth moment of the estimation error, with L being an integer greater than 1. The analysis is done for a time-invariant plant with even input probability density function. Dependence of the stability bound on the algorithm step-size, type of the noise distribution, signal-to-noise ratio (SNR), and L is studied. It is shown that the stability bound is decreasing in the step-size. The stability bound decreases as the tail of the noise probability density function becomes lighter for the same steady-state misadjustment. This result is surprising since, for example, it is expected that the stability of the least mean 2Lth algorithm for binary noise distribution is better than that for uniform distribution. The stability bound is proportional to the reciprocal of the SNR, another surprising result. Finally, the stability bound is decreasing in L, which implies a limitation on the ability to improve the performance of the adaptive filter by increasing the order of the cost function. Theoretical results are supported by simulations. [ABSTRACT FROM AUTHOR]

The first moment and second central moments of the portfolio return, a.k.a. mean and variance, have been widely employed to assess the expected profit and risk of the portfolio. Investors pursue higher mean and lower variance when designing the portfolios. The two moments can well describe the distribution of the portfolio return when it follows the Gaussian distribution. However, the real world distribution of assets return is usually asymmetric and heavy-tailed, which is far from being a Gaussian distribution. The asymmetry and the heavy-tailedness are characterized by the third and fourth central moments, i.e., skewness and kurtosis, respectively. Higher skewness and lower kurtosis are preferred to reduce the probability of extreme losses. However, incorporating high-order moments in the portfolio design is very difficult due to their non-convexity and rapidly increasing computational cost with the dimension. In this paper, we propose a very efficient and convergence-provable algorithm framework based on the successive convex approximation (SCA) algorithm to solve high-order portfolios. The efficiency of the proposed algorithm framework is demonstrated by the numerical experiments. [ABSTRACT FROM AUTHOR]

We correct errors in step 6 of Algorithm 1 given in the paper ‘'Sparse-Group Lasso for Graph Learning from Multi-Attribute Data.’' Other parts of the paper including numerical results are unchanged as the algorithm was implemented correctly. [ABSTRACT FROM AUTHOR]

Detecting periodicity in a short sequence is an important problem, with many applications across science and engineering. Several efficient algorithms have been proposed for this over the years. There is a wide choice available today in terms of the tradeoff between algorithmic complexity and estimation accuracy. In spite of such a rich history, one particular aspect of period estimation has received very little attention from a fundamental perspective. Namely, given a discrete time periodic signal and a list of candidate integer periods, what is the absolute minimum datalength required to estimate its integer period? Notice that the answer we seek must be a fundamental bound, i.e., independent of any particular period estimation technique. Common intuition suggests the minimum datalength as twice the largest expected period. However, this is true only under some special contexts. This paper derives the exact necessary and sufficient bounds to this problem. The above-mentioned question is also extended to the case of mixtures of periodic signals. First, a careful mathematical formulation discussing the unique identifiability of the component periods (hidden integer periods) is presented. Once again, a rigorous theoretical framework in this regard is missing in the existing literature but is a necessary platform to derive precise bounds on the minimum necessary datalength. The bounds given here are generic, that is, independent of the algorithms used. Specific algorithm-dependent bounds are also presented in the end for the case of dictionary-based integer period estimation reported in recent years. [ABSTRACT FROM AUTHOR]

In this paper, a novel augmented complex-valued least-mean kurtosis (ACLMK) algorithm is proposed for processing complex-valued signals. The negated kurtosis of the complex-valued error signal is defined as a cost function by using augmented statistics. As a result of the minimization of this cost function, the ACLMK algorithm containing all second-order statistical properties is obtained for processing noncircular complex-valued signals. Moreover, in this paper, convergence and misadjustment conditions of the proposed ACLMK algorithm are derived from the steady-state analysis. The simulation results on complex-valued system identification, prediction, and adaptive noise cancelling problems show that the use of the cost function defined by the negated kurtosis of the complex-valued error signal based on augmented statistics enables the processing of the noncircular complex-valued signals, and significantly improves the performance of the proposed ACLMK algorithm in terms of the mean square deviation, the mean square error, the prediction gain and the convergence rate when compared to other algorithms. [ABSTRACT FROM AUTHOR]

This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain of the optimization variable, which are difficult to project onto; and (b) deterministic or stochastic constraints that admit efficient projection. Problems of this form arise frequently in the context of semidefinite programming as well as when various NP-hard problems are solved approximately via semidefinite relaxation. Since projection onto the first set of constraints is difficult, it becomes necessary to explore projection-free algorithms, such as the stochastic Frank-Wolfe (FW) algorithm. On the other hand, the second set of constraints cannot be handled in the same way, and must be incorporated as an indicator function within the objective function, thereby complicating the application of FW methods. Similar problems have been studied before; however, they suffer from slow convergence rates. This work, equipped with momentum based gradient tracking technique, guarantees fast convergence rates on par with the best-known rates for problems without the second set of constraints. Zeroth-order variants of the proposed algorithms are also developed and again improve upon the state-of-the-art rate results. We further propose the novel trimmed FW variants that enjoy the same convergence rates as their classical counterparts, but are empirically shown to require significantly fewer calls to the linear minimization oracle speeding up the overall algorithm. The efficacy of the proposed algorithms is tested on relevant applications of sparse matrix estimation, clustering via semidefinite relaxation, and uniform sparsest cut problem. [ABSTRACT FROM AUTHOR]

In this paper, we design and analyze Mc2g (Matrix Completion with 2 Graphs), an efficient algorithm that performs matrix completion in the presence of social and item similarity graphs. Mc2g runs in quasilinear time and is parameter free. It is based on spectral clustering and local refinement steps. For the matrix completion problem which possesses additional block structures in its rows and columns, we derive the expected number of sampled entries required for Mc2g to succeed, and further show that it matches an information-theoretic lower bound up to a constant factor for a wide range of parameters. We perform extensive experiments on both synthetic datasets and a semi-real dataset inspired by real graphs. The experimental results show that Mc2g outperforms other state-of-the-art matrix completion algorithms. [ABSTRACT FROM AUTHOR]

This paper studies the 2D localization problem of a sensor network given anchor node positions in a common global coordinate frame and relative position measurements in local coordinate frames between node pairs. It is assumed that the local coordinate frames of different sensors have different orientations and the orientation difference with respect to the global coordinate frame are not known. In terms of graph connectivity, a necessary and sufficient condition is obtained for self-localizability that leads to a fully distributed localization algorithm. Moreover, a distributed verification algorithm is developed to check the graph connectivity condition, which can terminate successfully when the sensor network is self-localizable. Finally, a fully distributed, linear, and iterative algorithm based on the complex-valued Laplacian associated with the sensor network is proposed, which converges globally and gives the correct localization result. [ABSTRACT FROM PUBLISHER]

Bayesian filtering aims at estimating sequentially a hidden process from an observed one. In particular, sequential Monte Carlo (SMC) techniques propagate in time weighted trajectories which represent the posterior probability density function (pdf) of the hidden process given the available observations. On the other hand, conditional Monte Carlo (CMC) is a variance reduction technique which replaces the estimator of a moment of interest by its conditional expectation given another variable. In this paper, we show that up to some adaptations, one can make use of the time recursive nature of SMC algorithms in order to propose natural temporal CMC estimators of some point estimates of the hidden process, which outperform the associated crude Monte Carlo (MC) estimator whatever the number of samples. We next show that our Bayesian CMC estimators can be computed exactly, or approximated efficiently, in some hidden Markov chain (HMC) models; in some jump Markov state-space systems (JMSS); as well as in multitarget filtering. Finally our algorithms are validated via simulations. [ABSTRACT FROM PUBLISHER]

Due to the growth of modern dataset size and the desire to harness computing power of multiple machines, there is a recent surge of interest in the design of distributed machine learning algorithms. However, distributed algorithms are sensitive to Byzantine attackers who can send falsified data to prevent the convergence of algorithms or lead the algorithms to converge to value of the attackers’ choice. Some recent work proposed interesting algorithms that can deal with the scenario when up to half of the workers are compromised. In this paper, we propose a novel algorithm that can deal with an arbitrary number of Byzantine attackers. The main idea is to ask the parameter server to randomly select a small clean dataset and compute noisy gradient using this small dataset. This noisy gradient will then be used as a ground truth to filter out information sent by compromised workers. We show that the proposed algorithm converges to the neighborhood of the population minimizer regardless the number of Byzantine attackers. We further provide numerical examples to show that the proposed algorithm can benefit from the presence of good workers and achieve better performance than existing algorithms. [ABSTRACT FROM AUTHOR]

The affine rank minimization (ARM) problem arises in many real-world applications. The goal is to recover a low-rank matrix from a small amount of noisy affine measurements. The original problem is NP-hard, and so directly solving the problem is computationally prohibitive. Approximate low-complexity solutions for ARM have recently attracted much research interest. In this paper, we design an iterative algorithm for ARM based on message passing principles. The proposed algorithm is termed turbo-type ARM (TARM), as inspired by the recently developed turbo compressed sensing algorithm for sparse signal recovery. We show that, for right-orthogonally invariant linear (ROIL) operators, a scalar function called state evolution can be established to accurately predict the behaviour of the TARM algorithm. We also show that TARM converges faster than the counterpart algorithms when ROIL operators are used for low-rank matrix recovery. We further extend the TARM algorithm for matrix completion, where the measurement operator corresponds to a random selection matrix. Slight improvement of the matrix completion performance has been demonstrated for the TARM algorithm over the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper we present a generic framework for the asymptotic performance analysis of subspace-based parameter estimation schemes. It is based on earlier results on an explicit first-order expansion of the estimation error in the signal subspace obtained via an SVD of the noisy observation matrix. We extend these results in a number of aspects. Firstly, we demonstrate that an explicit first-order expansion of the Higher-Order SVD (HOSVD)-based subspace estimate can be derived. Secondly, we show how to obtain explicit first-order expansions of the estimation error of arbitrary ESPRIT-type algorithms and provide the expressions for R-D Standard ESPRIT, R-D Unitary ESPRIT, R-D Standard Tensor-ESPRIT, as well as R-D Unitary Tensor-ESPRIT. Thirdly, we derive closed-form expressions for the mean square error (MSE) and show that they only depend on the second-order moments of the noise. Hence, to apply this framework we only need the noise to be zero mean and possess finite second order moments. Additional assumptions such as Gaussianity or circular symmetry are not needed. [ABSTRACT FROM PUBLISHER]

This paper considers a method for improving physical layer security of wireless networks with full-duplex radio. In particular, fast algorithms are developed to compute power allocations in subcarriers, subject to power and rate constraints, to maximize the secrecy capacity of a three-node network consisting of a source, a full-duplex destination, and an eavesdropper. A residual level of radio self-interference channel is considered. The optimal power allocation at the destination is found to be significant especially when its power budget is high. Also studied in this paper are a network with multiple full-duplex destinations and another network with multiple sources. Using the algorithms developed in this paper, we are able to show that a multiuser strategy that optimizes the power distributions among the users (in terms of either the sources or the destinations) can yield a substantial gain of secrecy capacity over a single-user strategy. [ABSTRACT FROM PUBLISHER]

The use of a large-scale antenna array (LSAA) has become an important characteristic of multi-antenna communication systems to achieve beamforming gains such as in designing millimeter-wave (mmWave) systems to combat severe propagation losses. In such applications, each antenna element has to be driven by a radio frequency (RF) chain for the implementation of fully-digital beamformers, significantly increasing the hardware cost, complexity, and power consumption. Therefore, constant-modulus analog beamforming (CMAB) becomes a viable solution. In this paper, we consider the scaled analog beamforming (SAB) or constant-modulus analog beamforming (CMAB) architecture and design the system parameters by solving two variants of beampattern matching problem. In the first case, both the magnitude and phase of the beampattern are matched to the given desired beampattern whereas in the second case, only the magnitude of the beampattern is matched. Both the beampattern matching problems are cast as a variant of the constant-modulus least-squares (CLS) problem. We provide efficient algorithms based on the alternating majorization-minimization (AMM) framework that combines the alternating minimization and the MM frameworks and the conventional-cyclic coordinate descent (C-CCD) algorithms to solve the problem in each case. We also propose algorithms based on a new modified-CCD (M-CCD) based approach. For all the developed algorithms we prove convergence to a Karush-Kuhn-Tucker (KKT) point (or a stationary point). Numerical results demonstrate that the proposed algorithms converge faster than the state-of-the-art solutions. Among all the algorithms, the M-CCD-based algorithms have faster convergence when evaluated in terms of the number of iterations and the AMM-based algorithms offer lower complexity. [ABSTRACT FROM AUTHOR]

In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central machine is then responsible for learning the structure based on received messages from the other nodes. We present a set of communication-efficient strategies, which are theoretically proved to convey sufficient information for reliable learning of the structure. In particular, our analyses show that even if each machine sends only the signs of its local data samples to the central node, the tree structure can still be recovered with high accuracy. Our simulation results on both synthetic and real-world datasets show that our strategies achieve a desired accuracy in inferring the underlying structure while spending a small budget on communication. [ABSTRACT FROM AUTHOR]

Channel state information (CSI) at the base station (BS) is crucial to achieve beamforming and multiplexing gains in multiple-input multiple-output (MIMO) systems. State-of-the-art limited feedback schemes require feedback overhead that scales linearly with the number of BS antennas, which is prohibitive for 5G massive MIMO. This paper proposes novel limited feedback algorithms that lift this burden by exploiting the inherent sparsity in double-directional MIMO channel representation using overcomplete dictionaries. These dictionaries are associated with angle of arrival and angle of departure that specifically account for antenna directivity patterns at both ends of the link. The proposed algorithms achieve satisfactory channel estimation accuracy using a small number of feedback bits, even when the number of transmit antennas at the BS is large—making them ideal for 5G massive MIMO. Judicious simulations reveal that they outperform a number of popular feedback schemes and underscore the importance of using angle dictionaries matching the given antenna directivity patterns, as opposed to uniform dictionaries. The proposed algorithms are lightweight in terms of computation, especially on the user equipment side, making them ideal for actual deployment in 5G systems. [ABSTRACT FROM AUTHOR]

This paper studies the stochastic behavior of the LMS and NLMS algorithms in a system identification framework for a cyclostationary white input without assuming a Gaussian distribution for the input. The input cyclostationary signal is modeled by a white random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation behavior of the adaptive weights as a function of the input cyclostationarity. Analytical models are first derived for the LMS and NLMS algorithms for cyclostationary white inputs. These models show the dependence of the two algorithms upon the kurtosis of the input. Significant differences are found between the behaviors of the two algorithms when the analysis is applied to non-Gaussian cases. Monte Carlo simulations provide strong support for the theory. [ABSTRACT FROM AUTHOR]

In this paper, we consider the case in which one needs to carry out Gabor analysis and synthesis on large signals using a short support analysis window and its corresponding, possibly longer canonical dual window, respectively. In this asymmetric context, we propose a novel factorization of the Gabor frame operator that exploits its strong and well-known structure and leads to a computational cost for synthesis, which is comparable to the one needed for short support analysis. The proposed factorization applies to any Gabor system with very mild conditions and leads to a potentially promising alternative to current synthesis algorithms in the case of short analysis windows whose support is slightly above the number of frequency channels. [ABSTRACT FROM AUTHOR]

Source localization and spectral estimation are among the most fundamental problems in statistical and array signal processing. Methods that rely on the orthogonality of the signal and noise subspaces, such as Pisarenko's method, MUSIC, and root-MUSIC, are some of the most widely used algorithms to solve these problems. As a common feature, these methods require both a priori knowledge of the number of sources and an estimate of the noise subspace. Both requirements are complicating factors to the practical implementation of the algorithms and, when not satisfied exactly, can potentially lead to severe errors. In this paper, we propose a new localization criterion based on the algebraic structure of the noise subspace that is described for the first time to the best of our knowledge. Using this criterion and the relationship between the source localization problem and the problem of computing the greatest common divisor (GCD), or more practically approximate GCD, for polynomials, we propose two algorithms, which adaptively learn the number of sources and estimate their locations. Simulation results show a significant improvement over root-MUSIC in challenging scenarios such as closely located sources, both in terms of detection of the number of sources and their localization over a broad and practical range of signal-to-noise ratios. Furthermore, no performance sacrifice in simple scenarios is observed. [ABSTRACT FROM AUTHOR]

While many distributed optimization algorithms have been proposed for solving smooth or convex problems over the networks, few of them can handle non-convex and non-smooth problems. Based on a proximal primal-dual approach, this paper presents a new (stochastic) distributed algorithm with Nesterov momentum for accelerated optimization of non-convex and non-smooth problems. Theoretically, we show that the proposed algorithm can achieve an $\epsilon$ -stationary solution under a constant step size with $\mathcal {O}(1/\epsilon ^2)$ computation complexity and $\mathcal {O}(1/\epsilon)$ communication complexity when the epigraph of the non-smooth term is a polyhedral set. When compared to the existing gradient tracking based methods, the proposed algorithm has the same order of computation complexity but lower order of communication complexity. To the best of our knowledge, the presented result is the first stochastic algorithm with the $\mathcal {O}(1/\epsilon)$ communication complexity for non-convex and non-smooth problems. Numerical experiments for a distributed non-convex regression problem and a deep neural network based classification problem are presented to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel adaptive importance sampling (AIS) algorithm for probabilistic inference. The sampler learns a proposal distribution adaptation strategy by framing AIS as a reinforcement learning problem. Under this structure, the proposal distribution of the sampler is treated as an agent whose state is controlled using a parameterized policy. At each iteration of the algorithm, the agent earns a reward that is related to its contribution to the variance of the AIS estimator of the normalization constant of the target distribution. Policy gradient methods are employed to learn a locally optimal policy that maximizes the expected value of the sum of all rewards. Numerical simulations on two different examples demonstrate promising results for the future application of the proposed method to complex Bayesian models. [ABSTRACT FROM AUTHOR]

In this paper, we consider the policy evaluation problem in reinforcement learning with agents on a decentralized and directed network. In order to evaluate the quality of a fixed policy in this decentralized setting, one option is for agents to run decentralized temporal-difference (TD) collaboratively. To account for the practical scenarios where the state and action spaces are large and malicious attacks emerge, we focus on the decentralized TD learning with linear function approximation in the presence of malicious agents (often termed as Byzantine agents). We propose a trimmed mean-based Byzantine-resilient decentralized TD algorithm to perform policy evaluation in this setting. We establish the finite-time convergence rate, as well as the asymptotic learning error that depends on the number of Byzantine agents. Numerical experiments corroborate the robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents algorithms for the parallelization of inference in hidden Markov models (HMMs). In particular, we propose a parallel forward-backward type of filtering and smoothing algorithm as well as a parallel Viterbi-type maximum-a-posteriori (MAP) algorithm. We define associative elements and operators to pose these inference problems as all-prefix-sums computations and parallelize them using the parallel-scan algorithm. The advantage of the proposed algorithms is that they are computationally efficient in HMM inference problems with long time horizons. We empirically compare the performance of the proposed methods to classical methods on a highly parallel graphics processing unit (GPU). [ABSTRACT FROM AUTHOR]

In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as matrix-factorization problem arising in relay communication among others. Assuming statistically independent matrix entries with known priors, the new algorithm called ML-BiGAMP could approximate the general sum-product loopy belief propagation (LBP) in the high-dimensional limit enjoying a substantial reduction in computational complexity. We demonstrate that, in large system limit, the asymptotic MSE performance of ML-BiGAMP could be fully characterized via a set of simple one-dimensional equations termed state evolution (SE). We establish that the asymptotic MSE predicted by ML-BiGAMP’ SE matches perfectly the exact MMSE predicted by the replica method, which is well-known to be Bayes-optimal but infeasible in practice. This consistency indicates that the ML-BiGAMP may still retain the same Bayes-optimal performance as the MMSE estimator in high-dimensional applications, although ML-BiGAMP's computational burden is far lower. As an illustrative example of the general ML-BiGAMP, we provide a detector design that could estimate the channel fading and the data symbols jointly with high precision for the two-hop amplify-and-forward relay communication systems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate designs of linear precoders for vector Gaussian channels via stochastic optimizations and deep neural networks (DNNs). We assume that the channel inputs are drawn from practical finite alphabets, and we search for precoders maximizing the mutual information between channel inputs and outputs. Though the problem is generally non-convex, we prove that when the right singular matrix of precoder is fixed, any local optima of this problem is a global optima. Based on this fact, an efficient projected stochastic gradient descent (PSGD) algorithm is designed to search the optimal precoders. Moreover, to reduce the complexity of calculating a posterior means involved in gradients calculation, K-best algorithm is adopted to make approximations of a posterior means with negligible loss of accuracy. Furthermore, to avoid explicit calculation of mutual information and its gradients, DNN-based autoencoders (AEs) are constructed for this precoding task, and an efficient training algorithm is proposed. We also prove that the AEs, with ‘softmax’ activation function and ‘categorical cross entropy’ loss, maximize the mutual information under reasonable assumptions. Then, in order to extend the AE methods to large scale systems, ‘sigmoid’ activation function and ‘binary cross entropy’ loss are used such that the size of AEs will not grow prohibitively large. We prove that this maximizes a lower bound of the mutual information under reasonable assumptions. Finally, to make the precoders practical for high speed wireless scenarios, we propose an offline training paradigm which trains DNNs to infer optimal precoders given channel state information instead of training online for every different channel. Simulation results show that all the proposed methods work well in maximizing mutual information and improving bit error rate (BER) performance. [ABSTRACT FROM AUTHOR]

Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these approaches can be viewed within the mathematical context of functional composition. This paper re-interprets and generalizes within the functional composition framework one such approach known as filter sharpening, i.e., interconnecting filter modules which have significant approximation error in order to obtain improved filter characteristics. More specifically, filter sharpening is approached by determining the composing polynomial to minimize the infinity-norm of the approximation error, utilizing the First Algorithm of Remez. This is applied both to sharpening for FIR, even-symmetric filters and for the more general case of subfilters that have complex-valued frequency responses including causal IIR filters and for continuous-time filters. Within the framework of functional composition, this paper also explores the use of functional decomposition to approximate a desired system as a composition of simpler functions based on a two-norm on the approximation error. Among the potential advantages of this decomposition is the ability for modular implementation in which the inner component of the functional decomposition represents the subfilters and the outer the interconnection. [ABSTRACT FROM AUTHOR]

Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. This paper revisits the problem of data-driven learning of these geometric structures and puts forth two new nonlinear geometric models for data describing “related” objects/phenomena. The first one of these models straddles the two extremes of the subspace model and the union-of-subspaces model, and is termed the metric-constrained union-of-subspaces (MC-UoS) model. The second one of these models—suited for data drawn from a mixture of nonlinear manifolds—generalizes the kernel subspace model, and is termed the metric-constrained kernel union-of-subspaces (MC-KUoS) model. The main contributions of this paper in this regard include the following. First, it motivates and formalizes the problems of MC-UoS and MC-KUoS learning. Second, it presents algorithms that efficiently learn an MC-UoS or an MC-KUoS underlying data of interest. Third, it extends these algorithms to the case when parts of the data are missing. Last, but not least, it reports the outcomes of a series of numerical experiments involving both synthetic and real data that demonstrate the superiority of the proposed geometric models and learning algorithms over existing approaches in the literature. These experiments also help clarify the connections between this work and the literature on (subspace and kernel k-means) clustering. [ABSTRACT FROM AUTHOR]

In Part I of the study of the tensor deflation for CANDECOMP/PARAFAC, we have shown that the rank-1 tensor deflation is applicable under some conditions. Part II of the study presents several initialization algorithms suitable for the algorithm proposed in Part I. In addition, Part II contains an algorithm for the case when one or more factor matrices in the estimated model is constrained to be orthogonal. Finally, Part II provides an error analysis of the tensor deflation algorithm, which shows that there is a marginal loss of accuracy of the deflation algorithm compared to the ordinary CP decomposition. [ABSTRACT FROM PUBLISHER]

The success of compressed sensing relies essentially on the ability to efficiently find an approximately sparse solution to an under-determined linear system. In this paper, we developed an efficient algorithm for the sparsity promoting \ell^1-regularized least squares problem by coupling the primal dual active set strategy with a continuation technique (on the regularization parameter). In the active set strategy, we first determine the active set from primal and dual variables, and then update the primal and dual variables by solving a low-dimensional least square problem on the active set, which makes the algorithm very efficient. The continuation technique globalizes the convergence of the algorithm, with provable global convergence under restricted isometry property (RIP). Further, we adopt two alternative methods, i.e., a modified discrepancy principle and a Bayesian information criterion, to choose the regularization parameter automatically. Numerical experiments indicate that our algorithm is very competitive with state-of-the-art algorithms in terms of accuracy and efficiency, without a priori information about the regularization parameter. [ABSTRACT FROM AUTHOR]

Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filter that accounts for the spatio-temporal variations, and offers efficient online reconstruction, even for dynamically evolving network topologies. The kernel-based learning framework bypasses the need for statistical information by capitalizing on the smoothness that graph signals exhibit with respect to the underlying graph. To address the challenge of selecting the appropriate kernel, the proposed filter is combined with a multikernel selection module. Such a data-driven method selects a kernel attuned to the signal dynamics on-the-fly within the linear span of a preselected dictionary. The novel multikernel learning algorithm exploits the eigenstructure of Laplacian kernel matrices to reduce computational complexity. Numerical tests with synthetic and real data demonstrate the superior reconstruction performance of the novel approach relative to state-of-the-art alternatives. [ABSTRACT FROM AUTHOR]

The demand for accurate localization in complex environments continues to increase despite the difficulty in extracting positional information from measurements. Conventional range-based localization approaches rely on distance estimates obtained from measurements (e.g., delay or strength of received waveforms). This paper goes one step further and develops localization techniques that rely on all probable range values rather than on a single estimate of each distance. In particular, the concept of soft range information (SRI) is introduced, showing its essential role for network localization. We then establish a general framework for SRI-based localization and develop algorithms for obtaining the SRI using machine learning techniques. The performance of the proposed approach is quantified via network experimentation in indoor environments. The results show that SRI-based localization techniques can achieve performance approaching the Cramér–Rao lower bound and significantly outperform the conventional techniques especially in harsh wireless environments. [ABSTRACT FROM AUTHOR]

This paper considers the mean-reverting portfolio (MRP) design problem arising from statistical arbitrage (a.k.a. pairs trading) in the financial markets. It aims at designing a portfolio of underlying assets by optimizing the mean reversion strength of the portfolio, while taking into consideration the portfolio variance and an investment budget constraint. Several specific design problems are considered based on different mean reversion criteria. Efficient algorithms are proposed to solve the problems. Numerical results on both synthetic and market data show that the proposed MRP design methods can generate consistent profits and outperform the traditional design methods and the benchmark methods in the literature. [ABSTRACT FROM AUTHOR]

This paper develops a novel algorithm, termed SPARse Truncated Amplitude flow (SPARTA), to reconstruct a sparse signal from a small number of magnitude-only measurements. It deals with what is also known as sparse phase retrieval (PR), which is NP-hard in general and emerges in many science and engineering applications. Upon formulating sparse PR as an amplitude-based nonconvex optimization task, SPARTA works iteratively in two stages: In stage one, the support of the underlying sparse signal is recovered using an analytically well-justified rule, and subsequently a sparse orthogonality-promoting initialization is obtained via power iterations restricted on the support; and in the second stage, the initialization is successively refined by means of hard thresholding based gradient-type iterations. SPARTA is a simple yet effective, scalable, and fast sparse PR solver. On the theoretical side, for any n-dimensional k-sparse (k ≪ n) signal x with minimum (in modulus) nonzero entries on the order of (1/√k)||x||2, SPARTA recovers the signal exactly (up to a global unimodular constant) from about k2 log n random Gaussian measurements with high probability. Furthermore, SPARTA incurs computational complexity on the order of k2 n log n with total runtime proportional to the time required to read the data, which improves upon the state of the art by at least a factor of k. Finally, SPARTA is robust against additive noise of bounded support. Extensive numerical tests corroborate markedly improved recovery performance and speedups of SPARTA relative to existing alternatives. [ABSTRACT FROM AUTHOR]

In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into expectation-maximization-based sparse Bayesian learning (SBL). In particular, GGAMP is used to implement the E-step in SBL in place of matrix inversion, leveraging the fact that GGAMP is guaranteed to converge with appropriate damping. The resulting GGAMP-SBL algorithm is much more robust to arbitrary measurement matrix A than the standard damped GAMP algorithm while being much lower complexity than the standard SBL algorithm. We then extend the approach from the single measurement vector case to the temporally correlated multiple measurement vector case, leading to the GGAMP-TSBL algorithm. We verify the robustness and computational advantages of the proposed algorithms through numerical experiments. [ABSTRACT FROM AUTHOR]

This paper considers coordinated multicast beamforming in a multicell multigroup multiple-input single-output system. Each base station (BS) serves multiple groups of users by forming a single beam with common information per group. We propose centralized and distributed beamforming algorithms for two different optimization targets. The first objective is to minimize the total transmission power of all the BSs while guaranteeing the user-specific minimum quality-of-service targets. The semidefinite relaxation (SDR) method is used to approximate the nonconvex multicast problem as a semidefinite program (SDP), which is solvable via centralized processing. Subsequently, two alternative distributed methods are proposed. The first approach turns the SDP into a two-level optimization via primal decomposition. At the higher level, intercell interference powers are optimized for fixed beamformers, whereas the lower level locally optimizes the beamformers by minimizing BS-specific transmit powers for the given intercell interference constraints. The second distributed solution is enabled via an alternating direction method of multipliers, where the intercell interference optimization is divided into a local and a global optimization by forcing the equality via consistency constraints. We further propose a centralized and a simple distributed beamforming design for the signal-to-interference-plus-noise ratio (SINR) balancing problem in which the minimum SINR among the users is maximized with given per-BS power constraints. This problem is solved via the bisection method as a series of SDP feasibility problems. The simulation results show the superiority of the proposed coordinated beamforming algorithms over traditional noncoordinated transmission schemes, and illustrate the fast convergence of the distributed methods. [ABSTRACT FROM PUBLISHER]

This paper considers unimodular sequence synthesis under similarity constraint for both the continuous and discrete phase cases. A computationally efficient iterative algorithm for the continuous phase case (IA-CPC) is proposed to sequentially optimize the quadratic objective function. The quadratic optimization problem is turned into multiple one-dimensional optimization problems with closed-form solutions. For the discrete phase case, we present an iterative block optimization algorithm. Specifically, we partition the design variables into $K$ blocks, and then, we sequentially optimize each block via exhaustive search while fixing the remaining $K-1$ blocks. Finally, we evaluate the computational costs and performance gains of the proposed algorithms in comparison with power method-like and semidefinite relaxation related techniques. [ABSTRACT FROM PUBLISHER]

In this paper, a recursive sliding transform (RST) algorithm is proposed for the fast implementation of the Walsh Hadamard Transform (WHT) on sliding windows. The proposed RST algorithm accelerates the sliding WHT process by recursively reducing the order of WHT. Theoretical analysis shows that the proposed RST algorithm requires only 1.33 additions per sample for each WHT basis vector regardless of the size or dimension of the basis vector. The computational requirement of the proposed RST algorithm is the lowest among existing fast sliding WHT algorithms. [ABSTRACT FROM PUBLISHER]

Node self-localization is a key research topic for wireless sensor networks (WSNs). There are two main algorithms, the triangulation method and the maximum likelihood (ML) estimator, for angle of arrival (AOA) based self-localization. The ML estimator requires a good initialization close to the true location to avoid divergence, while the triangulation method cannot obtain the closed-form solution with high efficiency. In this paper, we develop a set of efficient closed-form AOA based self-localization algorithms using auxiliary variables based methods. First, we formulate the self-localization problem as a linear least squares problem using auxiliary variables. Based on its closed-form solution, a new auxiliary variables based pseudo-linear estimator (AVPLE) is developed. By analyzing its estimation error, we present a bias compensated AVPLE (BCAVPLE) to reduce the estimation error. Then we develop a novel BCAVPLE based weighted instrumental variable (BCAVPLE-WIV) estimator to achieve asymptotically unbiased estimation of locations and orientations of unknown nodes based on prior knowledge of the AOA noise variance. In the case that the AOA noise variance is unknown, a new AVPLE based WIV (AVPLE-WIV) estimator is developed to localize the unknown nodes. Also, we develop an autonomous coordinate rotation (ACR) method to overcome the tangent instability of the proposed algorithms when the orientation of the unknown node is near \pi/2. We also derive the Cramér-Rao lower bound (CRLB) of the ML estimator. Extensive simulations demonstrate that the new algorithms achieve much higher localization accuracy than the triangulation method and avoid local minima and divergence in iterative ML estimators. [ABSTRACT FROM PUBLISHER]

The linearization of nonlinear systems is an important digital enhancement technique. In this paper, a real-time capable post- and pre-linearization method for the widely applicable time-varying discrete-time Volterra series is presented. To this end, an alternative view on the Volterra series is established, which enables the utilization of certain modified linear iterative methods for linearization. For one particular linear iterative method, the Richardson iteration, the corresponding post- and pre-linearizers are discussed in detail. It is motivated that the resulting algorithm can be regarded as a generalization of some existing methods. Furthermore, a simply verifiable condition for convergence is presented, which allows the straightforward evaluation of applicability. The proposed method is demonstrated by means of the linearization of a time-varying nonlinear amplifier, which highlights its capability of linearizing significantly distorted signals, illustrates the advantageous convergence behavior, and depicts its robustness against modeling errors. [ABSTRACT FROM PUBLISHER]

In this paper we consider maximum-likelihood (ML) MIMO detection under one-bit quantized observations and binary symbol constellations. This problem is motivated by the recent interest in adopting coarse quantization in massive MIMO systems—as an effective way to scale down the hardware complexity and energy consumption. Classical MIMO detection techniques consider unquantized observations, and many of them are not applicable to the one-bit MIMO case. We develop a new non-convex optimization algorithm for the one-bit ML MIMO detection problem, using a strategy called homotopy optimization. The idea is to transform the ML problem into a sequence of approximate problems, from easy (convex) to hard (close to ML), and with each problem being a gradual modification of its previous. Then, our attempt is to iteratively trace the solution path of these approximate problems. This homotopy algorithm is well suited to the application of deep unfolding, a recently popular approach for turning certain model-based algorithms into data-driven, and performance enhanced, ones. While our initial focus is on one-bit MIMO detection, the proposed technique also applies naturally to the classical unquantized MIMO detection. We performed extensive simulations and show that the proposed homotopy algorithms, both non-deep and deep, have satisfactory bit-error probability performance compared to many state-of-the-art algorithms. Also, the deep homotopy algorithm has attractively low computational complexity. [ABSTRACT FROM AUTHOR]

The emergence of big data has caused a dramatic shift in the operating regime for optimization algorithms. The performance bottleneck, which used to be computations, is now often communications. Several gradient compression techniques have been proposed to reduce the communication load at the price of a loss in solution accuracy. Recently, it has been shown how compression errors can be compensated for in the optimization algorithm to improve the solution accuracy. Even though convergence guarantees for error-compensated algorithms have been established, there is very limited theoretical support for quantifying the observed improvements in solution accuracy. In this paper, we show that Hessian-aided error compensation, unlike other existing schemes, avoids accumulation of compression errors on quadratic problems. We also present strong convergence guarantees of Hessian-based error compensation for stochastic gradient descent. Our numerical experiments highlight the benefits of Hessian-based error compensation, and demonstrate that similar convergence improvements are attained when only a diagonal Hessian approximation is used. [ABSTRACT FROM AUTHOR]