More Like this

1. Traffic Rate Network Tomography via Moment Generating Function Matching

   Ephraim, Yariv; Coblenz, Joshua; Mark, Brian L.; Lev-Ari, Hanoch (March 2022, Conference on Information Sciences and Systems)

   Network tomography aims at estimating source-destination traffic rates from link traffic measurements. This inverse problem was formulated by Vardi in 1996 for independent Poisson traffic over networks operating under deterministic as well as random routing regimes. Vardi used a second-order moment matching approach to estimate the rates where a solution for the resulting linear matrix equation was obtained using an iterative minimum I-divergence procedure. Vardi’s second-order moment matching approach was recently extended to higher order cumulant matching approach with the goal of improving the rank of the system of linear equations. In this paper we go one step further and develop a moment generating function matching approach for rate estimation, and seek a least squares as well as an iterative minimum I-divergence solution of the resulting linear equations. We also specialize this approach to a characteristic function matching approach which exhibits some advantages. These follow from the fact that the characteristic function matching approach results in fewer conflicting equations involving the empirical estimates. We demonstrate that the new approach outperforms the cumulant matching approach while being conceptually simpler. 

   more » « less
2. Mixed Poisson traffic rate network tomography

   Ephraim, Yariv; Coblenz, Joshua; Mark, Brian L.; Lev-Ari, Hanoch (March 2021, 55rd Annual Conference on Information Sciences and Systems (CISS 2021))

   null (Ed.)

   We extend network tomography to traffic flows that are not necessarily Poisson random processes. This assumption has governed the field since its inception in 1996 by Y. Vardi. We allow the distribution of the packet count of each traffic flow in a given time interval to be a mixture of Poisson random variables. Both discrete as well as continuous mixtures are studied. For the latter case, we focus on mixed Poisson distributions with Gamma mixing distribution. As is well known, this mixed Poisson distribution is the negative binomial distribution. Other mixing distributions, such as Wald or the inverse Gaussian distribution can be used. Mixture distributions are overdispersed with variance larger than the mean. Thus, they are more suitable for Internet traffic than the Poisson model. We develop a second-order moment matching approach for estimating the mean traffic rate for each source-destination pair using least squares and the minimum I-divergence iterative procedure. We demonstrate the performance of the proposed approach by several numerical examples. The results show that the averaged normalized mean squared error in rate estimation is of the same order as in the classic Poisson based network tomography. Furthermore, no degradation in performance was observed when traffic rates are Poisson but Poisson mixtures are assumed. 

   more » « less
3. Bayesian Iterative Channel Estimation and Turbo Equalization for Multiple-Input–Multiple-Output Underwater Acoustic Communications

   https://doi.org/10.1109/JOE.2019.2956299  

   Qin, Xiangzhao; Qu, Fengzhong; Zheng, Yahong Rosa (July 2020, IEEE Journal of Oceanic Engineering)

   This article investigates a robust receiver scheme for a single carrier, multiple-input–multiple-output (MIMO) underwater acoustic (UWA) communications, which uses the sparse Bayesian learning algorithm for iterative channel estimation embedded in Turbo equalization (TEQ). We derive a block-wise sparse Bayesian learning framework modeling the spatial correlation of the MIMO UWA channels, where a more robust expectation–maximization algorithm is proposed for updating the joint estimates of channel impulse response, residual noise, and channel covariance matrix. By exploiting the spatially correlated sparsity of MIMO UWA channels and the second-order a priori channel statistics from the training sequence, the proposed Bayesian channel estimator enjoys not only relatively low complexity but also more stable control of the hyperparameters that determine the channel sparsity and recovery accuracy. Moreover, this article proposes a low complexity space-time soft decision feedback equalizer (ST-SDFE) with successive soft interference cancellation. Evaluated by the undersea 2008 Surface Processes and Acoustic Communications Experiment, the improved sparse Bayesian learning channel estimation algorithm outperforms the conventional Bayesian algorithms in terms of the robustness and complexity, while enjoying better estimation accuracy than the orthogonal matching pursuit and the improved proportionate normalized least mean squares algorithms. We have also verified that the proposed ST-SDFE TEQ significantly outperforms the low-complexity minimum mean square error TEQ in terms of the bit error rate and error propagation. 

   more » « less
4. On Suboptimality of Least Squares with Application to Estimation of Convex Bodies

   Kur, Gil; Rakhlin, Alexander; Guntuboyina, Adityanand (October 2020, Proceedings of Thirty Third Conference on Learning Theory, PMLR)

   Abernethy, Jacob; Agarwal, Shivani (Ed.)

   We develop a technique for establishing lower bounds on the sample complexity of Least Squares (or, Empirical Risk Minimization) for large classes of functions. As an application, we settle an open problem regarding optimality of Least Squares in estimating a convex set from noisy support function measurements in dimension d \geq 6. Specifically, we establish that Least Squares is mimi- max sub-optimal, and achieves a rate of n^{-2/(d-1)} whereas the minimax rate is n^{-4/(d+3)}. 

   more » « less
5. A sequential estimation problem with control and discretionary stopping

   https://doi.org/10.3934/puqr.2022011  

   Ekström, Erik; Karatzas, Ioannis (January 2022, Probability, Uncertainty and Quantitative Risk)

   We show that “full-bang” control is optimal in a problem which combines features of (i) sequential least-squares estimation with Bayesian updating, for a random quantity observed in a bath of white noise; (ii) bounded control of the rate at which observations are received, with a superquadratic cost per unit time; and (iii) “fast” discretionary stopping. We develop also the optimal filtering and stopping rules in this context. 

   more » « less