Sparse Multivariate Factor Regression

We consider the problem of multivariate regression in a setting where the relevant predictors could be shared among different responses. We propose an algorithm which decomposes the coefficient matrix into the product of a long matrix and a wide matrix, with an elastic net penalty on the former and an $\ell_1$ penalty on the latter. The first matrix linearly transforms the predictors to a set of latent factors, and the second one regresses the responses on these factors. Our algorithm simultaneously performs dimension reduction and coefficient estimation and automatically estimates the number of latent factors from the data. Our formulation results in a non-convex optimization problem, which despite its flexibility to impose effective low-dimensional structure, is difficult, or even impossible, to solve exactly in a reasonable time. We specify an optimization algorithm based on alternating minimization with three different sets of updates to solve this non-convex problem and provide theoretical results on its convergence and optimality. Finally, we demonstrate the effectiveness of our algorithm via experiments on simulated and real data

Analysis of error propagation in particle filters with approximation

This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling the particles or by generating a parametric approximation. For such algorithms, we derive time-uniform bounds on the weak-sense $L_p$ error and present associated exponential inequalities. We motivate the theoretical analysis by considering the leader node particle filter and present numerical experiments exploring its performance and the relationship to the error bounds.Comment: Published in at http://dx.doi.org/10.1214/11-AAP760 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Large scale probabilistic available bandwidth estimation

The common utilization-based definition of available bandwidth and many of the existing tools to estimate it suffer from several important weaknesses: i) most tools report a point estimate of average available bandwidth over a measurement interval and do not provide a confidence interval; ii) the commonly adopted models used to relate the available bandwidth metric to the measured data are invalid in almost all practical scenarios; iii) existing tools do not scale well and are not suited to the task of multi-path estimation in large-scale networks; iv) almost all tools use ad-hoc techniques to address measurement noise; and v) tools do not provide enough flexibility in terms of accuracy, overhead, latency and reliability to adapt to the requirements of various applications. In this paper we propose a new definition for available bandwidth and a novel framework that addresses these issues. We define probabilistic available bandwidth (PAB) as the largest input rate at which we can send a traffic flow along a path while achieving, with specified probability, an output rate that is almost as large as the input rate. PAB is expressed directly in terms of the measurable output rate and includes adjustable parameters that allow the user to adapt to different application requirements. Our probabilistic framework to estimate network-wide probabilistic available bandwidth is based on packet trains, Bayesian inference, factor graphs and active sampling. We deploy our tool on the PlanetLab network and our results show that we can obtain accurate estimates with a much smaller measurement overhead compared to existing approaches.Comment: Submitted to Computer Network

Multi-path Probabilistic Available Bandwidth Estimation through Bayesian Active Learning

Knowing the largest rate at which data can be sent on an end-to-end path such that the egress rate is equal to the ingress rate with high probability can be very practical when choosing transmission rates in video streaming or selecting peers in peer-to-peer applications. We introduce probabilistic available bandwidth, which is defined in terms of ingress rates and egress rates of traffic on a path, rather than in terms of capacity and utilization of the constituent links of the path like the standard available bandwidth metric. In this paper, we describe a distributed algorithm, based on a probabilistic graphical model and Bayesian active learning, for simultaneously estimating the probabilistic available bandwidth of multiple paths through a network. Our procedure exploits the fact that each packet train provides information not only about the path it traverses, but also about any path that shares a link with the monitored path. Simulations and PlanetLab experiments indicate that this process can dramatically reduce the number of probes required to generate accurate estimates