The Statistical Performance of Collaborative Inference

The statistical analysis of massive and complex data sets will require the development of algorithms that depend on distributed computing and collaborative inference. Inspired by this, we propose a collaborative framework that aims to estimate the unknown mean $\theta$ of a random variable $X$. In the model we present, a certain number of calculation units, distributed across a communication network represented by a graph, participate in the estimation of $\theta$ by sequentially receiving independent data from $X$ while exchanging messages via a stochastic matrix $A$ defined over the graph. We give precise conditions on the matrix $A$ under which the statistical precision of the individual units is comparable to that of a (gold standard) virtual centralized estimate, even though each unit does not have access to all of the data. We show in particular the fundamental role played by both the non-trivial eigenvalues of $A$ and the Ramanujan class of expander graphs, which provide remarkable performance for moderate algorithmic cost

Computational Complexity versus Statistical Performance on Sparse Recovery Problems

We show that several classical quantities controlling compressed sensing performance directly match classical parameters controlling algorithmic complexity. We first describe linearly convergent restart schemes on first-order methods solving a broad range of compressed sensing problems, where sharpness at the optimum controls convergence speed. We show that for sparse recovery problems, this sharpness can be written as a condition number, given by the ratio between true signal sparsity and the largest signal size that can be recovered by the observation matrix. In a similar vein, Renegar's condition number is a data-driven complexity measure for convex programs, generalizing classical condition numbers for linear systems. We show that for a broad class of compressed sensing problems, the worst case value of this algorithmic complexity measure taken over all signals matches the restricted singular value of the observation matrix which controls robust recovery performance. Overall, this means in both cases that, in compressed sensing problems, a single parameter directly controls both computational complexity and recovery performance. Numerical experiments illustrate these points using several classical algorithms.Comment: Final version, to appear in information and Inferenc

Statistical performance analysis with dynamic workload using S-NET

Volkmar Wieser, Philip K. F. Hölzenspies, Michael Roßbory, and Raimund Kirner, 'Statistical performance analysis with dynamic workload using S-NET'. Paper presented at the Workshop on Feedback-Directed Compiler Optimization for Multi-Core Architectures. Paris, France 23-25 January 2012In this paper the ADVANCE approach for engineering con- current software systems with well-balanced hardware ef- ficiency is adressed using the stream processing language S-Net. To obtain the cost information in the concurrent system the metrics throughput, latency, and jitter are evalu- ated by analyzing generated synthetical data as well as using an industrial related application in the future. As fall-out an Eclipse plugin for S-Net has been developed to provide sup- port for syntax highlighting, content assistance, hover help, and more, for easier and faster development. The presented results of the current work are on the one hand an indicator for the status quo of the ADVANCE vision and on the other hand used to improve the applied statistical analysis tech- niques within ADVANCE. Like the ADVANCE project, this work is still under development, but further improvements and speedups are expected in the near future

Statistical performance analysis of a fast super-resolution technique using noisy translations

It is well known that the registration process is a key step for super-resolution reconstruction. In this work, we propose to use a piezoelectric system that is easily adaptable on all microscopes and telescopes for controlling accurately their motion (down to nanometers) and therefore acquiring multiple images of the same scene at different controlled positions. Then a fast super-resolution algorithm \cite{eh01} can be used for efficient super-resolution reconstruction. In this case, the optimal use of $r^2$ images for a resolution enhancement factor $r$ is generally not enough to obtain satisfying results due to the random inaccuracy of the positioning system. Thus we propose to take several images around each reference position. We study the error produced by the super-resolution algorithm due to spatial uncertainty as a function of the number of images per position. We obtain a lower bound on the number of images that is necessary to ensure a given error upper bound with probability higher than some desired confidence level.Comment: 15 pages, submitte

Statistical Performance Analysis of an Ant-Colony Optimisation Application in S-NET

Kenneth MacKenzie, Philip K. F. Hölzenspies, Kevin Hammond, Raimund Kirner, Vu Thien Nga Nguyen, Iraneus te Boekhorst, Clemens Grelck, Raphael Poss, Merijn Verstraaten, 'Statistical Performance Analysis of an Ant-Colony Optimisation Application in S-NET'. Paper presented at the 2nd Workshop on Feedback-Directed Compiler Optimization for Multi-Core Architectures. Berlin, Germany, 12 January 2013.We consider an ant-colony optimsation problem implemented on a multicore system as a collection of asynchronous stream- processing components under the control of the S-NET coordina- tion language. Statistical analysis and visualisation techniques are used to study the behaviour of the application, and this enables us to discover and correct problems in both the application program and the run-time system underlying S-NET

Sensitivity of Inequality Measures to Extreme Values

We examine the sensitivity of estimates and inequality indices to extreme values, in the sense of their robustness properties and of their statistical performance. We establish that these measures are very sensitive to the properties of the income distribution. Estimation and inference can be dramatically affected, especially when the tail of the income distribution is heavy.Inequality measures, statistical performance, robustness.

Income distribution and inequality measurement: The problem of extreme values

We examine the statistical performance of inequality indices in the presence of extreme values in the data and show that these indices are very sensitive to the properties of the income distribution. Estimation and inference can be dramatically affected, especially when the tail of the income distribution is heavy, even when standard bootstrap methods are employed. However, use of appropriate semiparametric methods for modelling the upper tail can greatly improve the performance of even those inequality indices that are normally considered particularly sensitive to extreme values.inequality measures ; statistical performance ; robustness