Bayesian Lower Bounds for Dense or Sparse (Outlier) Noise in the RMT Framework

Robust estimation is an important and timely research subject. In this paper, we investigate performance lower bounds on the mean-square-error (MSE) of any estimator for the Bayesian linear model, corrupted by a noise distributed according to an i.i.d. Student's t-distribution. This class of prior parametrized by its degree of freedom is relevant to modelize either dense or sparse (accounting for outliers) noise. Using the hierarchical Normal-Gamma representation of the Student's t-distribution, the Van Trees' Bayesian Cram\'er-Rao bound (BCRB) on the amplitude parameters is derived. Furthermore, the random matrix theory (RMT) framework is assumed, i.e., the number of measurements and the number of unknown parameters grow jointly to infinity with an asymptotic finite ratio. Using some powerful results from the RMT, closed-form expressions of the BCRB are derived and studied. Finally, we propose a framework to fairly compare two models corrupted by noises with different degrees of freedom for a fixed common target signal-to-noise ratio (SNR). In particular, we focus our effort on the comparison of the BCRBs associated with two models corrupted by a sparse noise promoting outliers and a dense (Gaussian) noise, respectively

Sparse-Based Estimation Performance for Partially Known Overcomplete Large-Systems

We assume the direct sum o for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace and the goal is to estimate the LA am- plitudes corresponding to subspace . Taking into account the knowledge of the orthogonal "interfering" subspace \perp, the Bayesian estimation lower bound is de- rivedfortheLA-sparsevectorinthedoublyasymptoticscenario,i.e. N,LA,LB -> \infty with a finite asymptotic ratio. By jointly exploiting the Compressed Sensing (CS) and the Random Matrix Theory (RMT) frameworks, closed-form expressions for the lower bound on the estimation of the non-zero entries of a sparse vector of interest are derived and studied. The derived closed-form expressions enjoy several interesting features: (i) a simple interpretable expression, (ii) a very low computational cost especially in the doubly asymptotic scenario, (iii) an accurate prediction of the mean-square-error (MSE) of popular sparse-based estimators and (iv) the lower bound remains true for any amplitudes vector priors. Finally, several idealized scenarios are compared to the derived bound for a common output signal-to-noise-ratio (SNR) which shows the in- terest of the joint estimation/rejection methodology derived herein.Comment: 10 pages, 5 figures, Journal of Signal Processin

Features extraction using random matrix theory.

Representing the complex data in a concise and accurate way is a special stage in data mining methodology. Redundant and noisy data affects generalization power of any classification algorithm, undermines the results of any clustering algorithm and finally encumbers the monitoring of large dynamic systems. This work provides several efficient approaches to all aforementioned sides of the analysis. We established, that notable difference can be made, if the results from the theory of ensembles of random matrices are employed. Particularly important result of our study is a discovered family of methods based on projecting the data set on different subsets of the correlation spectrum. Generally, we start with traditional correlation matrix of a given data set. We perform singular value decomposition, and establish boundaries between essential and unimportant eigen-components of the spectrum. Then, depending on the nature of the problem at hand we either use former or later part for the projection purpose. Projecting the spectrum of interest is a common technique in linear and non-linear spectral methods such as Principal Component Analysis, Independent Component Analysis and Kernel Principal Component Analysis. Usually the part of the spectrum to project is defined by the amount of variance of overall data or feature space in non-linear case. The applicability of these spectral methods is limited by the assumption that larger variance has important dynamics, i.e. if the data has a high signal-to-noise ratio. If it is true, projection of principal components targets two problems in data mining, reduction in the number of features and selection of more important features. Our methodology does not make an assumption of high signal-to-noise ratio, instead, using the rigorous instruments of Random Matrix Theory (RNIT) it identifies the presence of noise and establishes its boundaries. The knowledge of the structure of the spectrum gives us possibility to make more insightful projections. For instance, in the application to router network traffic, the reconstruction error procedure for anomaly detection is based on the projection of noisy part of the spectrum. Whereas, in bioinformatics application of clustering the different types of leukemia, implicit denoising of the correlation matrix is achieved by decomposing the spectrum to random and non-random parts. For temporal high dimensional data, spectrum and eigenvectors of its correlation matrix is another representation of the data. Thus, eigenvalues, components of the eigenvectors, inverse participation ratio of eigenvector components and other operators of eigen analysis are spectral features of dynamic system. In our work we proposed to extract spectral features using the RMT. We demonstrated that with extracted spectral features we can monitor the changing dynamics of network traffic. Experimenting with the delayed correlation matrices of network traffic and extracting its spectral features, we visualized the delayed processes in the system. We demonstrated in our work that broad range of applications in feature extraction can benefit from the novel RMT based approach to the spectral representation of the data

Computer-Assisted Electroanatomical Guidance for Cardiac Electrophysiology Procedures

Cardiac arrhythmias are serious life-threatening episodes affecting both the aging population and younger patients with pre-existing heart conditions. One of the most effective therapeutic procedures is the minimally-invasive catheter-driven endovascular electrophysiology study, whereby electrical potentials and activation patterns in the affected cardiac chambers are measured and subsequent ablation of arrhythmogenic tissue is performed. Despite emerging technologies such as electroanatomical mapping and remote intraoperative navigation systems for improved catheter manipulation and stability, successful ablation of arrhythmias is still highly-dependent on the operator’s skills and experience. This thesis proposes a framework towards standardisation in the electroanatomical mapping and ablation planning by merging knowledge transfer from previous cases and patient-specific data. In particular, contributions towards four different procedural aspects were made: optimal electroanatomical mapping, arrhythmia path computation, catheter tip stability analysis, and ablation simulation and optimisation. In order to improve the intraoperative electroanatomical map, anatomical areas of high mapping interest were proposed, as learned from previous electrophysiology studies. Subsequently, the arrhythmic wave propagation on the endocardial surface and potential ablation points were computed. The ablation planning is further enhanced, firstly by the analysis of the catheter tip stability and the probability of slippage at sparse locations on the endocardium and, secondly, by the simulation of the ablation result from the computation of convolutional matrices which model mathematically the ablation process. The methods proposed by this thesis were validated on data from patients with complex congenital heart disease, who present unusual cardiac anatomy and consequently atypical arrhythmias. The proposed methods also build a generic framework for computer guidance of electrophysiology, with results showing complementary information that can be easily integrated into the clinical workflow.Open Acces

Multitask and transfer learning for multi-aspect data

Supervised learning aims to learn functional relationships between inputs and outputs. Multitask learning tackles supervised learning tasks by performing them simultaneously to exploit commonalities between them. In this thesis, we focus on the problem of eliminating negative transfer in order to achieve better performance in multitask learning. We start by considering a general scenario in which the relationship between tasks is unknown. We then narrow our analysis to the case where data are characterised by a combination of underlying aspects, e.g., a dataset of images of faces, where each face is determined by a person's facial structure, the emotion being expressed, and the lighting conditions. In machine learning there have been numerous efforts based on multilinear models to decouple these aspects but these have primarily used techniques from the field of unsupervised learning. In this thesis we take inspiration from these approaches and hypothesize that supervised learning methods can also benefit from exploiting these aspects. The contributions of this thesis are as follows: 1. A multitask learning and transfer learning method that avoids negative transfer when there is no prescribed information about the relationships between tasks. 2. A multitask learning approach that takes advantage of a lack of overlapping features between known groups of tasks associated with different aspects. 3. A framework which extends multitask learning using multilinear algebra, with the aim of learning tasks associated with a combination of elements from different aspects. 4. A novel convex relaxation approach that can be applied both to the suggested framework and more generally to any tensor recovery problem. Through theoretical validation and experiments on both synthetic and real-world datasets, we show that the proposed approaches allow fast and reliable inferences. Furthermore, when performing learning tasks on an aspect of interest, accounting for secondary aspects leads to significantly more accurate results than using traditional approaches

Advanced Techniques for Ground Penetrating Radar Imaging

Ground penetrating radar (GPR) has become one of the key technologies in subsurface sensing and, in general, in non-destructive testing (NDT), since it is able to detect both metallic and nonmetallic targets. GPR for NDT has been successfully introduced in a wide range of sectors, such as mining and geology, glaciology, civil engineering and civil works, archaeology, and security and defense. In recent decades, improvements in georeferencing and positioning systems have enabled the introduction of synthetic aperture radar (SAR) techniques in GPR systems, yielding GPR–SAR systems capable of providing high-resolution microwave images. In parallel, the radiofrequency front-end of GPR systems has been optimized in terms of compactness (e.g., smaller Tx/Rx antennas) and cost. These advances, combined with improvements in autonomous platforms, such as unmanned terrestrial and aerial vehicles, have fostered new fields of application for GPR, where fast and reliable detection capabilities are demanded. In addition, processing techniques have been improved, taking advantage of the research conducted in related fields like inverse scattering and imaging. As a result, novel and robust algorithms have been developed for clutter reduction, automatic target recognition, and efficient processing of large sets of measurements to enable real-time imaging, among others. This Special Issue provides an overview of the state of the art in GPR imaging, focusing on the latest advances from both hardware and software perspectives

Conditional asymmetries and downside risks in macroeconomic and financial time series

Macroeconomic and financial time series often display non-Gaussian features. In this thesis, I study the importance of conditional asymmetry in economic decisions, related to policy making or portfolio management. A novel toolbox to aid decision makers to evaluate the balance of risks in a coherent way is proposed and employed to investigate the relevance of modeling time-varying skewness in the context of improving the prediction accuracy of policy variables. The thesis consists of four papers. The first paper introduces the modeling framework which features permanent and transitory dynamics, robustness to tail events, allows for both dense or sparse predictor designs, and delivers competitive out-of-sample (point, density and tail) forecasts. We document procyclical movements in the conditional skewness of US business cycle, and a substantial increase in downside risk to US economic growth the last 30 years. In the second paper we investigate the historical determinants of US core inflation. We find substantial non-linearities in the relation between price growth and fiscal and monetary developments in the post war era. These generate asymmetric inflation risks over the long-run, which shape the balance of risks to the inflation outlook. We show that, when inflation risks are skewed, policy makers need to adjust their actions to offset the perceived level skewness. The third paper studies the impact of conditional asymmetry in a portfolio allocation context. Focusing on momentum returns, we show that the risk return trade-off of the strategy reflects a non-linear interaction between conditional volatility and skewness. We derive a dynamic skewness adjustment within a maximum Sharpe ratio strategy and find improvements upon existing volatility managed momentum portfolios. In the last paper I review the properties of the Epsilon-Skew-t distribution, a building-block of this thesis, and I develop a parametric procedure to test for the presence of conditional asymmetry in time series data

Detecting changepoints in multivariate data

In this thesis, we propose new methodology for detecting changepoints in multivariate data, focusing on the setting where the number of variables and the length of the data can be very large. We begin by considering the problem of detecting changepoints where only a sub- set of the variables are affected by the change. Previous work demonstrated that the changepoint locations and affected variables can be simultaneously estimated by solving a discrete optimisation problem. We propose two new methods PSMOP (Pruned Subset Multivariate Optimal Partitioning) and SPOT (Subset Partitioning Optimal Time) for solving this problem. PSMOP uses novel search space reduction techniques to efficiently compute an exact solution for data of moderate size. SPOT is an approximate method, which gives near optimal solutions at a very low computational cost, and can be applied to very large datasets. We use this new methodology to study changes in sales data due to the effect of promotions. We then examine the problem of detecting changes in the covariance structure of high dimensional data. Using results from Random Matrix Theory, we introduce a novel test statistic for detecting such changes. Importantly, under the null hypothesis of no change, the distribution of this test statistic is independent of the underlying covariance matrix. We utilise this test statistic to study changes in the amount of water on the surface of a plot of soil

Online learning on the programmable dataplane

This thesis makes the case for managing computer networks with datadriven methods automated statistical inference and control based on measurement data and runtime observations—and argues for their tight integration with programmable dataplane hardware to make management decisions faster and from more precise data. Optimisation, defence, and measurement of networked infrastructure are each challenging tasks in their own right, which are currently dominated by the use of hand-crafted heuristic methods. These become harder to reason about and deploy as networks scale in rates and number of forwarding elements, but their design requires expert knowledge and care around unexpected protocol interactions. This makes tailored, per-deployment or -workload solutions infeasible to develop. Recent advances in machine learning offer capable function approximation and closed-loop control which suit many of these tasks. New, programmable dataplane hardware enables more agility in the network— runtime reprogrammability, precise traffic measurement, and low latency on-path processing. The synthesis of these two developments allows complex decisions to be made on previously unusable state, and made quicker by offloading inference to the network. To justify this argument, I advance the state of the art in data-driven defence of networks, novel dataplane-friendly online reinforcement learning algorithms, and in-network data reduction to allow classification of switchscale data. Each requires co-design aware of the network, and of the failure modes of systems and carried traffic. To make online learning possible in the dataplane, I use fixed-point arithmetic and modify classical (non-neural) approaches to take advantage of the SmartNIC compute model and make use of rich device local state. I show that data-driven solutions still require great care to correctly design, but with the right domain expertise they can improve on pathological cases in DDoS defence, such as protecting legitimate UDP traffic. In-network aggregation to histograms is shown to enable accurate classification from fine temporal effects, and allows hosts to scale such classification to far larger flow counts and traffic volume. Moving reinforcement learning to the dataplane is shown to offer substantial benefits to stateaction latency and online learning throughput versus host machines; allowing policies to react faster to fine-grained network events. The dataplane environment is key in making reactive online learning feasible—to port further algorithms and learnt functions, I collate and analyse the strengths of current and future hardware designs, as well as individual algorithms

An Initial Framework Assessing the Safety of Complex Systems

Trabajo presentado en la Conference on Complex Systems, celebrada online del 7 al 11 de diciembre de 2020.Atmospheric blocking events, that is large-scale nearly stationary atmospheric pressure patterns, are often associated with extreme weather in the mid-latitudes, such as heat waves and cold spells which have significant consequences on ecosystems, human health and economy. The high impact of blocking events has motivated numerous studies. However, there is not yet a comprehensive theory explaining their onset, maintenance and decay and their numerical prediction remains a challenge. In recent years, a number of studies have successfully employed complex network descriptions of fluid transport to characterize dynamical patterns in geophysical flows. The aim of the current work is to investigate the potential of so called Lagrangian flow networks for the detection and perhaps forecasting of atmospheric blocking events. The network is constructed by associating nodes to regions of the atmosphere and establishing links based on the flux of material between these nodes during a given time interval. One can then use effective tools and metrics developed in the context of graph theory to explore the atmospheric flow properties. In particular, Ser-Giacomi et al. [1] showed how optimal paths in a Lagrangian flow network highlight distinctive circulation patterns associated with atmospheric blocking events. We extend these results by studying the behavior of selected network measures (such as degree, entropy and harmonic closeness centrality)at the onset of and during blocking situations, demonstrating their ability to trace the spatio-temporal characteristics of these events.This research was conducted as part of the CAFE (Climate Advanced Forecasting of sub-seasonal Extremes) Innovative Training Network which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 813844