Data-adaptive harmonic spectra and multilayer Stuart-Landau models

Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure. The corresponding eigenvalues can be grouped per Fourier frequency, and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey furthermore a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum. The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coefficients stacked by Fourier frequency which can be efficiently modeled---provided the decay of temporal correlations is sufficiently well-resolved---within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators. Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise, are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence.Comment: 26 pages, double columns; 15 figure

A Survey of Bayesian Statistical Approaches for Big Data

The modern era is characterised as an era of information or Big Data. This has motivated a huge literature on new methods for extracting information and insights from these data. A natural question is how these approaches differ from those that were available prior to the advent of Big Data. We present a review of published studies that present Bayesian statistical approaches specifically for Big Data and discuss the reported and perceived benefits of these approaches. We conclude by addressing the question of whether focusing only on improving computational algorithms and infrastructure will be enough to face the challenges of Big Data

Efficient Human Activity Recognition in Large Image and Video Databases

Vision-based human action recognition has attracted considerable interest in recent research for its applications to video surveillance, content-based search, healthcare, and interactive games. Most existing research deals with building informative feature descriptors, designing efficient and robust algorithms, proposing versatile and challenging datasets, and fusing multiple modalities. Often, these approaches build on certain conventions such as the use of motion cues to determine video descriptors, application of off-the-shelf classifiers, and single-factor classification of videos. In this thesis, we deal with important but overlooked issues such as efficiency, simplicity, and scalability of human activity recognition in different application scenarios: controlled video environment (e.g.~indoor surveillance), unconstrained videos (e.g.~YouTube), depth or skeletal data (e.g.~captured by Kinect), and person images (e.g.~Flicker). In particular, we are interested in answering questions like (a) is it possible to efficiently recognize human actions in controlled videos without temporal cues? (b) given that the large-scale unconstrained video data are often of high dimension low sample size (HDLSS) nature, how to efficiently recognize human actions in such data? (c) considering the rich 3D motion information available from depth or motion capture sensors, is it possible to recognize both the actions and the actors using only the motion dynamics of underlying activities? and (d) can motion information from monocular videos be used for automatically determining saliency regions for recognizing actions in still images

The Extreme Risk of Personal Data Breaches & The Erosion of Privacy

Personal data breaches from organisations, enabling mass identity fraud, constitute an \emph{extreme risk}. This risk worsens daily as an ever-growing amount of personal data are stored by organisations and on-line, and the attack surface surrounding this data becomes larger and harder to secure. Further, breached information is distributed and accumulates in the hands of cyber criminals, thus driving a cumulative erosion of privacy. Statistical modeling of breach data from 2000 through 2015 provides insights into this risk: A current maximum breach size of about 200 million is detected, and is expected to grow by fifty percent over the next five years. The breach sizes are found to be well modeled by an \emph{extremely heavy tailed} truncated Pareto distribution, with tail exponent parameter decreasing linearly from 0.57 in 2007 to 0.37 in 2015. With this current model, given a breach contains above fifty thousand items, there is a ten percent probability of exceeding ten million. A size effect is unearthed where both the frequency and severity of breaches scale with organisation size like $s^{0.6}$. Projections indicate that the total amount of breached information is expected to double from two to four billion items within the next five years, eclipsing the population of users of the Internet. This massive and uncontrolled dissemination of personal identities raises fundamental concerns about privacy.Comment: 16 pages, 3 sets of figures, and 4 table

Surfing the Brain—An Overview of Wavelet-Based Techniques for fMRI Data Analysis

The measurement of brain activity in a noninvasive way is an essential element in modern neurosciences. Modalities such as electroencephalography (EEG) and magnetoencephalography (MEG) recently gained interest, but two classical techniques remain predominant. One of them is positron emission tomography (PET), which is costly and lacks temporal resolution but allows the design of tracers for specific tasks; the other main one is functional magnetic resonance imaging (fMRI), which is more affordable than PET from a technical, financial, and ethical point of view, but which suffers from poor contrast and low signal-to-noise ratio (SNR). For this reason, advanced methods have been devised to perform the statistical analysis of fMRI data

Bioinformatics applied to human genomics and proteomics: development of algorithms and methods for the discovery of molecular signatures derived from omic data and for the construction of co-expression and interaction networks

[EN] The present PhD dissertation develops and applies Bioinformatic methods and tools to address key current problems in the analysis of human omic data. This PhD has been organised by main objectives into four different chapters focused on: (i) development of an algorithm for the analysis of changes and heterogeneity in large-scale omic data; (ii) development of a method for non-parametric feature selection; (iii) integration and analysis of human protein-protein interaction networks and (iv) integration and analysis of human co-expression networks derived from tissue expression data and evolutionary profiles of proteins. In the first chapter, we developed and tested a new robust algorithm in R, called DECO, for the discovery of subgroups of features and samples within large-scale omic datasets, exploring all feature differences possible heterogeneity, through the integration of both data dispersion and predictor-response information in a new statistic parameter called h (heterogeneity score). In the second chapter, we present a simple non-parametric statistic to measure the cohesiveness of categorical variables along any quantitative variable, applicable to feature selection in all types of big data sets. In the third chapter, we describe an analysis of the human interactome integrating two global datasets from high-quality proteomics technologies: HuRI (a human protein-protein interaction network generated by a systematic experimental screening based on Yeast-Two-Hybrid technology) and Cell-Atlas (a comprehensive map of subcellular localization of human proteins generated by antibody imaging). This analysis aims to create a framework for the subcellular localization characterization supported by the human protein-protein interactome. In the fourth chapter, we developed a full integration of three high-quality proteome-wide resources (Human Protein Atlas, OMA and TimeTree) to generate a robust human co-expression network across tissues assigning each human protein along the evolutionary timeline. In this way, we investigate how old in evolution and how correlated are the different human proteins, and we place all them in a common interaction network. As main general comment, all the work presented in this PhD uses and develops a wide variety of bioinformatic and statistical tools for the analysis, integration and enlighten of molecular signatures and biological networks using human omic data. Most of this data corresponds to sample cohorts generated in recent biomedical studies on specific human diseases