Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.

Spontaneous Cirrhosis Regression in an IFN-beta-induced AIH-like Syndrome Following Drug Withdrawal: Art of Facts or Artifacts?

Autoimmune hepatitis (AIH) is a disease of unknown aetiology with drug-induced AIH being the most complex and not fully understood type. We present the case of a 57-year-old female patient with acute icteric hepatitis after interferon-beta-1b (IFNβ-1b) administration for multiple sclerosis (MS). Based on liver autoimmune serology, histology and appropriate exclusion of other liver diseases, a diagnosis of AIH-related cirrhosis was established. Following discontinuation of IFNβ-1b, a complete resolution of biochemical activity indices was observed and the patient remained untreated on her own decision. However, 3 years later, after a course of intravenous methylprednisolone for MS, a new acute transaminase flare was recorded which subsided again spontaneously after 3 weeks. Liver biopsy and elastography showed significant fibrosis regression (F2 fibrosis). To our knowledge, this is the first report showing spontaneous cirrhosis regression in an IFNβ-1b-induced AIH-like syndrome following drug withdrawal, suggesting that cirrhosis might be reversible if the offending fibrogenic stimulus is withdrawn.

Explaining dinophysis cf. acuminata abundance in Antifer (Normandy, France) using dynamic linear regression

Classical regression analysis can be used to model time series. However, the assumption that model parameters are constant over time is not necessarily adapted to the data. In phytoplankton ecology, the relevance of time-varying parameter values has been shown using a dynamic linear regression model (DLRM). DLRMs, belonging to the class of Bayesian dynamic models, assume the existence of a non-observable time series of model parameters, which are estimated on-line, i.e. after each observation. The aim of this paper was to show how DLRM results could be used to explain variation of a time series of phytoplankton abundance. We applied DLRM to daily concentrations of Dinophysis cf. acuminata, determined in Antifer harbour (French coast of the English Channel), along with physical and chemical covariates (e.g. wind velocity, nutrient concentrations). A single model was built using 1989 and 1990 data, and then applied separately to each year. Equivalent static regression models were investigated for the purpose of comparison. Results showed that most of the Dinophysis cf. acuminata concentration variability was explained by the configuration of the sampling site, the wind regime and tide residual flow. Moreover, the relationships of these factors with the concentration of the microalga varied with time, a fact that could not be detected with static regression. Application of dynamic models to phytoplankton time series, especially in a monitoring context, is discussed.

Use of posterior predictive assessments to evaluate model fit in multilevel logistic regression

Assessing the fit of a model is an important final step in any statistical analysis, but this is not straightforward when complex discrete response models are used. Cross validation and posterior predictions have been suggested as methods to aid model criticism. In this paper a comparison is made between four methods of model predictive assessment in the context of a three level logistic regression model for clinical mastitis in dairy cattle; cross validation, a prediction using the full posterior predictive distribution and two “mixed” predictive methods that incorporate higher level random effects simulated from the underlying model distribution. Cross validation is considered a gold standard method but is computationally intensive and thus a comparison is made between posterior predictive assessments and cross validation. The analyses revealed that mixed prediction methods produced results close to cross validation whilst the full posterior predictive assessment gave predictions that were over-optimistic (closer to the observed disease rates) compared with cross validation. A mixed prediction method that simulated random effects from both higher levels was best at identifying the outlying level two (farm-year) units of interest. It is concluded that this mixed prediction method, simulating random effects from both higher levels, is straightforward and may be of value in model criticism of multilevel logistic regression, a technique commonly used for animal health data with a hierarchical structure.

Bahadur representation of linear kernel quantile estimator of VaR under mixing assumptions

Bahadur representation and its applications have attracted a large number of publications and presentations on a wide variety of problems. Mixing dependency is weak enough to describe the dependent structure of random variables, including observations in time series and longitudinal studies. This note proves the Bahadur representation of sample quantiles for strongly mixing random variables (including ½-mixing and Á-mixing) under very weak mixing coe±cients. As application, the asymptotic normality is derived. These results greatly improves those recently reported in literature.

Diseño e implementación del kernel de xDEVS, versión distribuida

Para entender nuestro proyecto, debemos comprender DEVS. Dentro de los formalismos más populares de representación de sistemas de eventos discretos se encuentra DES. En la década de los 70, el matemático Bernard Zeigler propuso un formalismo general para la representación de dichos sistemas. Este formalismo denominado DEVS (Discrete EVent System Specification) es el formalismo más general para el tratamiento de DES. DEVS permite representar todos aquellos sistemas cuyo comportamiento pueda describirse mediante una secuencia de eventos discretos. Estos eventos se caracterizan por un tiempo base en el que solo un número de eventos finitos puede ocurrir. DEVS Modelado y Simulación tiene múltiples implementaciones en varios lenguajes de programación como por ejemplo en Java, C# o C++. Pero surge la necesidad de implementar una plataforma distribuida estable para proporcionar la mecánica de interoperabilidad e integrar modelos DEVS diversificados. En este proyecto, se nos dará como código base el core de xDEVS en java, aplicado de forma secuencial y paralelizada. Nuestro trabajo será implementar el core de manera distribuida de tal forma que se pueda dividir un sistema DEVS en diversas máquinas. Para esto hemos utilizado sockets de java para hacer la transmisión de datos lo más eficiente posible. En un principio deberemos especificar el número de máquinas que se conectarán al servidor. Una vez estas se hayan conectado se les enviará el trabajo específico que deberán simular. Cabe destacar que hay dos formas de dividir un sistema DEVS las cuales están implementadas en nuestro proyecto. La primera es dividirlo en módulos atómicos los cuales son subsistemas indivisibles en un sistema DEVS. Y la segunda es dividir las funciones de todos los subsistemas en grupos y repartirlos entre las máquinas. En resumen el funcionamiento de nuestro sistema distribuido será comenzar ejecutando el trabajo asignado al primer cliente, una vez finalizado actualizará la información del servidor y este mandara la orden al siguiente y así sucesivamente.

Probabilistic methods for seasonal forecasting in a changing climate: Cox-type regression models.

For climate risk management, cumulative distribution functions (CDFs) are an important source of information. They are ideally suited to compare probabilistic forecasts of primary (e.g. rainfall) or secondary data (e.g. crop yields). Summarised as CDFs, such forecasts allow an easy quantitative assessment of possible, alternative actions. Although the degree of uncertainty associated with CDF estimation could influence decisions, such information is rarely provided. Hence, we propose Cox-type regression models (CRMs) as a statistical framework for making inferences on CDFs in climate science. CRMs were designed for modelling probability distributions rather than just mean or median values. This makes the approach appealing for risk assessments where probabilities of extremes are often more informative than central tendency measures. CRMs are semi-parametric approaches originally designed for modelling risks arising from time-to-event data. Here we extend this original concept beyond time-dependent measures to other variables of interest. We also provide tools for estimating CDFs and surrounding uncertainty envelopes from empirical data. These statistical techniques intrinsically account for non-stationarities in time series that might be the result of climate change. This feature makes CRMs attractive candidates to investigate the feasibility of developing rigorous global circulation model (GCM)-CRM interfaces for provision of user-relevant forecasts. To demonstrate the applicability of CRMs, we present two examples for El Ni ? no/Southern Oscillation (ENSO)-based forecasts: the onset date of the wet season (Cairns, Australia) and total wet season rainfall (Quixeramobim, Brazil). This study emphasises the methodological aspects of CRMs rather than discussing merits or limitations of the ENSO-based predictors.

A demand-driven analysis of tourist accommodation price: A quantile regression of room bookings

Tourist accommodation expenditure is a widely investigated topic as it represents a major contribution to the total tourist expenditure. The identification of the determinant factors is commonly based on supply-driven applications while little research has been made on important travel characteristics. This paper proposes a demand-driven analysis of tourist accommodation price by focusing on data generated from room bookings. The investigation focuses on modeling the relationship between key travel characteristics and the price paid to book the accommodation. To accommodate the distributional characteristics of the expenditure variable, the analysis is based on the estimation of a quantile regression model. The findings support the econometric approach used and enable the elaboration of relevant managerial implications.

A survey on multi-output regression

In recent years, a plethora of approaches have been proposed to deal with the increasingly challenging task of multi-output regression. This paper provides a survey on state-of-the-art multi-output regression methods, that are categorized as problem transformation and algorithm adaptation methods. In addition, we present the mostly used performance evaluation measures, publicly available data sets for multi-output regression real-world problems, as well as open-source software frameworks.

SVR-GARCH com misturas de kernels gaussianos

Dissertação (mestrado)—Universidade de Brasília, Departamento de Administração, Programa de Pós-graduação em Administração, 2016.

SCALABLE APPROXIMATION OF KERNEL FUZZY C-MEANS

Virtually every sector of business and industry that uses computing, including financial analysis, search engines, and electronic commerce, incorporate Big Data analysis into their business model. Sophisticated clustering algorithms are popular for deducing the nature of data by assigning labels to unlabeled data. We address two main challenges in Big Data. First, by definition, the volume of Big Data is too large to be loaded into a computer’s memory (this volume changes based on the computer used or available, but there is always a data set that is too large for any computer). Second, in real-time applications, the velocity of new incoming data prevents historical data from being stored and future data from being accessed. Therefore, we propose our Streaming Kernel Fuzzy c-Means (stKFCM) algorithm, which reduces both computational complexity and space complexity significantly. The proposed stKFCM only requires O(n2) memory where n is the (predetermined) size of a data subset (or data chunk) at each time step, which makes this algorithm truly scalable (as n can be chosen based on the available memory). Furthermore, only 2n2 elements of the full N × N (where N >> n) kernel matrix need to be calculated at each time-step, thus reducing both the computation time in producing the kernel elements and also the complexity of the FCM algorithm. Empirical results show that stKFCM, even with relatively very small n, can provide clustering performance as accurately as kernel fuzzy c-means run on the entire data set while achieving a significant speedup.

GIS-integrated mathematical modeling of social phenomena at macro- and micro- levels—a multivariate geographically-weighted regression model for identifying locations vulnerable to hosting terrorist safe-houses: France as case study

Adaptability and invisibility are hallmarks of modern terrorism, and keeping pace with its dynamic nature presents a serious challenge for societies throughout the world. Innovations in computer science have incorporated applied mathematics to develop a wide array of predictive models to support the variety of approaches to counterterrorism. Predictive models are usually designed to forecast the location of attacks. Although this may protect individual structures or locations, it does not reduce the threat—it merely changes the target. While predictive models dedicated to events or social relationships receive much attention where the mathematical and social science communities intersect, models dedicated to terrorist locations such as safe-houses (rather than their targets or training sites) are rare and possibly nonexistent. At the time of this research, there were no publically available models designed to predict locations where violent extremists are likely to reside. This research uses France as a case study to present a complex systems model that incorporates multiple quantitative, qualitative and geospatial variables that differ in terms of scale, weight, and type. Though many of these variables are recognized by specialists in security studies, there remains controversy with respect to their relative importance, degree of interaction, and interdependence. Additionally, some of the variables proposed in this research are not generally recognized as drivers, yet they warrant examination based on their potential role within a complex system. This research tested multiple regression models and determined that geographically-weighted regression analysis produced the most accurate result to accommodate non-stationary coefficient behavior, demonstrating that geographic variables are critical to understanding and predicting the phenomenon of terrorism. This dissertation presents a flexible prototypical model that can be refined and applied to other regions to inform stakeholders such as policy-makers and law enforcement in their efforts to improve national security and enhance quality-of-life.