Adaptive model selection using empirical complexities

Given $n$ independent replicates of a jointly distributed pair $(X,Y)\in {\cal R}^d \times {\cal R}$, we wish to select from a fixed sequence of model classes ${\cal F}_1, {\cal F}_2, \ldots$ a deterministic prediction rule $f: {\cal R}^d \to {\cal R}$ whose risk is small. We investigate the possibility of empirically assessingthe {\em complexity} of each model class, that is, the actual difficulty of the estimation problem within each class. The estimated complexities are in turn used to define an adaptive model selection procedure, which is based on complexity penalized empirical risk.The available data are divided into two parts. The first is used to form an empirical cover of each model class, and the second is used to select a candidate rule from each cover based on empirical risk. The covering radii are determined empirically to optimize a tight upper bound on the estimation error. An estimate is chosen from the list of candidates in order to minimize the sum of class complexity and empirical risk. A distinguishing feature of the approach is that the complexity of each model class is assessed empirically, based on the size of its empirical cover.Finite sample performance bounds are established for the estimates, and these bounds are applied to several non-parametric estimation problems. The estimates are shown to achieve a favorable tradeoff between approximation and estimation error, and to perform as well as if the distribution-dependent complexities of the model classes were known beforehand. In addition, it is shown that the estimate can be consistent,and even possess near optimal rates of convergence, when each model class has an infinite VC or pseudo dimension.For regression estimation with squared loss we modify our estimate to achieve a faster rate of convergence.

Portfolio choice beyond the traditional approach

This paper surveys asset allocation methods that extend the traditional approach. An important feature of the the traditional approach is that measures the risk and return tradeoff in terms of mean and variance of final wealth. However, there are also other important features that are not always made explicit in terms of investor s wealth, information, and horizon: The investor makes a single portfolio choice based only on the mean and variance of her final financial wealth and she knows the relevant parameters in that computation. First, the paper describes traditional portfolio choice based on four basic assumptions, while the rest of the sections extend those assumptions. Each section will describe the corresponding equilibrium implications in terms of portfolio advice and asset pricing.

Advanced geostatistical and machine-learning models for spatial data analysis of radioactively contaminated regions

Radioactive soil-contamination mapping and risk assessment is a vital issue for decision makers. Traditional approaches for mapping the spatial concentration of radionuclides employ various regression-based models, which usually provide a single-value prediction realization accompanied (in some cases) by estimation error. Such approaches do not provide the capability for rigorous uncertainty quantification or probabilistic mapping. Machine learning is a recent and fast-developing approach based on learning patterns and information from data. Artificial neural networks for prediction mapping have been especially powerful in combination with spatial statistics. A data-driven approach provides the opportunity to integrate additional relevant information about spatial phenomena into a prediction model for more accurate spatial estimates and associated uncertainty. Machine-learning algorithms can also be used for a wider spectrum of problems than before: classification, probability density estimation, and so forth. Stochastic simulations are used to model spatial variability and uncertainty. Unlike regression models, they provide multiple realizations of a particular spatial pattern that allow uncertainty and risk quantification. This paper reviews the most recent methods of spatial data analysis, prediction, and risk mapping, based on machine learning and stochastic simulations in comparison with more traditional regression models. The radioactive fallout from the Chernobyl Nuclear Power Plant accident is used to illustrate the application of the models for prediction and classification problems. This fallout is a unique case study that provides the challenging task of analyzing huge amounts of data ('hard' direct measurements, as well as supplementary information and expert estimates) and solving particular decision-oriented problems.

Robust power allocation algorithms for MIMO OFDM systems with imperfect CSI

This paper presents a Bayesian approach to the design of transmit prefiltering matrices in closed-loop schemes robust to channel estimation errors. The algorithms are derived for a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system. Two different optimizationcriteria are analyzed: the minimization of the mean square error and the minimization of the bit error rate. In both cases, the transmitter design is based on the singular value decomposition (SVD) of the conditional mean of the channel response, given the channel estimate. The performance of the proposed algorithms is analyzed,and their relationship with existing algorithms is indicated. As withother previously proposed solutions, the minimum bit error rate algorithmconverges to the open-loop transmission scheme for very poor CSI estimates.

Soybean yield maps using regular and optimized sample with different configurations by simulated annealing

ABSTRACT This study aimed to compare thematic maps of soybean yield for different sampling grids, using geostatistical methods (semivariance function and kriging). The analysis was performed with soybean yield data in t ha-1 in a commercial area with regular grids with distances between points of 25x25 m, 50x50 m, 75x75 m, 100x100 m, with 549, 188, 66 and 44 sampling points respectively; and data obtained by yield monitors. Optimized sampling schemes were also generated with the algorithm called Simulated Annealing, using maximization of the overall accuracy measure as a criterion for optimization. The results showed that sample size and sample density influenced the description of the spatial distribution of soybean yield. When the sample size was increased, there was an increased efficiency of thematic maps used to describe the spatial variability of soybean yield (higher values of accuracy indices and lower values for the sum of squared estimation error). In addition, more accurate maps were obtained, especially considering the optimized sample configurations with 188 and 549 sample points.

Choix de portefeuille de grande taille et mesures de risque pour preneurs de décision pessimistes

Cette thèse de doctorat consiste en trois chapitres qui traitent des sujets de choix de portefeuilles de grande taille, et de mesure de risque. Le premier chapitre traite du problème d’erreur d’estimation dans les portefeuilles de grande taille, et utilise le cadre d'analyse moyenne-variance. Le second chapitre explore l'importance du risque de devise pour les portefeuilles d'actifs domestiques, et étudie les liens entre la stabilité des poids de portefeuille de grande taille et le risque de devise. Pour finir, sous l'hypothèse que le preneur de décision est pessimiste, le troisième chapitre dérive la prime de risque, une mesure du pessimisme, et propose une méthodologie pour estimer les mesures dérivées. Le premier chapitre améliore le choix optimal de portefeuille dans le cadre du principe moyenne-variance de Markowitz (1952). Ceci est motivé par les résultats très décevants obtenus, lorsque la moyenne et la variance sont remplacées par leurs estimations empiriques. Ce problème est amplifié lorsque le nombre d’actifs est grand et que la matrice de covariance empirique est singulière ou presque singulière. Dans ce chapitre, nous examinons quatre techniques de régularisation pour stabiliser l’inverse de la matrice de covariance: le ridge, spectral cut-off, Landweber-Fridman et LARS Lasso. Ces méthodes font chacune intervenir un paramètre d’ajustement, qui doit être sélectionné. La contribution principale de cette partie, est de dériver une méthode basée uniquement sur les données pour sélectionner le paramètre de régularisation de manière optimale, i.e. pour minimiser la perte espérée d’utilité. Précisément, un critère de validation croisée qui prend une même forme pour les quatre méthodes de régularisation est dérivé. Les règles régularisées obtenues sont alors comparées à la règle utilisant directement les données et à la stratégie naïve 1/N, selon leur perte espérée d’utilité et leur ratio de Sharpe. Ces performances sont mesurée dans l’échantillon (in-sample) et hors-échantillon (out-of-sample) en considérant différentes tailles d’échantillon et nombre d’actifs. Des simulations et de l’illustration empirique menées, il ressort principalement que la régularisation de la matrice de covariance améliore de manière significative la règle de Markowitz basée sur les données, et donne de meilleurs résultats que le portefeuille naïf, surtout dans les cas le problème d’erreur d’estimation est très sévère. Dans le second chapitre, nous investiguons dans quelle mesure, les portefeuilles optimaux et stables d'actifs domestiques, peuvent réduire ou éliminer le risque de devise. Pour cela nous utilisons des rendements mensuelles de 48 industries américaines, au cours de la période 1976-2008. Pour résoudre les problèmes d'instabilité inhérents aux portefeuilles de grandes tailles, nous adoptons la méthode de régularisation spectral cut-off. Ceci aboutit à une famille de portefeuilles optimaux et stables, en permettant aux investisseurs de choisir différents pourcentages des composantes principales (ou dégrées de stabilité). Nos tests empiriques sont basés sur un modèle International d'évaluation d'actifs financiers (IAPM). Dans ce modèle, le risque de devise est décomposé en deux facteurs représentant les devises des pays industrialisés d'une part, et celles des pays émergents d'autres part. Nos résultats indiquent que le risque de devise est primé et varie à travers le temps pour les portefeuilles stables de risque minimum. De plus ces stratégies conduisent à une réduction significative de l'exposition au risque de change, tandis que la contribution de la prime risque de change reste en moyenne inchangée. Les poids de portefeuille optimaux sont une alternative aux poids de capitalisation boursière. Par conséquent ce chapitre complète la littérature selon laquelle la prime de risque est importante au niveau de l'industrie et au niveau national dans la plupart des pays. Dans le dernier chapitre, nous dérivons une mesure de la prime de risque pour des préférences dépendent du rang et proposons une mesure du degré de pessimisme, étant donné une fonction de distorsion. Les mesures introduites généralisent la mesure de prime de risque dérivée dans le cadre de la théorie de l'utilité espérée, qui est fréquemment violée aussi bien dans des situations expérimentales que dans des situations réelles. Dans la grande famille des préférences considérées, une attention particulière est accordée à la CVaR (valeur à risque conditionnelle). Cette dernière mesure de risque est de plus en plus utilisée pour la construction de portefeuilles et est préconisée pour compléter la VaR (valeur à risque) utilisée depuis 1996 par le comité de Bâle. De plus, nous fournissons le cadre statistique nécessaire pour faire de l’inférence sur les mesures proposées. Pour finir, les propriétés des estimateurs proposés sont évaluées à travers une étude Monte-Carlo, et une illustration empirique en utilisant les rendements journaliers du marché boursier américain sur de la période 2000-2011.

Modelling the partitioning of evapotranspiration in a maize-sunflower intercrop

The primary purpose of this study was to model the partitioning of evapotranspiration in a maize-sunflower intercrop at various canopy covers. The Shuttleworth-Wallace (SW) model was extended for intercropping systems to include both crop transpiration and soil evaporation and allowing interaction between the two. To test the accuracy of the extended SW model, two field experiments of maize-sunflower intercrop were conducted in 1998 and 1999. Plant transpiration and soil evaporation were measured using sap flow gauges and lysimeters, respectively. The mean prediction error (simulated minus measured values) for transpiration was zero (which indicated no overall bias in estimation error), and its accuracy was not affected by the plant growth stages, but simulated transpiration during high measured transpiration rates tended to be slightly underestimated. Overall, the predictions for daily soil evaporation were also accurate. Model estimation errors were probably due to the simplified modelling of soil water content, stomatal resistances and soil heat flux as well as due to the uncertainties in characterising the 2 micrometeorological conditions. The SW’s prediction of transpiration was most sensitive to parameters most directly related to the canopy characteristics such as the partitioning of captured solar radiation, canopy resistance, and bulk boundary layer resistance.

Performance comparison of the optimal and the zero-forcing beamforming algorithms under practical conditions

The optimal and the zero-forcing beamformers are two commonly used algorithms in the subspace-based blind beamforming technology. The optimal beamformer is regarded as the algorithm with the best output SINR. The zero-forcing algorithm emphasizes the co-channel interference cancellation. This paper compares the performance of these two algorithms under some practical conditions: the effect of the finite data length and the existence of the angle estimation error. The investigation reveals that the zero-forcing algorithm can be more robust in the practical environment than the optimal algorithm.

A regionally informed abundance index for supporting integrative analyses across butterfly monitoring schemes

1. The rapid expansion of systematic monitoring schemes necessitates robust methods to reliably assess species' status and trends. Insect monitoring poses a challenge where there are strong seasonal patterns, requiring repeated counts to reliably assess abundance. Butterfly monitoring schemes (BMSs) operate in an increasing number of countries with broadly the same methodology, yet they differ in their observation frequency and in the methods used to compute annual abundance indices. 2. Using simulated and observed data, we performed an extensive comparison of two approaches used to derive abundance indices from count data collected via BMS, under a range of sampling frequencies. Linear interpolation is most commonly used to estimate abundance indices from seasonal count series. A second method, hereafter the regional generalized additive model (GAM), fits a GAM to repeated counts within sites across a climatic region. For the two methods, we estimated bias in abundance indices and the statistical power for detecting trends, given different proportions of missing counts. We also compared the accuracy of trend estimates using systematically degraded observed counts of the Gatekeeper Pyronia tithonus (Linnaeus 1767). 3. The regional GAM method generally outperforms the linear interpolation method. When the proportion of missing counts increased beyond 50%, indices derived via the linear interpolation method showed substantially higher estimation error as well as clear biases, in comparison to the regional GAM method. The regional GAM method also showed higher power to detect trends when the proportion of missing counts was substantial. 4. Synthesis and applications. Monitoring offers invaluable data to support conservation policy and management, but requires robust analysis approaches and guidance for new and expanding schemes. Based on our findings, we recommend the regional generalized additive model approach when conducting integrative analyses across schemes, or when analysing scheme data with reduced sampling efforts. This method enables existing schemes to be expanded or new schemes to be developed with reduced within-year sampling frequency, as well as affording options to adapt protocols to more efficiently assess species status and trends across large geographical scales.

Prevalência e localização espacial dos casos de tracoma detectados em escolares de Botucatu, São Paulo - Brasil

OBJETIVO: Avaliar a prevalência de tracoma em escolares de Botucatu/SP-Brasil e a distribuição espacial dos casos. MÉTODOS: Foi realizado um estudo transversal, em crianças de 7-14 anos, que frequentavam as escolas do ensino fundamental de Botucatu/SP, em novembro/2005. O tamanho da amostra foi estimado em 2.092 crianças, considerando-se a prevalência histórica de 11,2%, aceitando-se erro de estimação de 10% e nível de confiança de 95%. A amostra foi probabilística, ponderada e acrescida de 20%, devido à possível ocorrência de perdas. Examinaram-se 2.692 crianças. O diagnóstico foi clínico, baseado na normatização da Organização Mundial da Saúde (OMS). Para avaliação dos dados espaciais, utilizou-se o programa CartaLinx (v1.2), sendo os setores de demanda escolar digitalizados de acordo com as divisões do planejamento da Secretaria de Educação. Os dados foram analisados estatisticamente, sendo a análise da estrutura espacial dos eventos calculadas usando o programa Geoda. RESULTADOS: A prevalência de tracoma nos escolares de Botucatu foi de 2,9%, tendo sido detectados casos de tracoma folicular. A análise exploratória espacial não permitiu rejeitar a hipótese nula de aleatoriedade (I= -0,45, p>0,05), não havendo setores de demanda significativos. A análise feita para os polígonos de Thiessen também mostrou que o padrão global foi aleatório (I= -0,07; p=0,49). Entretanto, os indicadores locais apontaram um agrupamento do tipo baixo-baixo para um polígono ao norte da área urbana. CONCLUSÃO: A prevalência de tracoma em escolares de Botucatu foi de 2,9%. A análise da distribuição espacial não revelou áreas de maior aglomeração de casos. Embora o padrão global da doença não reproduza as condições socioeconômicas da população, a prevalência mais baixa do tracoma foi encontrada em setores de menor vulnerabilidade social.

Another prefiltering algorithm for adaptive IIR filtering

An algorithm for adaptive IIR filtering that uses prefiltering structure in direct form is presented. This structure has an estimation error that is a linear function of the coefficients. This property greatly simplifies the derivation of gradient-based algorithms. Computer simulations show that the proposed structure improves convergence speed.

Observer-based control design for switched affine systems and applications to DC-DC converters

This paper deals with the problem of establishing a state estimator for switched affine systems. For that matter, a modification on the Luenberger observer is proposed, the switched Luenberger observer, whose idea is to design one output gain matrix for each mode of the original system. The efficiency of the proposed method relies on a simplification on estimation error which is proved always valid, guaranteeing the estimation error to asymptotically converge to zero, for any initial state and switching law. Next, a dynamic output-dependent switching law is formulated. Then, design methodologies using linear matrix inequalities are proposed, which, to the authors's knowledge, have not yet been applied to this problem. Finally, observers for DC-DC converters are designed and simulated as application examples. © 2013 Brazilian Society for Automatics - SBA.

Algorithms for spacecraft formation flying navigation based on wireless positioning system measurements

Spacecraft formation flying navigation continues to receive a great deal of interest. The research presented in this dissertation focuses on developing methods for estimating spacecraft absolute and relative positions, assuming measurements of only relative positions using wireless sensors. The implementation of the extended Kalman filter to the spacecraft formation navigation problem results in high estimation errors and instabilities in state estimation at times. This is due tp the high nonlinearities in the system dynamic model. Several approaches are attempted in this dissertation aiming at increasing the estimation stability and improving the estimation accuracy. A differential geometric filter is implemented for spacecraft positions estimation. The differential geometric filter avoids the linearization step (which is always carried out in the extended Kalman filter) through a mathematical transformation that converts the nonlinear system into a linear system. A linear estimator is designed in the linear domain, and then transformed back to the physical domain. This approach demonstrated better estimation stability for spacecraft formation positions estimation, as detailed in this dissertation. The constrained Kalman filter is also implemented for spacecraft formation flying absolute positions estimation. The orbital motion of a spacecraft is characterized by two range extrema (perigee and apogee). At the extremum, the rate of change of a spacecraft’s range vanishes. This motion constraint can be used to improve the position estimation accuracy. The application of the constrained Kalman filter at only two points in the orbit causes filter instability. Two variables are introduced into the constrained Kalman filter to maintain the stability and improve the estimation accuracy. An extended Kalman filter is implemented as a benchmark for comparison with the constrained Kalman filter. Simulation results show that the constrained Kalman filter provides better estimation accuracy as compared with the extended Kalman filter. A Weighted Measurement Fusion Kalman Filter (WMFKF) is proposed in this dissertation. In wireless localizing sensors, a measurement error is proportional to the distance of the signal travels and sensor noise. In this proposed Weighted Measurement Fusion Kalman Filter, the signal traveling time delay is not modeled; however, each measurement is weighted based on the measured signal travel distance. The obtained estimation performance is compared to the standard Kalman filter in two scenarios. The first scenario assumes using a wireless local positioning system in a GPS denied environment. The second scenario assumes the availability of both the wireless local positioning system and GPS measurements. The simulation results show that the WMFKF has similar accuracy performance as the standard Kalman Filter (KF) in the GPS denied environment. However, the WMFKF maintains the position estimation error within its expected error boundary when the WLPS detection range limit is above 30km. In addition, the WMFKF has a better accuracy and stability performance when GPS is available. Also, the computational cost analysis shows that the WMFKF has less computational cost than the standard KF, and the WMFKF has higher ellipsoid error probable percentage than the standard Measurement Fusion method. A method to determine the relative attitudes between three spacecraft is developed. The method requires four direction measurements between the three spacecraft. The simulation results and covariance analysis show that the method’s error falls within a three sigma boundary without exhibiting any singularity issues. A study of the accuracy of the proposed method with respect to the shape of the spacecraft formation is also presented.

Reconstructed pCO2 data from tree ring cellulose d13C during 1902-2005 at 10 sites in the Tropics and Northern Subtropics

This is the reconstructed pCO2 data from Tree ring cellulose d13C data with estimation errors for 10 sites (location given below) by a geochemical model as given in the publication by Trina Bose, Supriyo Chakraborty, Hemant Borgaonkar, Saikat Sengupta. This data was generated in Stable Isotope Laboratory, Indian Institute of Tropical Meteorology, Pune - 411008, India

Analysis of the geometric altimetry to support aircraft optimal trajectories within the future 4d trajectory management

Over the past few years, the common practice within air traffic management has been that commercial aircraft fly by following a set of predefined routes to reach their destination. Currently, aircraft operators are requesting more flexibility to fly according to their prefer- ences, in order to achieve their business objectives. Due to this reason, much research effort is being invested in developing different techniques which evaluate aircraft optimal trajectory and traffic synchronisation. Also, the inefficient use of the airspace using barometric altitude overall in the landing and takeoff phases or in Continuous Descent Approach (CDA) trajectories where currently it is necessary introduce the necessary reference setting (QNH or QFE). To solve this problem and to permit a better airspace management born the interest of this research. Where the main goals will be to evaluate the impact, weakness and strength of the use of geometrical altitude instead of the use of barometric altitude. Moreover, this dissertation propose the design a simplified trajectory simulator which is able to predict aircraft trajectories. The model is based on a three degrees of freedom aircraft point mass model that can adapt aircraft performance data from Base of Aircraft Data, and meteorological information. A feature of this trajectory simulator is to support the improvement of the strategic and pre-tactical trajectory planning in the future Air Traffic Management. To this end, the error of the tool (aircraft Trajectory Simulator) is measured by comparing its performance variables with actual flown trajectories obtained from Flight Data Recorder information. The trajectory simulator is validated by analysing the performance of different type of aircraft and considering different routes. A fuel consumption estimation error was identified and a correction is proposed for each type of aircraft model. In the future Air Traffic Management (ATM) system, the trajectory becomes the fundamental element of a new set of operating procedures collectively referred to as Trajectory-Based Operations (TBO). Thus, governmental institutions, academia, and industry have shown a renewed interest for the application of trajectory optimisation techniques in com- mercial aviation. The trajectory optimisation problem can be solved using optimal control methods. In this research we present and discuss the existing methods for solving optimal control problems focusing on direct collocation, which has received recent attention by the scientific community. In particular, two families of collocation methods are analysed, i.e., Hermite-Legendre-Gauss-Lobatto collocation and the pseudospectral collocation. They are first compared based on a benchmark case study: the minimum fuel trajectory problem with fixed arrival time. For the sake of scalability to more realistic problems, the different meth- ods are also tested based on a real Airbus 319 El Cairo-Madrid flight. Results show that pseudospectral collocation, which has shown to be numerically more accurate and computa- tionally much faster, is suitable for the type of problems arising in trajectory optimisation with application to ATM. Fast and accurate optimal trajectory can contribute properly to achieve the new challenges of the future ATM. As atmosphere uncertainties are one of the most important issues in the trajectory plan- ning, the final objective of this dissertation is to have a magnitude order of how different is the fuel consumption under different atmosphere condition. Is important to note that in the strategic phase planning the optimal trajectories are determined by meteorological predictions which differ from the moment of the flight. The optimal trajectories have shown savings of at least 500 [kg] in the majority of the atmosphere condition (different pressure, and temperature at Mean Sea Level, and different lapse rate temperature) with respect to the conventional procedure simulated at the same atmosphere condition.This results show that the implementation of optimal profiles are beneficial under the current Air traffic Management (ATM).