A basis function approach to Bayesian inference in diffusion processes

In this paper, we present a framework for Bayesian inference in continuous-time diffusion processes. The new method is directly related to the recently proposed variational Gaussian Process approximation (VGPA) approach to Bayesian smoothing of partially observed diffusions. By adopting a basis function expansion (BF-VGPA), both the time-dependent control parameters of the approximate GP process and its moment equations are projected onto a lower-dimensional subspace. This allows us both to reduce the computational complexity and to eliminate the time discretisation used in the previous algorithm. The new algorithm is tested on an Ornstein-Uhlenbeck process. Our preliminary results show that BF-VGPA algorithm provides a reasonably accurate state estimation using a small number of basis functions.

CAUSAL INFERENCE WITH A CONTINUOUS TREATMENT AND OUTCOME: ALTERNATIVE ESTIMATORS FOR PARAMETRIC DOSE-RESPONSE FUNCTIONS WITH APPLICATIONS.

Causal inference with a continuous treatment is a relatively under-explored problem. In this dissertation, we adopt the potential outcomes framework. Potential outcomes are responses that would be seen for a unit under all possible treatments. In an observational study where the treatment is continuous, the potential outcomes are an uncountably infinite set indexed by treatment dose. We parameterize this unobservable set as a linear combination of a finite number of basis functions whose coefficients vary across units. This leads to new techniques for estimating the population average dose-response function (ADRF). Some techniques require a model for the treatment assignment given covariates, some require a model for predicting the potential outcomes from covariates, and some require both. We develop these techniques using a framework of estimating functions, compare them to existing methods for continuous treatments, and simulate their performance in a population where the ADRF is linear and the models for the treatment and/or outcomes may be misspecified. We also extend the comparisons to a data set of lottery winners in Massachusetts. Next, we describe the methods and functions in the R package causaldrf using data from the National Medical Expenditure Survey (NMES) and Infant Health and Development Program (IHDP) as examples. Additionally, we analyze the National Growth and Health Study (NGHS) data set and deal with the issue of missing data. Lastly, we discuss future research goals and possible extensions.

Sensitivity and specificity of machine learning classifiers for glaucoma diagnosis using Spectral Domain OCT and standard automated perimetry

PURPOSE: To evaluate the sensitivity and specificity of machine learning classifiers (MLCs) for glaucoma diagnosis using Spectral Domain OCT (SD-OCT) and standard automated perimetry (SAP). METHODS: Observational cross-sectional study. Sixty two glaucoma patients and 48 healthy individuals were included. All patients underwent a complete ophthalmologic examination, achromatic standard automated perimetry (SAP) and retinal nerve fiber layer (RNFL) imaging with SD-OCT (Cirrus HD-OCT; Carl Zeiss Meditec Inc., Dublin, California). Receiver operating characteristic (ROC) curves were obtained for all SD-OCT parameters and global indices of SAP. Subsequently, the following MLCs were tested using parameters from the SD-OCT and SAP: Bagging (BAG), Naive-Bayes (NB), Multilayer Perceptron (MLP), Radial Basis Function (RBF), Random Forest (RAN), Ensemble Selection (ENS), Classification Tree (CTREE), Ada Boost M1(ADA),Support Vector Machine Linear (SVML) and Support Vector Machine Gaussian (SVMG). Areas under the receiver operating characteristic curves (aROC) obtained for isolated SAP and OCT parameters were compared with MLCs using OCT+SAP data. RESULTS: Combining OCT and SAP data, MLCs' aROCs varied from 0.777(CTREE) to 0.946 (RAN).The best OCT+SAP aROC obtained with RAN (0.946) was significantly larger the best single OCT parameter (p<0.05), but was not significantly different from the aROC obtained with the best single SAP parameter (p=0.19). CONCLUSION: Machine learning classifiers trained on OCT and SAP data can successfully discriminate between healthy and glaucomatous eyes. The combination of OCT and SAP measurements improved the diagnostic accuracy compared with OCT data alone.

Analyzing the n→π* Electronic Transition of Formaldehyde in Water. A Sequential Monte Carlo/Time-Dependent Density Functional Theory

The n→π* absorption transition of formaldehyde in water is analyzed using combined and sequential classical Monte Carlo (MC) simulations and quantum mechanics (QM) calculations. MC simulations generate the liquid solute-solvent structures for subsequent QM calculations. Using time-dependent density functional theory in a localized set of gaussian basis functions (TD-DFT/6-311++G(d,p)) calculations are made on statistically relevant configurations to obtain the average solvatochromic shift. All results presented here use the electrostatic embedding of the solvent. The statistically converged average result obtained of 2300 cm-1 is compared to previous theoretical results available. Analysis is made of the effective dipole moment of the hydrogen-bonded shell and how it could be held responsible for the polarization of the solvent molecules in the outer solvation shells.

Virtual simulation of the postsurgical cosmetic outcome in patientswith pectus excavatum

Pectus excavatum is the most common congenital deformity of the anterior chest wall, in which several ribs and the sternum grow abnormally. Nowadays, the surgical correction is carried out in children and adults through Nuss technic. This technic has been shown to be safe with major drivers as cosmesis and the prevention of psychological problems and social stress. Nowadays, no application is known to predict the cosmetic outcome of the pectus excavatum surgical correction. Such tool could be used to help the surgeon and the patient in the moment of deciding the need for surgery correction. This work is a first step to predict postsurgical outcome in pectus excavatum surgery correction. Facing this goal, it was firstly determined a point cloud of the skin surface along the thoracic wall using Computed Tomography (before surgical correction) and the Polhemus FastSCAN (after the surgical correction). Then, a surface mesh was reconstructed from the two point clouds using a Radial Basis Function algorithm for further affine registration between the meshes. After registration, one studied the surgical correction influence area (SCIA) of the thoracic wall. This SCIA was used to train, test and validate artificial neural networks in order to predict the surgical outcome of pectus excavatum correction and to determine the degree of convergence of SCIA in different patients. Often, ANN did not converge to a satisfactory solution (each patient had its own deformity characteristics), thus invalidating the creation of a mathematical model capable of estimating, with satisfactory results, the postsurgical outcome

Automatic modeling of an orthotic bracing for nonoperative correction of PectusCarinatum

Pectus Carinatum is a deformity of the chest wall, characterized by an anterior protrusion of the sternum, often corrected surgically due to cosmetic motivation. This work presents an alternative approach to the current open surgery option, proposing a novel technique based on a personalized orthosis. Two different processes for the orthosis’ personalization are presented. One based on a 3D laser scan of the patient chest, followed by the reconstruction of the thoracic wall mesh using a radial basis function, and a second one, based on a computer tomography scan followed by a neighbouring cells algorithm. The axial position where the orthosis is to be located is automatically calculated using a Ray-Triangle intersection method, whose outcome is input to a pseudo Kochenek interpolating spline method to define the orthosis curvature. Results show that no significant differences exist between the patient chest physiognomy and the curvature angle and size of the orthosis, allowing a better cosmetic outcome and less initial discomfort

Automatic modeling of an orthotic bracing for nonoperative correction of pectus carinatum

Pectus Carinatum is a deformity of the chest wall, characterized by an anterior protrusion of the sternum, often corrected surgically due to cosmetic motivation. This work presents an alternative approach to the current open surgery option, proposing a novel technique based on a personalized orthosis. Two different processes for the orthosis’ personalization are presented. One based on a 3D laser scan of the patient chest, followed by the reconstruction of the thoracic wall mesh using a radial basis function, and a second one, based on a computer tomography scan followed by a neighbouring cells algorithm. The axial position where the orthosis is to be located is automatically calculated using a Ray-Triangle intersection method, whose outcome is input to a pseudo Kochenek interpolating spline method to define the orthosis curvature. Results show that no significant differences exist between the patient chest physiognomy and the curvature angle and size of the orthosis, allowing a better cosmetic outcome and less initial discomfort.

Chronic liver disease staging classification based on ultrasound, clinical and laboratorial data

In this work the identification and diagnosis of various stages of chronic liver disease is addressed. The classification results of a support vector machine, a decision tree and a k-nearest neighbor classifier are compared. Ultrasound image intensity and textural features are jointly used with clinical and laboratorial data in the staging process. The classifiers training is performed by using a population of 97 patients at six different stages of chronic liver disease and a leave-one-out cross-validation strategy. The best results are obtained using the support vector machine with a radial-basis kernel, with 73.20% of overall accuracy. The good performance of the method is a promising indicator that it can be used, in a non invasive way, to provide reliable information about the chronic liver disease staging.

Conforto bioclimático em Portugal continental no período 1941-2000: cartografia e detecção de evolução

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Ciência e Sistemas de Informação Geográfica

Solar Intensity Forecasting using Artificial Neural Networks and Support Vector Machines

This paper presents several forecasting methodologies based on the application of Artificial Neural Networks (ANN) and Support Vector Machines (SVM), directed to the prediction of the solar radiance intensity. The methodologies differ from each other by using different information in the training of the methods, i.e, different environmental complementary fields such as the wind speed, temperature, and humidity. Additionally, different ways of considering the data series information have been considered. Sensitivity testing has been performed on all methodologies in order to achieve the best parameterizations for the proposed approaches. Results show that the SVM approach using the exponential Radial Basis Function (eRBF) is capable of achieving the best forecasting results, and in half execution time of the ANN based approaches.

Chebyshev polynomial approximation to approximate partial differential equations

This paper suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

Haar wavelets-based approach for quantifying credit portfolio losses

This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelet basis functions and calculate the coefficients of the approximation by inverting its Laplace transform. The Wavelet Approximation (WA) method is specially suitable for non-smooth distributions, often arising in small or concentrated portfolios, when the hypothesis of the Basel II formulas are violated. To test the methodology we consider the Vasicek one-factor portfolio credit loss model as our model framework. WA is an accurate, robust and fast method, allowing to estimate VaR much more quickly than with a Monte Carlo (MC) method at the same level of accuracy and reliability.

Textural classification of land cover using support vector machines: an empirical comparison with parametric, non parametric and hybrid classifiers in the Bolivian Amazon

Land cover classification is a key research field in remote sensing and land change science as thematic maps derived from remotely sensed data have become the basis for analyzing many socio-ecological issues. However, land cover classification remains a difficult task and it is especially challenging in heterogeneous tropical landscapes where nonetheless such maps are of great importance. The present study aims to establish an efficient classification approach to accurately map all broad land cover classes in a large, heterogeneous tropical area of Bolivia, as a basis for further studies (e.g., land cover-land use change). Specifically, we compare the performance of parametric (maximum likelihood), non-parametric (k-nearest neighbour and four different support vector machines - SVM), and hybrid classifiers, using both hard and soft (fuzzy) accuracy assessments. In addition, we test whether the inclusion of a textural index (homogeneity) in the classifications improves their performance. We classified Landsat imagery for two dates corresponding to dry and wet seasons and found that non-parametric, and particularly SVM classifiers, outperformed both parametric and hybrid classifiers. We also found that the use of the homogeneity index along with reflectance bands significantly increased the overall accuracy of all the classifications, but particularly of SVM algorithms. We observed that improvements in producer’s and user’s accuracies through the inclusion of the homogeneity index were different depending on land cover classes. Earlygrowth/degraded forests, pastures, grasslands and savanna were the classes most improved, especially with the SVM radial basis function and SVM sigmoid classifiers, though with both classifiers all land cover classes were mapped with producer’s and user’s accuracies of around 90%. Our approach seems very well suited to accurately map land cover in tropical regions, thus having the potential to contribute to conservation initiatives, climate change mitigation schemes such as REDD+, and rural development policies.

Density functional energy decomposition into one- and two-atom contributions

The present work provides a generalization of Mayer's energy decomposition for the density-functional theory (DFT) case. It is shown that one- and two-atom Hartree-Fock energy components in Mayer's approach can be represented as an action of a one-atom potential VA on a one-atom density ρ A or ρ B. To treat the exchange-correlation term in the DFT energy expression in a similar way, the exchange-correlation energy density per electron is expanded into a linear combination of basis functions. Calculations carried out for a number of density functionals demonstrate that the DFT and Hartree-Fock two-atom energies agree to a reasonable extent with each other. The two-atom energies for strong covalent bonds are within the range of typical bond dissociation energies and are therefore a convenient computational tool for assessment of individual bond strength in polyatomic molecules. For nonspecific nonbonding interactions, the two-atom energies are low. They can be either repulsive or slightly attractive, but the DFT results more frequently yield small attractive values compared to the Hartree-Fock case. The hydrogen bond in the water dimer is calculated to be between the strong covalent and nonbonding interactions on the energy scale

Equivalence of piecewise-linear approximation and Lagrangian relaxation for network revenue management

The network revenue management (RM) problem arises in airline, hotel, media,and other industries where the sale products use multiple resources. It can be formulatedas a stochastic dynamic program but the dynamic program is computationallyintractable because of an exponentially large state space, and a number of heuristicshave been proposed to approximate it. Notable amongst these -both for their revenueperformance, as well as their theoretically sound basis- are approximate dynamic programmingmethods that approximate the value function by basis functions (both affinefunctions as well as piecewise-linear functions have been proposed for network RM)and decomposition methods that relax the constraints of the dynamic program to solvesimpler dynamic programs (such as the Lagrangian relaxation methods). In this paperwe show that these two seemingly distinct approaches coincide for the network RMdynamic program, i.e., the piecewise-linear approximation method and the Lagrangianrelaxation method are one and the same.