New Inference Concepts for Analysing Complex Data

The main purpose of this workshop was to assemble international leaders from statistics and machine learning to identify important research problems, to cross-fertilize between the disciplines, and to ultimately start coordinated research efforts toward better solutions. The workshop focused on discussing modern methods for analysis complex high dimensional data with applications to econometrics, finance, biomedicine, genomics etc

Locally adaptive factor processes for multivariate time series

In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If such time-varying smoothness is not accounted for, one can obtain misleading inferences and predictions, with over-smoothing across erratic time intervals and under-smoothing across times exhibiting slow variation. This can lead to mis-calibration of predictive intervals, which can be substantially too narrow or wide depending on the time. We propose a locally adaptive factor process for characterizing multivariate mean-covariance changes in continuous time, allowing locally varying smoothness in both the mean and covariance matrix. This process is constructed utilizing latent dictionary functions evolving in time through nested Gaussian processes and linearly related to the observed data with a sparse mapping. Using a differential equation representation, we bypass usual computational bottlenecks in obtaining MCMC and online algorithms for approximate Bayesian inference. The performance is assessed in simulations and illustrated in a financial application

Predicting loss given default

The topic of credit risk modeling has arguably become more important than ever before given the recent financial turmoil. Conform the international Basel accords on banking supervision, financial institutions need to prove that they hold sufficient capital to protect themselves and the financial system against unforeseen losses caused by defaulters. In order to determine the required minimal capital, empirical models can be used to predict the loss given default (LGD). The main objectives of this doctoral thesis are to obtain new insights in how to develop and validate predictive LGD models through regression techniques. The first part reveals how good real-life LGD can be predicted and which techniques are best. Its value is in particular in the use of default data from six major international financial institutions and the evaluation of twenty-four different regression techniques, making this the largest LGD benchmarking study so far. Nonetheless, it is found that the resulting models have limited predictive performance no matter what technique is employed, although non-linear techniques yield higher performances than traditional linear techniques. The results of this study strongly advocate the need for financial institutions to invest in the collection of more relevant data. The second part introduces a novel validation framework to backtest the predictive performance of LGD models. The proposed key idea is to assess the test performance relative to the performance during model development with statistical hypothesis tests based on commonly used LGD predictive performance metrics. The value of this framework comprises a solution to the lack of reference values to determine acceptable performance and to possible performance bias caused by too little data. This study offers financial institutions a practical tool to prove the validity of their LGD models and corresponding predictions as required by national regulators. The third part uncovers whether the optimal regression technique can be selected based on typical characteristics of the data. Its value is especially in the use of the recently introduced concept of datasetoids which allows the generation of thousands of datasets representing real-life relations, thereby circumventing the scarcity problem of publicly available real-life datasets, making this the largest meta learning regression study so far. It is found that typical data based characteristics do not play any role in the performance of a technique. Nonetheless, it is proven that algorithm based characteristics are good drivers to select the optimal technique. This thesis may be valuable for any financial institution implementing credit risk models to determine their minimal capital requirements compliant with the Basel accords. The new insights provided in this thesis may support financial institutions to develop and validate their own LGD models. The results of the benchmarking and meta learning study can help financial institutions to select the appropriate regression technique to model their LGD portfolio's. In addition, the proposed backtesting framework, together with the benchmarking results can be employed to support the validation of the internally developed LGD models

Artificial intelligence techniques for predicting tidal effects based on geographic locations in Ghana

Tidal forces as a result of attraction of external bodies (Sun, Moon and Stars) through gravity and are a source of noise in many geoscientific field observations. The solid earth tides cause deformation. This deformation results in displacement in geographic positions on the surface of the earth. The displacement due to tidal effects can result in deformation of engineering structures, loss of lives, and economic cost. Tidal forces also help in detecting other environmental and tectonic signals. This study quantifies the effects of solid earth tides on stationary survey controls in five regions of Ghana. The study is in two stages: firstly, the solid earth tides were estimated for each control by a geometric approach (combining Navier’s equation of motion and Love theories). Secondly, estimation using two artificial intelligence methods (Multivariate Adaptive Regression Splines (MARS) and Backpropagation Artificial Neural Network (ANN)). Based on statistical indices of Mean Square Error (MSE) and Correlation Coefficient (R), BPANN, and MARS models can be used as a realistic alternative technique in quantifying solid earth tides for the study area. The MSE and R (MSE; BPANN = 1.3249 × 10–04 and MSE; MARS = 2.2052 × 10–06; R; BPANN = –0.6067 and R; MARS 0.6570) values indicate that MARS outperforms BPANN in quantifying solid earth tides in the study area. BPANN and MARS can be used as an efficient tool for quantifying tidal values based on geographic positions for geodetic deformation studies within the study area

Application of Higher-Order Neural Networks to Financial Time-Series Prediction

Financial time series data is characterized by non-linearities, discontinuities and high frequency, multi-polynomial components. Not surprisingly, conventional Artificial Neural Networks (ANNs) have difficulty in modelling such complex data. A more appropriate approach is to apply Higher-Order ANNs, which are capable of extracting higher order polynomial coefficients in the data. Moreover, since there is a one-to-one correspondence between network weights and polynomial coefficients, HONNs (unlike ANNs generally) can be considered open-, rather than 'closed box' solutions, and thus hold more appeal to the financial community. After developing Polynomial and Trigonometric HONNs, we introduce the concept of HONN groups. The latter incorporate piecewise continuous activation functions and thresholds, and as a result are capable of modelling discontinuous (piecewise continuous) data, and what's more to any degree of accuracy. Several other PHONN variants are also described. The performance of P(T)HONNs and HONN groups on representative financial time series is described (credit ratings and exchange rates). In short, HONNs offer roughly twice the performance of MLP/BP on financial time series prediction, and HONN groups around 10% further improvement

A comparative study on global wavelet and polynomial models for nonlinear regime-switching systems

A comparative study of wavelet and polynomial models for non-linear Regime-Switching (RS) systems is carried out. RS systems, considered in this study, are a class of severely non-linear systems, which exhibit abrupt changes or dramatic breaks in behaviour, due to RS caused by associated events. Both wavelet and polynomial models are used to describe discontinuous dynamical systems, where it is assumed that no a priori information about the inherent model structure and the relative regime switches of the underlying dynamics is known, but only observed input-output data are available. An Orthogonal Least Squares (OLS) algorithm interfered with by an Error Reduction Ratio (ERR) index and regularised by an Approximate Minimum Description Length (AMDL) criterion, is used to construct parsimonious wavelet and polynomial models. The performance of the resultant wavelet models is compared with that of the relative polynomial models, by inspecting the predictive capability of the associated representations. It is shown from numerical results that wavelet models are superior to polynomial models, in respect of generalisation properties, for describing severely non-linear RS systems

Linear quantile mixed models

Dependent data arise in many studies. For example, children with the same parents or living in neighbouring geographic areas tend to be more alike in many characteristics than individuals chosen at random from the population at large; observations taken repeatedly on the same individual are likely to be more similar than observations from different individuals. Frequently adopted sampling designs, such as cluster, multilevel, spatial, and repeated measures (or longitudinal or panel), may induce this dependence, which the analysis of the data needs to take into due account. In a previous publication (Geraci and Bottai, Biostatistics 2007), we proposed a conditional quantile regression model for continuous responses where a random intercept was included along with fixed-coefficient predictors to account for between-subjects dependence in the context of longitudinal data analysis. Conditional on the random intercept, the response was assumed to follow an asymmetric Laplace distribution. The approach hinged upon the link existing between the minimization of weighted least absolute deviations, typically used in quantile regression, and the maximization of Laplace likelihood. As a follow up to that study, here we consider an extension of those models to more complex dependence structures in the data, which are modelled by including multiple random effects in the linear conditional quantile functions. Differently from the Gibbs sampling expectation-maximization approach proposed previously, the estimation of the fixed regression coefficients and of the random effects covariance matrix is based on a combination of Gaussian quadrature approximations and optimization algorithms. The former include Gauss-Hermite and Gauss-Laguerre quadratures for, respectively, normal and double exponential (i.e., symmetric Laplace) random effects; the latter include a gradient search algorithm and general purpose optimizers. As a result, some of the computational burden associated with large Gibbs sample sizes is avoided. We also discuss briefly an estimation approach based on generalized Clarke derivatives. Finally, a simulation study is presented and some preliminary results are shown