Sparse Learning for Variable Selection with Structures and Nonlinearities

In this thesis we discuss machine learning methods performing automated variable selection for learning sparse predictive models. There are multiple reasons for promoting sparsity in the predictive models. By relying on a limited set of input variables the models naturally counteract the overfitting problem ubiquitous in learning from finite sets of training points. Sparse models are cheaper to use for predictions, they usually require lower computational resources and by relying on smaller sets of inputs can possibly reduce costs for data collection and storage. Sparse models can also contribute to better understanding of the investigated phenomenons as they are easier to interpret than full models.Comment: PhD thesi

Proportionate Recursive Maximum Correntropy Criterion Adaptive Filtering Algorithms and their Performance Analysis

The maximum correntropy criterion (MCC) has been employed to design outlier-robust adaptive filtering algorithms, among which the recursive MCC (RMCC) algorithm is a typical one. Motivated by the success of our recently proposed proportionate recursive least squares (PRLS) algorithm for sparse system identification, we propose to introduce the proportionate updating (PU) mechanism into the RMCC, leading to two sparsity-aware RMCC algorithms: the proportionate recursive MCC (PRMCC) algorithm and the combinational PRMCC (CPRMCC) algorithm. The CPRMCC is implemented as an adaptive convex combination of two PRMCC filters. For PRMCC, its stability condition and mean-square performance were analyzed. Based on the analysis, optimal parameter selection in nonstationary environments was obtained. Performance study of CPRMCC was also provided and showed that the CPRMCC performs at least as well as the better component PRMCC filter in steady state. Numerical simulations of sparse system identification corroborate the advantage of proposed algorithms as well as the validity of theoretical analysis

Seismic Ray Impedance Inversion

This thesis investigates a prestack seismic inversion scheme implemented in the ray parameter domain. Conventionally, most prestack seismic inversion methods are performed in the incidence angle domain. However, inversion using the concept of ray impedance, as it honours ray path variation following the elastic parameter variation according to Snell’s law, shows the capacity to discriminate different lithologies if compared to conventional elastic impedance inversion. The procedure starts with data transformation into the ray-parameter domain and then implements the ray impedance inversion along constant ray-parameter profiles. With different constant-ray-parameter profiles, mixed-phase wavelets are initially estimated based on the high-order statistics of the data and further refined after a proper well-to-seismic tie. With the estimated wavelets ready, a Cauchy inversion method is used to invert for seismic reflectivity sequences, aiming at recovering seismic reflectivity sequences for blocky impedance inversion. The impedance inversion from reflectivity sequences adopts a standard generalised linear inversion scheme, whose results are utilised to identify rock properties and facilitate quantitative interpretation. It has also been demonstrated that we can further invert elastic parameters from ray impedance values, without eliminating an extra density term or introducing a Gardner’s relation to absorb this term. Ray impedance inversion is extended to P-S converted waves by introducing the definition of converted-wave ray impedance. This quantity shows some advantages in connecting prestack converted wave data with well logs, if compared with the shearwave elastic impedance derived from the Aki and Richards approximation to the Zoeppritz equations. An analysis of P-P and P-S wave data under the framework of ray impedance is conducted through a real multicomponent dataset, which can reduce the uncertainty in lithology identification.Inversion is the key method in generating those examples throughout the entire thesis as we believe it can render robust solutions to geophysical problems. Apart from the reflectivity sequence, ray impedance and elastic parameter inversion mentioned above, inversion methods are also adopted in transforming the prestack data from the offset domain to the ray-parameter domain, mixed-phase wavelet estimation, as well as the registration of P-P and P-S waves for the joint analysis. The ray impedance inversion methods are successfully applied to different types of datasets. In each individual step to achieving the ray impedance inversion, advantages, disadvantages as well as limitations of the algorithms adopted are detailed. As a conclusion, the ray impedance related analyses demonstrated in this thesis are highly competent compared with the classical elastic impedance methods and the author would like to recommend it for a wider application

Accelerating proximal Markov chain Monte Carlo by using an explicit stabilised method

We present a highly efficient proximal Markov chain Monte Carlo methodology to perform Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo approaches, the proposed method is derived from an approximation of the Langevin diffusion. However, instead of the conventional Euler-Maruyama approximation that underpins existing proximal Monte Carlo methods, here we use a state-of-the-art orthogonal Runge-Kutta-Chebyshev stochastic approximation that combines several gradient evaluations to significantly accelerate its convergence speed, similarly to accelerated gradient optimisation methods. The proposed methodology is demonstrated via a range of numerical experiments, including non-blind image deconvolution, hyperspectral unmixing, and tomographic reconstruction, with total-variation and $\ell_1$-type priors. Comparisons with Euler-type proximal Monte Carlo methods confirm that the Markov chains generated with our method exhibit significantly faster convergence speeds, achieve larger effective sample sizes, and produce lower mean square estimation errors at equal computational budget.Comment: 28 pages, 13 figures. Accepted for publication in SIAM Journal on Imaging Sciences (SIIMS