Traditional approaches to analysing functional data typically follow a two-step procedure, consisting in first smoothing and then carrying out a functional principal component analysis. The idea underlying this procedure is that functional data are well ap ...
In this thesis, we present a Riemannian framework for the solution of high-dimensional optimization problems with an underlying low-rank tensor structure. Here, the high-dimensionality refers to the size of the search space, while the cost function is scal ...
Many data-intensive applications require real-time analytics over streaming data. In a growing number of domains -- sensor network monitoring, social web applications, clickstream analysis, high-frequency algorithmic trading, and fraud detections to name a ...
Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector corresponding to the smal ...
Radical changes are taking place in the landscape of modern power systems. This massive shift in the way the system is designed and operated has been termed the advent of the ``smart grid''. One of its implications is a strong market pull for faster power ...
Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is their poor scalabili ...
Effective representation methods and proper signal priors are crucial in most signal processing applications. In this thesis we focus on different structured models and we design appropriate schemes that allow the discovery of low dimensional latent struct ...
This thesis focuses on developing efficient algorithmic tools for processing large datasets. In many modern data analysis tasks, the sheer volume of available datasets far outstrips our abilities to process them. This scenario commonly arises in tasks incl ...
This work is concerned with the numerical solution of large-scale linear matrix equations A1XB1T++AKXBKT=C. The most straightforward approach computes XRmxn from the solution of an mn x mn linear system, typically limiting the feasible values of m,n to a f ...
This thesis studies the valuation and hedging of financial derivatives, which is fundamental for trading and risk-management operations in financial institutions. The three chapters in this thesis deal with derivatives whose payoffs are linked to interest ...
Appearing frequently in applications, generalized eigenvalue problems represent one of the core problems in numerical linear algebra. The QZ algorithm of Moler and Stewart is the most widely used algorithm for addressing such problems. Despite its importan ...
We present a non-parametric method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closed-form. The method is eas ...
We infer a term structure of interbank risk from spreads between rates on interest rate swaps indexed to the London Interbank Offered Rate (LIBOR) and overnight indexed swaps. We develop a tractable model of interbank risk to decompose the term structure i ...
