A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination with no pivoting as well as block Gaussian elimination, approximation of the leading and trailing singular spaces of an ill conditioned matrix, associated wit...

As the standard method for solving systems of linear equations, Gaussian elimination (GE) is one of the most important and ubiquitous numerical algorithms. However, its successful use relies on understanding its numerical stability properties and how to organize its computations for efficient execution on modern computers. We give an overview of GE, ranging from theory to computation. We explai...

We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing point approximation that is well-tailored to the convolutional kernel. This allows us to gain the generalisation benefit of a convolutional kernel, together wit...

The problem of consistently estimating the sparsity pattern of a vector β∗ ∈ R based on observations contaminated by noise arises in various contexts, including subset selection in regression, structure estimation in graphical models, sparse approximation, and signal denoising. We analyze the behavior of l1-constrained quadratic programming (QP), also referred to as the Lasso, for recovering th...

Gaussian or multivariate normal distributions are very popular and important probability models. Gaussian potentials [5] are multivariate normal density functions. Such a distribution is often given as a product of conditional Gaussian densities, which are more general than Gaussian potentials. These are related to Gaussian hints [11] and Gaussian belief functions [9, 10]. Gaussian potentials, ...

The following paper deals with the estimation of partial parameters for non stationary sinusoids. First the existing bias for the analysis of non stationary sinusoids in a standard estimator is discussed. Then a new approach to bias reduction is proposed that consists of frequency slope estimation and demodulation to reduce the bias of the standard parameter estimator. The new approach does not...

A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination with no pivoting as well as block Gaussian elimination, approximation of the leading and trailing singular spaces of an ill conditioned matrix, associated wit...

In this paper we introduce a new method for performing computational inference on log-Gaussian Cox processes (LGCP). Contrary to current practice, we do not approximate by a counting process on a partition of the domain, but rather attack the point process likelihood directly. In order to do this, we use the continuously specified Markovian random fields introduced by Lindgren et al. (2011). Th...

This paper analyzes transient characteristics of Gaussian queues. More specifically, we determine the logarithmic asymptotics of P(Q0 > pB,QTB > qB), where Qt denotes the workload at time t . For any pair (p, q), three regimes can be distinguished: (A) For small values of T , one of the events {Q0 > pB} and {QTB > qB} will essentially imply the other. (B) Then there is an intermediate range of ...

Abstract We investigate the use of certain data-dependent estimates of the complexity of a function class, called Rademacher and Gaussian complexities. In a decision theoretic setting, we prove general risk bounds in terms of these complexities. We consider function classes that can be expressed as combinations of functions from basis classes and show how the Rademacher and Gaussian complexitie...