Related papers: Revisiting the D-iteration method: from theoretica…
We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…
This paper deals with the problem of estimating the volume of the excursion set of a function $f:\mathbb{R}^d \to \mathbb{R}$ above a given threshold, under a probability measure on $\mathbb{R}^d$ that is assumed to be known. In the…
We examine some numerical iterative methods for computing the eigenvalues and eigenvectors of real matrices. The five methods examined here range from the simple power iteration method to the more complicated QR iteration method. The…
In this paper we analyze the computational costs of various operations and algorithms in algebraic number fields using exact arithmetic. Let $K$ be an algebraic number field. In the first half of the paper, we calculate the running time and…
There are thousands of papers on rootfinding for nonlinear scalar equations. Here is one more, to talk about an apparently new method, which I call ``Inverse Cubic Iteration'' (ICI) in analogy to the Inverse Quadratic Iteration in Richard…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…
A computer simulation, such as a genetic algorithm, that uses IEEE standard floating-point arithmetic may not produce exactly the same results in two different runs, even if it is rerun on the same computer with the same input and random…
This paper gives specific divergence examples of value-iteration for several major Reinforcement Learning and Adaptive Dynamic Programming algorithms, when using a function approximator for the value function. These divergence examples…
The implicit Euler method integrates systems of ordinary differential equations $$\frac{d x}{d t}=G(t,x(t))$$ with differentiable right-hand side $G : {\mathbb R} \times {\mathbb R}^n \rightarrow {\mathbb R}^n$ from an initial state $x=x(0)…
There has recently been a growing interest in the development of statistical methods to compare medical costs between treatment groups. When cumulative cost is the outcome of interest, right-censoring poses the challenge of informative…
We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error…
Value iteration is a fundamental algorithm for solving Markov Decision Processes (MDPs). It computes the maximal $n$-step payoff by iterating $n$ times a recurrence equation which is naturally associated to the MDP. At the same time, value…
We compare different methods for the computation of the real dilogarithm regarding their ability for using instruction-level parallelism when executed on appropriate CPUs. As a result we present an instruction-level-aware method and compare…
Results about existence and uniqueness of solutions of initial value problem for certain types of partial differential equations are recalled as well as iterative scheme and an error estimate for approximate solutions obtained using this…
In practical computations, the (preconditioned) conjugate gradient (P)CG method is the iterative method of choice for solving systems of linear algebraic equations $Ax=b$ with a real symmetric positive definite matrix $A$. During the…
Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this…
Inference algorithms based on evolving interactions between replicated solutions are introduced and analyzed on a prototypical NP-hard problem - the capacity of the binary Ising perceptron. The efficiency of the algorithm is examined…
We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…