Related papers: Sequential search based on kriging: convergence an…
Kriging based on Gaussian random fields is widely used in reconstructing unknown functions. The kriging method has pointwise predictive distributions which are computationally simple. However, in many applications one would like to predict…
In spatial statistics, a common method for prediction over a Gaussian random field (GRF) is maximum likelihood estimation combined with kriging. For massive data sets, kriging is computationally intensive, both in terms of CPU time and…
We provide a new kriging procedure of processes on graphs. Based on the construction of Gaussian random processes indexed by graphs, we extend to this framework the usual linear prediction method for spatial random fields, known as kriging.…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is…
We propose a randomized greedy search algorithm to find a point estimate for a random partition based on a loss function and posterior Monte Carlo samples. Given the large size and awkward discrete nature of the search space, the…
The estimation of small probabilities of failure from computer simulations is a classical problem in engineering, and the Subset Simulation algorithm proposed by Au & Beck (Prob. Eng. Mech., 2001) has become one of the most popular method…
In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables…
Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…
Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of…
The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given…
Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…
We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive…
Sparse approximation is important in many applications because of concise form of an approximant and good accuracy guarantees. The theory of compressed sensing, which proved to be very useful in the image processing and data sciences, is…
Approaches to learning Bayesian networks from data typically combine a scoring function with a heuristic search procedure. Given a Bayesian network structure, many of the scoring functions derived in the literature return a score for the…
Backtracking search is a powerful algorithmic paradigm that can be used to solve many problems. It is in a certain sense the dual of variable elimination; but on many problems, e.g., SAT, it is vastly superior to variable elimination in…
This paper investigates the problem of determining a binary-valued function through a sequence of strategically selected queries. The focus is an algorithm called Generalized Binary Search (GBS). GBS is a well-known greedy algorithm for…
This article proposes a new kriging that has a rational form. It is shown that the generalized least squares estimate of the mean from rational kriging is much more well behaved than that from ordinary kriging. Parameter estimation and…
The paper presents a comprehensive performance evaluation of some heuristic search algorithms in the context of autonomous systems and robotics. The objective of the study is to evaluate and compare the performance of different search…
This paper deals with the Gaussian process based approximation of a code which can be run at different levels of accuracy. This method, which is a particular case of co-kriging, allows us to improve a surrogate model of a complex computer…