Related papers: Online minimum search for Brownian motion and the …
Line search is a fundamental part of iterative optimization methods for unconstrained and bound-constrained optimization problems to determine suitable step lengths that provide sufficient improvement in each iteration. Traditional line…
We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure,…
Given a pre-trained classifier and multiple human experts, we investigate the task of online classification where model predictions are provided for free but querying humans incurs a cost. In this practical but under-explored setting,…
Online detection of instantaneous changes in the generative process of a data sequence generally focuses on retrospective inference of such change points without considering their future occurrences. We extend the Bayesian Online Change…
We propose an algorithm for Bayesian functional optimisation - that is, finding the function to optimise a process - guided by experimenter beliefs and intuitions regarding the expected characteristics (length-scale, smoothness, cyclicity…
Bayesian inference is useful to obtain a predictive distribution with a small generalization error. However, since posterior distributions are rarely evaluated analytically, we employ the variational Bayesian inference or sampling method to…
The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…
We study fractional Brownian motion (fBm) characterized by the Hurst exponent H. Using a Monte Carlo sampling technique, we are able to numerically generate fBm processes with an absorbing boundary at the origin at discrete times for a…
Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the interior of a domain and on its boundary. It arises in various applications such as in biology, materials science, and finance.…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
The popularity of Bayesian optimization methods for efficient exploration of parameter spaces has lead to a series of papers applying Gaussian processes as surrogates in the optimization of functions. However, most proposed approaches only…
We address the problem of searching for a change point in an anomalous process among a finite set of M processes. Specifically, we address a composite hypothesis model in which each process generates measurements following a common…
The purpose of this article is to give a rather thorough understanding of the compact support property for measure-valued processes corresponding to semi-linear equations of the form \[ \begin{aligned}& u_t=Lu+\beta u-\alpha u^p \text{in}…
We consider the issue of reporting the result of search experiment in the most unbiased and efficient way, i.e. in a way which allows an easy interpretation and combination of results and which do not depend on whether the experimenters…
Divide-and-conquer Bayesian methods consist of three steps: dividing the data into smaller computationally manageable subsets, running a sampling algorithm in parallel on all the subsets, and combining parameter draws from all the subsets.…
The online search problem is a fundamental problem in finance. The numerous direct applications include searching for optimal prices for commodity trading and trading foreign currencies. In this paper, we analyze the advice complexity of…
This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson…
Using the measurements collected at a number of known locations by a moving binary sensor, characterised by an unknown threshold, the problem is to estimate the parameters of a biochemical source, continuously releasing material into the…
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…
Most traditional online learning algorithms are based on variants of mirror descent or follow-the-leader. In this paper, we present an online algorithm based on a completely different approach, tailored for transductive settings, which…