Related papers: Online minimum search for Brownian motion and the …
In this short note we consider the computational problem of numerically finding the minimum and arg-min of a Brownian bridge. Using well-known results by Pitman, Tanaka, Vervaat and Williams we are able to show that the bisection method has…
Efficiency of search for randomly distributed targets is a prominent problem in many branches of the sciences. For the stochastic process of L\'evy walks, a specific range of optimal efficiencies was suggested under variation of search…
In this paper we resolve an open problem proposed by Lai, Poor, Xin, and Georgiadis (2011, IEEE Transactions on Information Theory). Consider a sequence of Brownian Motions with unknown drift equal to one or zero, which we may be observed…
In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an…
We implement Bayesian model selection and parameter estimation for the case of fractional Brownian motion with measurement noise and a constant drift. The approach is tested on artificial trajectories and shown to make estimates that match…
We present Bayesian Binary Search (BBS), a novel probabilistic variant of the classical binary search/bisection algorithm. BBS leverages machine learning/statistical techniques to estimate the probability density of the search space and…
In this paper, a sequential search method for finding the global minimum of an objective function is presented, The descent gradient search is repeated until the global minimum is obtained. The global minimum is located by a process of…
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…
A Bayesian approach is presented for detecting and characterising the signal from discrete objects embedded in a diffuse background. The approach centres around the evaluation of the posterior distribution for the parameters of the discrete…
Online learning is an inferential paradigm in which parameters are updated incrementally from sequentially available data, in contrast to batch learning, where the entire dataset is processed at once. In this paper, we assume that…
In networks of dynamic systems, one challenge is to identify the interconnection structure on the basis of measured signals. Inspired by a Bayesian approach in [1], in this paper, we explore a Bayesian model selection method for identifying…
Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…
This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior…
The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact…
Predictive business process monitoring aims at providing predictions about running instances by analyzing logs of completed cases in a business process. Recently, a lot of research focuses on increasing productivity and efficiency in a…
Model-based sequential approaches to discrete "black-box" optimization, including Bayesian optimization techniques, often access the same points multiple times for a given objective function in interest, resulting in many steps to find the…
We report our progress in data analysis on two-point correlation functions of the $B$ meson using sequential Bayesian method. The data set of measurement is obtained using the Oktay-Kronfeld (OK) action for the bottom quarks (valence…
We introduce a simulation-based, amortised Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks' parameters with a likelihood-free method. In the first step a graph…
Estimating parameters of quantum systems is usually done by performing a sequence of predetermined experiments and post-processing the resulting data. It is known that online design, where the choice of the next experiment is based on the…
The purpose of this note is to collect in one place a few results about simple random walk and Brownian motion which are often useful. These include standard results such as Beurling estimates, large deviation estimates, and a method for…