Background and purpose: Machine learning is a class of modern and strong tools that can solve many important problems that nowadays humans may be faced with. Support vector regression (SVR) is a way to build a regression model which is an incredible member of the machine learning family. SVR has been proven to be an effective tool in real-value function estimation. As a supervised-learning appr...

In this short article, we describe how the correlation of typical diffusion processes arising e.g. in financial modelling can be exploited – by means of asymptotic analysis of principal components – to make Feynman-Kac PDEs of high dimension computationally tractable. We explore the links to dimension adaptive sparse grids [GG03], anchored ANOVA decompositions and dimension-wise integration [GH...

Clustering is the problem of identifying the distribution of patterns and intrinsic correlations in large data sets by partitioning the data points into similarity classes. The clustering problem has been widely studied in machine learning, databases, and statistics. This paper studies the problem of clustering high dimensional data. The paper proposes an algorithm called the CoFD algorithm, wh...

Random projection trees have proven to be effective for approximate nearest neighbor searches in high dimensional spaces where conventional methods are not applicable due to excessive usage of memory and computational time. We show that building multiple trees on the same data can improve the performance even further, without significantly increasing the total computational cost of queries when...

We propose MUMBO, the first high-performing yet computationally efficient acquisition function for multi-task Bayesian optimization. Here, challenge is to perform optimization by evaluating low-cost functions somehow related our true target function. This a broad class of problems including popular task multi-fidelity However, while information-theoretic are known provide state-of-the-art optim...

In this paper we target at developing discretization-invariant, namely dimension-independent, Markov chain Monte Carlo (MCMC) methods to explore PDEconstrained Bayesian inverse problems in infinite dimensional parameter spaces. In particular, we present two frameworks to achieve this goal: Metropolize-then-discretize and discretize-then-Metropolize. The former refers to the method of first prop...

With constantly increasing software and architectural complexities and machine scales, creating accurate performance models for applications with large parameter spaces becomes extremely challenging. Approaches using analytic models are difficult and time consuming to construct, limited in scope, and can fail to capture full system and application complexity. To retain these details and at the ...

We present a direct discretization of the electronic Schrödinger equation. It is based on one-dimensional Meyer wavelets from which we build an anisotropic multiresolution analysis for general particle spaces by a tensor product construction. We restrict these spaces to the case of antisymmetric functions. To obtain finite-dimensional subspaces we first discuss semi-discretization with respect ...