Related papers: Random construction of interpolating sets for high…

The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…

The problems of computational data processing involving regression, interpolation, reconstruction and imputation for multidimensional big datasets are becoming more important these days, because of the availability of data and their widely…

Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An…

An efficient algorithm is proposed for Bayesian model calibration, which is commonly used to estimate the model parameters of non-linear, computationally expensive models using measurement data. The approach is based on Bayesian statistics:…

The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…

High-dimensional clustering often relies on geometric or local-similarity structure, but the dominant separation between groups may not always be location-based. Differences in dispersion can create asymmetric local-neighborhood patterns:…

This paper introduces the concept of hyperpolation: a way of generalising from a limited set of data points that is a peer to the more familiar concepts of interpolation and extrapolation. Hyperpolation is the task of estimating the value…

A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively splits the set of classes into two subsets, and trains a binary classifier to distinguish…

Our understanding of physical systems generally depends on our ability to match complex computational modelling with measured experimental outcomes. However, simulations with large parameter spaces suffer from inverse problem instabilities,…

Bayesian inference with nested sampling requires a likelihood-restricted prior sampling method, which draws samples from the prior distribution that exceed a likelihood threshold. For high-dimensional problems, Markov Chain Monte Carlo…

Conventional sampling and interpolation commonly rely on discrete measurements. In this paper, we develop a theoretical framework for extrapolation of signals in higher dimensions from knowledge of the continuous waveform on bounded…

The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general…

Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…

The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…

When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimates. If the estimates are good there is an infinite family of power…

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…

One way to investigate the precision of estimates likely to result from planned experiments and planned epidemiological studies is to simulate a large number of possible outcomes and analyse the sets of possible results. This appears to be…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…

Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can…