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The brittle fragmentation of spheres is studied numerically by a 3D Discrete Element Model. Large scale computer simulations are performed with models that consist of agglomerates of many spherical particles, interconnected by beam-truss…
Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
In this paper, we present a method for factor analysis of discrete data. This is accomplished by fitting a dependent Poisson model with a factor structure. To be able to analyze ordinal data, we also consider a truncated Poisson…
Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…
The permeability of two-dimensional fractures with self-affine fractal roughness is studied via analytic arguments and numerical simulations. The limit where the roughness amplitude is small compared with average fracture aperture is…
This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…
We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…
Sign-Perturbed Sum (SPS) is a powerful finite-sample system identification algorithm which can construct confidence regions for the true data generating system with exact coverage probabilities, for any finite sample size. SPS was developed…
Fr\'echet means, conceptually appealing, generalize the Euclidean expectation to general metric spaces. We explore how well Fr\'echet means can be estimated from independent and identically distributed samples and uncover a fundamental…
Developing meaningful and efficient representations that separate the fundamental structure of the data generation mechanism is crucial in representation learning. However, Disentangled Representation Learning has not fully shown its…
Sampling strategies are important for sparse imaging methodologies, especially those employing the discrete Fourier transform (DFT). Chaotic sensing is one such methodology that employs deterministic, fractal sampling in conjunction with…
Estimation of optical aberrations from volumetric intensity images is a key step in sensorless adaptive optics for 3D microscopy. Recent approaches based on deep learning promise accurate results at fast processing speeds. However,…
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…
The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably…
With appropriately chosen sampling probabilities, sampling-based random projection can be used to implement large-scale statistical methods, substantially reducing computational cost while maintaining low statistical error. However,…
We present FPDetect, a low overhead approach for detecting logical errors and soft errors affecting stencil computations without generating false positives. We develop an offline analysis that tightly estimates the number of floating-point…
Assessing the validity of a real-world system with respect to given quality criteria is a common yet costly task in industrial applications due to the vast number of required real-world tests. Validating such systems by means of simulation…
This paper describes, in detail, techniques for measuring the Hurst parameter. Measurements are given on artificial data both in a raw form and corrupted in various ways to check the robustness of the tools in question. Measurements are…
Neutron and x-ray scattering experiments traditionally rely upon histogrammed data sets, which are analysed using least-squares curve fitting of multiple probability distribution components to quantify separately the various scientific…