Related papers: A linear dispersive mechanism for numerical error …

We consider one of the most basic multiple testing problems that compares expectations of multivariate data among several groups. As a test statistic, a conventional (approximate) $t$-statistic is considered, and we determine its rejection…

Predictive models -- learned from observational data not covering the complete data distribution -- can rely on spurious correlations in the data for making predictions. These correlations make the models brittle and hinder generalization.…

We show in detail how to determine the time-reversed representation of a stationary hidden stochastic process from linear combinations of its forward-time $\epsilon$-machine causal states. This also gives a check for the $k$-cryptic…

One of approaches to quantum gravity is different models of a discrete pregeometry. An example of a discrete pregeometry on a microscopic scale is introduced. This is the particular case of a causal set. The causal set is a locally finite…

This article presents a new spectral analysis approach for dispersion error and a methodology to numerically evaluate it. In practice, this new analysis allows the numerical study of dispersion errors on all types of mesh and for multiple…

If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution,…

Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process…

Spurious currents, which are often observed near a curved interface in the multiphase simulations by diffuse interface methods, are unphysical phenomena and usually damage the computational accuracy and stability. In this paper, the…

Methods based on polynomial chaos expansion allow to approximate the behavior of systems with uncertain parameters by deterministic dynamics. These methods are used in a wide range of applications, spanning from simulation of uncertain…

Asymmetric systematic errors arise when there is a non-linear dependence of a result on a nuisance parameter. Their combination is traditionally done by adding positive and negative deviations separately in quadrature. There is no sound…

Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…

Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…

Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…

Causal effect estimation is important for many tasks in the natural and social sciences. We design algorithms for the continuous partial identification problem: bounding the effects of multivariate, continuous treatments when unmeasured…

This paper studies the propagation of finite-sample uncertainty under nonlinear transformations commonly used in statistical decision systems. In particular, we consider process capability indices, which are widely used in manufacturing…

This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…

We develop a new randomized iterative algorithm---stochastic dual ascent (SDA)---for finding the projection of a given vector onto the solution space of a linear system. The method is dual in nature: with the dual being a non-strongly…

The Kullback-Leibler (KL) divergence is frequently used in data science. For discrete distributions on large state spaces, approximations of probability vectors may result in a few small negative entries, rendering the KL divergence…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

K-means is a classical clustering algorithm with wide applications. However, soft K-means, or fuzzy c-means at m=1, remains unsolved since 1981. To address this challenging open problem, we propose a novel clustering model, i.e.…