Related papers: Reliable Adaptive Cubature Using Digital Sequences
The efficiency of a Markov chain Monte Carlo algorithm might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated…
We study approximation of the embedding $\ell_p^m \hookrightarrow \ell_q^m$, $1 \leq p < q \leq \infty$, based on randomized algorithms that use up to $n$ arbitrary linear functionals as information on a problem instance where $n \ll m$. By…
Making calibrated online predictions is a central challenge in modern AI systems. Much of the existing literature focuses on fully adversarial environments where outcomes may be arbitrary, leading to conservative algorithms that can perform…
Monte Carlo integration using quantum computers has been widely investigated, including applications to concrete problems. It is known that quantum algorithms based on quantum amplitude estimation (QAE) can compute an integral with a…
The efficient approximation of quantity of interest derived from PDEs with lognormal diffusivity is a central challenge in uncertainty quantification. In this study, we propose a multilevel quasi-Monte Carlo framework to approximate…
In this paper, we describe a framework to compute expected convergence rates for residuals based on the Calder\'on identities for general second order differential operators for which fundamental solutions are known. The idea is that these…
This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…
Approximating adequate number of clusters in multidimensional data is an open area of research, given a level of compromise made on the quality of acceptable results. The manuscript addresses the issue by formulating a transductive…
This paper studies a generalization of hyperinterpolation over the high-dimensional unit cube. Hyperinterpolation of degree \( m \) serves as a discrete approximation of the \( L_2 \)-orthogonal projection of the same degree, using Fourier…
We introduce kernel thinning, a new procedure for compressing a distribution $\mathbb{P}$ more effectively than i.i.d. sampling or standard thinning. Given a suitable reproducing kernel $\mathbf{k}_{\star}$ and $O(n^2)$ time, kernel…
A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for good…
Most commonly used \emph{adaptive} algorithms for univariate real-valued function approximation and global minimization lack theoretical guarantees. Our new locally adaptive algorithms are guaranteed to provide answers that satisfy a…
QM (quantum mechenics) and MM (molecular mechenics) coupling methods are widely used in simulations of crystalline defects. In this paper, we construct a residual based a posteriori error indicator for QM/MM coupling approximations. We…
Distortion risk measures play a critical role in quantifying risks associated with uncertain outcomes. Accurately estimating these risk measures in the context of computationally expensive simulation models that lack analytical tractability…
In interactive imitation learning (IL), uncertainty quantification offers a way for the learner (i.e. robot) to contend with distribution shifts encountered during deployment by actively seeking additional feedback from an expert (i.e.…
We consider the problem of estimating the measure of subsets in very large networks. A prime tool for this purpose is the Markov Chain Monte Carlo (MCMC) algorithm. This algorithm, while extremely useful in many cases, still often suffers…
In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neural network controller and disturbances. Based on an estimate…
A novel theoretical and numerical framework for the estimation of Sobol sensitivity indices for models in which inputs are confined to a non-rectangular domain (e.g., in presence of inequality constraints) is developed. Two numerical…
Slice sampling is a standard Monte Carlo technique for Dirichlet process (DP)-based models, widely used in posterior simulation. However, formal assessments of the scalability of posterior slice samplers have remained largely unexplored,…
Most existing examples of full conformal predictive systems, split-conformal predictive systems, and cross-conformal predictive systems impose severe restrictions on the adaptation of predictive distributions to the test object at hand. In…