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Inverse imaging problems rely on limited and indirect measurements, making reconstruction highly dependent on both regularization and sample locations. We introduce a novel greedy framework for the optimal selection of indirect measurements…
Quantifying uncertainty in automatically generated text is important for letting humans check potential hallucinations and making systems more reliable. Conformal prediction is an attractive framework to provide predictions imbued with…
In recent years, advanced model-based and data-driven control methods are unlocking the potential of complex robotics systems, and we can expect this trend to continue at an exponential rate in the near future. However, ensuring safety with…
Data imbalance remains one of the factors negatively affecting the performance of contemporary machine learning algorithms. One of the most common approaches to reducing the negative impact of data imbalance is preprocessing the original…
In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great significance for improving the computational efficiency and…
A popular assumption for out-of-distribution generalization is that the training data comprises sub-datasets, each drawn from a distinct distribution; the goal is then to "interpolate" these distributions and "extrapolate" beyond them --…
The paper proposes a general quasi-interpolation scheme for high-dimensional function approximation. To facilitate error analysis, we view our quasi-interpolation as a two-step procedure. In the first step, we approximate a target function…
Singular and oscillatory functions feature in numerous applications. The high-accuracy approximation of such functions shall greatly help us develop high-order methods for solving applied mathematics problems. This paper demonstrates that…
A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias…
In the frequentist program, inferential methods with exact control on error rates are a primary focus. The standard approach, however, is to rely on asymptotic approximations, which may not be suitable. This paper presents a general…
We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all…
Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Convolutional and differential distance estimation schemes are considered and, for…
Extrapolation methods use the last few iterates of an optimization algorithm to produce a better estimate of the optimum. They were shown to achieve optimal convergence rates in a deterministic setting using simple gradient iterates. Here,…
We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…
Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems. As a…
We describe a theoretically-motivated algorithm for extrapolation of antenna radiation patterns from a small number of measurements. This algorithm exploits constraints on the antenna's underlying design to avoid ambiguities, but is…
We give new bounds on the reliability function of a typewriter channel with 5 inputs and crossover probability $1/2$. The lower bound is more of theoretical than practical importance; it improves very marginally the expurgated bound,…
We assess the accuracy of Bayesian polynomial extrapolations from small parameter values, x, to large values of x. We consider a set of polynomials of fixed order, intended as a proxy for a fixed-order effective field theory (EFT)…
In computational social science, researchers often use a pre-trained, black box classifier to estimate the frequency of each class in unlabeled datasets. A variety of prevalence estimation techniques have been developed in the literature,…
The paper suggests a method of extrapolation of notion of one-sided semi-infinite sequences representing traces of two-sided band-limited sequences; this features ensure uniqueness of this extrapolation and possibility to use this for…