Related papers: Anchor-Based Function Extrapolation with Proven Bo…
This paper deals with probabilistic upper bounds for the error in functional estimation defined on some interpolation and extrapolation designs, when the function to estimate is supposed to be analytic. The error pertaining to the estimate…
This paper addresses the problem of accurately estimating a function on one domain when only its discrete samples are available on another domain. To answer this challenge, we utilize a neural network, which we train to incorporate prior…
Recent advances in uncertainty quantification increasingly emphasise the distinction between aleatory and epistemic uncertainty in machine learning, motivating the need for more unified frameworks. However, despite much progress in…
We define extrapolation as any type of statistical inference on a conditional function (e.g., a conditional expectation or conditional quantile) evaluated outside of the support of the conditioning variable. This type of extrapolation…
This paper examines the problem of extrapolation of an analytic function for $x > 1$ given perturbed samples from an equally spaced grid on $[-1,1]$. Mathematical folklore states that extrapolation is in general hopelessly ill-conditioned,…
Soft extrapolation refers to the problem of recovering a function from its samples, multiplied by a fast-decaying window and perturbed by an additive noise, over an interval which is potentially larger than the essential support of the…
In this present paper, I propose a derivation of unified interpolation and extrapolation function that predicts new values inside and outside the given range by expanding direct Taylor series on the middle point of given data set.…
Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by…
We present a method that allows efficient and safe approximation of model predictive controllers using kernel interpolation. Since the computational complexity of the approximating function scales linearly with the number of data points, we…
The challenge to measure exposures regularly forces financial institutions into a choice between an overwhelming computational burden or oversimplification of risk. To resolve this unsettling dilemma, we systematically investigate replacing…
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 method is suggested allowing for the improvement of accuracy of self-similar factor and root approximants, constructed from asymptotic series. The method is based on performing a power transform of the given asymptotic series, with the…
Artificial Neural Networks (ANNs) implement a specific form of multi-variate extrapolation and will generate an output for any input pattern, even when there is no similar training pattern. Extrapolations are not necessarily to be trusted,…
The problem of regression extrapolation, or out-of-distribution generalization, arises when predictions are required at test points outside the range of the training data. In such cases, the non-parametric guarantees for regression methods…
Almost every numerical task can be cast as extrapolation with respect to the fidelity or tolerance parameters of a consistent numerical method. This perspective enables probabilistic uncertainty quantification and optimal experimental…
The problem is addressed of defining the values of functions, whose variables tend to infinity, from the knowledge of these functions at asymptotically small variables close to zero. For this purpose, the extrapolation by means of different…
The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical…
The notion of interpolation and extrapolation is fundamental in various fields from deep learning to function approximation. Interpolation occurs for a sample $x$ whenever this sample falls inside or on the boundary of the given dataset's…
Meta-learning approaches enable machine learning systems to adapt to new tasks given few examples by leveraging knowledge from related tasks. However, a large number of meta-training tasks are still required for generalization to unseen…
Canonical work handling distribution shifts typically necessitates an entire target distribution that lands inside the training distribution. However, practical scenarios often involve only a handful of target samples, potentially lying…