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We study multivariate numerical integration of smooth functions in weighted Sobolev spaces with dominating mixed smoothness $\alpha\geq 2$ defined over the $s$-dimensional unit cube. We propose a new quasi-Monte Carlo (QMC)-based quadrature…
We propose a simple interpolation-based method for the efficient approximation of gradients in neural ODE models. We compare it with the reverse dynamic method (known in the literature as "adjoint method") to train neural ODEs on…
Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In this context, the iterates are vectors generated from a…
This paper is the companion article of [Gloria, M3AS, 21 (2011), No. 3, pp 1601-1630]. One common drawback among numerical homogenization methods is the presence of the so-called resonance error, which roughly speaking is a function of the…
Learning from Demonstration depends on a robot learner generalising its learned model to unseen conditions, as it is not feasible for a person to provide a demonstration set that accounts for all possible variations in non-trivial tasks.…
This report mainly focused on the basic concepts and the recovery methods for the random sampling. The recovery methods involve the orthogonal matching pursuit algorithm and the gradient-based total variation strategy. In particular, a fast…
Machine learning systems perform well on pattern matching tasks, but their ability to perform algorithmic or logical reasoning is not well understood. One important reasoning capability is algorithmic extrapolation, in which models trained…
Time series observations can be seen as realizations of an underlying dynamical system governed by rules that we typically do not know. For time series learning tasks, we need to understand that we fit our model on available data, which is…
In many applications of machine learning, certain categories of examples may be underrepresented in the training data, causing systems to underperform on such "few-shot" cases at test time. A common remedy is to perform data augmentation,…
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…
This work investigates finite differences and the use of interpolation models to obtain approximations to the first and second derivatives of a function. Here, it is shown that if a particular set of points is used in the interpolation…
We present a novel method for controlling extrapolation in the prediction profiler in the JMP software. The prediction profiler is a graphical tool for exploring high dimensional prediction surfaces for statistical and machine learning…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
We investigate the acceleration of stationary iterations for multi-term Sylvester equation by means of reduced rank extrapolation (RRE). Theoretical convergence results and implementations are provided for both small and large-scale…
Time delay estimation has long been an active area of research. In this work, we show that compressive sensing with interpolation may be used to achieve good estimation precision while lowering the sampling frequency. We propose an…
In non-private stochastic convex optimization, stochastic gradient methods converge much faster on interpolation problems -- problems where there exists a solution that simultaneously minimizes all of the sample losses -- than on…
Extrapolation from a source to a target, e.g., from adults to children, is a promising approach to utilizing external information when data are sparse. In the context of meta-analysis, one is commonly faced with a small number of studies,…
Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification,…
Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined…
Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…