Professor Karl Morgenstern : zur Erinnerung seines Andenkens

https://www.ester.ee/record=b1434291*es

Functions Returning Values of Dynamic Size

Modern programming languages, such as Ada (Ichbiah 80), permit the definition of functions that return values whose size can not be determined until the function returns. This paper discusses five implementation techniques that can be used to implement this capability. Comparisons of the techniques are provided and guidelines for selecting a particular technique for a compiler are given

Fast Nonlinear Vector Quantile Regression

Quantile regression (QR) is a powerful tool for estimating one or more conditional quantiles of a target variable $\mathrm{Y}$ given explanatory features $\boldsymbol{\mathrm{X}}$. A limitation of QR is that it is only defined for scalar target variables, due to the formulation of its objective function, and since the notion of quantiles has no standard definition for multivariate distributions. Recently, vector quantile regression (VQR) was proposed as an extension of QR for vector-valued target variables, thanks to a meaningful generalization of the notion of quantiles to multivariate distributions via optimal transport. Despite its elegance, VQR is arguably not applicable in practice due to several limitations: (i) it assumes a linear model for the quantiles of the target $\boldsymbol{\mathrm{Y}}$ given the features $\boldsymbol{\mathrm{X}}$; (ii) its exact formulation is intractable even for modestly-sized problems in terms of target dimensions, number of regressed quantile levels, or number of features, and its relaxed dual formulation may violate the monotonicity of the estimated quantiles; (iii) no fast or scalable solvers for VQR currently exist. In this work we fully address these limitations, namely: (i) We extend VQR to the non-linear case, showing substantial improvement over linear VQR; (ii) We propose {vector monotone rearrangement}, a method which ensures the quantile functions estimated by VQR are monotone functions; (iii) We provide fast, GPU-accelerated solvers for linear and nonlinear VQR which maintain a fixed memory footprint, and demonstrate that they scale to millions of samples and thousands of quantile levels; (iv) We release an optimized python package of our solvers as to widespread the use of VQR in real-world applications.Comment: 35 pages, 15 figures, code: https://github.com/vistalab-technion/vq

Literaturwissenschaft und Literaturforschung an der ehemaligen Universität Dorpat : ein historischer Rückblick

Digiteeritud Euroopa Regionaalarengu Fondi rahastusel, projekti "Eesti teadus- ja õppekirjandus" (2014-2020.12.03.21-0848) raames.https://www.ester.ee/record=b4259601*es

Vector Quantile Regression on Manifolds

Quantile regression (QR) is a statistical tool for distribution-free estimation of conditional quantiles of a target variable given explanatory features. QR is limited by the assumption that the target distribution is univariate and defined on an Euclidean domain. Although the notion of quantiles was recently extended to multi-variate distributions, QR for multi-variate distributions on manifolds remains underexplored, even though many important applications inherently involve data distributed on, e.g., spheres (climate and geological phenomena), and tori (dihedral angles in proteins). By leveraging optimal transport theory and c-concave functions, we meaningfully define conditional vector quantile functions of high-dimensional variables on manifolds (M-CVQFs). Our approach allows for quantile estimation, regression, and computation of conditional confidence sets and likelihoods. We demonstrate the approach's efficacy and provide insights regarding the meaning of non-Euclidean quantiles through synthetic and real data experiments

Rapid iterative design of tandem-core virus-like particles using Escherichia Coli-based cell-free protein synthesis

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