Related papers: Rejoinder to "Multivariate quantiles and multiple-…
Due to its length and several inaccuracies, this article is no longer suggested for reading. Moreover, in the meantime certain results presented herein could be improved by the author in a non-trivial fashion. Instead, the reader is…
We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. We…
Multivariate data that combine binary, categorical, count and continuous outcomes are common in the social and health sciences. We propose a semiparametric Bayesian latent variable model for multivariate data of arbitrary type that does not…
This expository monograph cuts a short path from the common, elementary background in geometry (linear algebra, vector bundles, and algebraic ideals) to the most advanced theorems about involutive exterior differential systems: (1) The…
In [Y.~K.~Hu, K.~A.~Kopotun, X.~M.~Yu, Constr. Approx. 2000], the authors have obtained a characterization of best $n$-term piecewise polynomial approximation spaces as real interpolation spaces between $L^p$ and some spaces of bounded…
Margin has played an important role on the design and analysis of learning algorithms during the past years, mostly working with the maximization of the minimum margin. Recent years have witnessed the increasing empirical studies on the…
This paper also has excessove overlap with the following papers also written by the authors or their collaborators: gr-qc/0502060, gr-qc/0606028, gr-qc/0511095, gr-qc/0505078, gr-qc/0603044, gr-qc/0608014, gr-qc/0510123, gr-qc/0607109,…
This work provides simple algorithms for multi-class (and multi-label) prediction in settings where both the number of examples n and the data dimension d are relatively large. These robust and parameter free algorithms are essentially…
In the present paper, a notion of M-basis and multi dimension of a multi vector space is introduced and some of its properties are studied.
The novel Riemannian view on shape optimization developed in [Schulz, FoCM, 2014] is extended to a Lagrange-Newton approach for PDE constrained shape optimization problems. The extension is based on optimization on Riemannian vector space…
This is a contribution to the proceedings of the 2016 "Loops and legs" conference, based on the talk by HF. The talk was based on the paper "On the reduction of Generalized Polylogarithms to $\text{Li}_n$ and $\text{Li}_{2,2}$ and on the…
We offer new results and new directions in the study of operator-valued kernels and their factorizations. Our approach provides both more explicit realizations and new results, as well as new applications. These include: (i) an explicit…
Rejoinder of ``Objective Priors: An Introduction for Frequentists'' by M. Ghosh [arXiv:1108.2120]
Basic derivative formulas are presented for hypoelliptic heat semigroups and harmonic functions extending earlier work in the elliptic case. Emphasis is placed on developing integration by parts formulas at the level of local martingales.…
Apart from an account of classical preliminaries, this volume contains a systematic introduction to Sobolev spaces and functions of bounded variation with selected applications. This is installment III of a four part discussion of certain…
We tackle the problem of multiscale regression for predictors that are spatially or temporally indexed, or with a pre-specified multiscale structure, with a Bayesian modular approach. The regression function at the finest scale is expressed…
Dimension reduction and variable selection are performed routinely in case-control studies, but the literature on the theoretical aspects of the resulting estimates is scarce. We bring our contribution to this literature by studying…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms…
This work studies the computational aspects of multivariate convex regression in dimensions $d \ge 5$. Our results include the \emph{first} estimators that are minimax optimal (up to logarithmic factors) with polynomial runtime in the…