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We provide a simple proof of the radial symmetry of any nonnegative minimizer for a general class of quasi-linear minimization problems.
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
We propose a computational framework for computing low-rank approximations to the ensemble of solutions of a parametrized system of the form $A(\xi)x(\xi)+g(x(\xi))=b(\xi)$ for multiple parameter values. The central idea is to reinterpret…
We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…
Confidence calibration - the process to calibrate the output probability distribution of neural networks - is essential for safety-critical applications of such networks. Recent works verify the link between mis-calibration and overfitting.…
We study the problem of semantic segmentation calibration. Lots of solutions have been proposed to approach model miscalibration of confidence in image classification. However, to date, confidence calibration research on semantic…
The minimal network problem is a classical topic in geometric measure theory and the calculus of variations, which aims to find networks of minimal length connecting given points. Most classical results are established in the Euclidean…
We establish that regular flat partitions are locally minimizing for the interface energy with respect to $L^1$ perturbations of the phases. Regular flat partitions are partitions of open sets in $\mathbb{R}^2$ whose network of interfaces…
Screening classifiers are increasingly used to identify qualified candidates in a variety of selection processes. In this context, it has been recently shown that, if a classifier is calibrated, one can identify the smallest set of…
Optimization networks are a new methodology for holistically solving interrelated problems that have been developed with combinatorial optimization problems in mind. In this contribution we revisit the core principles of optimization…
In this work, we propose a mean-squared error-based risk that enables the comparison and optimization of estimators of squared calibration errors in practical settings. Improving the calibration of classifiers is crucial for enhancing the…
For the minimization of state-based systems (i.e. the reduction of the number of states while retaining the system's semantics), there are two obvious aspects: removing unnecessary states of the system and merging redundant states in the…
Image segmentation algorithms can be understood as a collection of pixel classifiers, for which the outcomes of nearby pixels are correlated. Classifier models can be calibrated using Inductive Conformal Prediction, but this requires…
We study a variational problem motivated by models of species population density in a nonhomogeneous environment. We first analyze local minimizers and the structure of the saturated region (where the population attains its maximal density)…
For classification models based on neural networks, the maximum predicted class probability is often used as a confidence score. This score rarely predicts well the probability of making a correct prediction and requires a post-processing…
In this paper we prove two new abstract compactness criteria in normed spaces. To this end we first introduce the notion of an equinormed set using a suitable family of semi-norms on the given normed space satisfying some natural…
A set $A$ is said to split a finite set $B$ if exactly half the elements of $B$ (up to rounding) are contained in $A$. We study the dual notions: (1) splitting family, which is a collection of sets such that any subset of $\{1,\ldots,k\}$…
A primary challenge in metagenomics is reconstructing individual microbial genomes from the mixture of short fragments created by sequencing. Recent work leverages the sparsity of the assembly graph to find $r$-dominating sets which enable…
We study the problem of computing the minimum adversarial perturbation of the Nearest Neighbor (NN) classifiers. Previous attempts either conduct attacks on continuous approximations of NN models or search for the perturbation by some…
In this work, I collect and discuss a series of open questions in one-dimensional geometric optimization in Euclidean spaces. The focus is on two classes of problems: maximal distance minimizers and Steiner trees. Maximal distance…