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The Hilbert Schmidt Independence Criterion (HSIC) is a kernel dependence measure that has applications in various aspects of machine learning. Conveniently, the objectives of different dimensionality reduction applications using HSIC often…

Segmentation of microscopy images constitutes an ill-posed inverse problem due to measurement noise, weak object boundaries, and limited labeled data. Although deep neural networks provide flexible nonparametric estimators, unconstrained…

Superpixel algorithms aim to over-segment the image by grouping pixels that belong to the same object. Many state-of-the-art superpixel algorithms rely on minimizing objective functions to enforce color ho- mogeneity. The optimization is…

We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group $SE(2) = \mathbb{R}^2 \rtimes S^1$ with a metric tensor depending on a smooth external…

We develop a new approach for distributed distance computation in planar graphs that is based on a variant of the metric compression problem recently introduced by Abboud et al. [SODA'18]. One of our key technical contributions is in…

Unlike conventional mechanisms, compliant mechanisms produce the desired deformations by exploiting elastic strain and do not need, therefore, moving parts. The number of degrees of freedom of a conventional mechanism, also called mobility,…

Cardinality constrained submodular function maximization, which aims to select a subset of size at most $k$ to maximize a monotone submodular utility function, is the key in many data mining and machine learning applications such as data…

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…

In the decremental single-source shortest paths problem, the goal is to maintain distances from a fixed source $s$ to every vertex $v$ in an $m$-edge graph undergoing edge deletions. In this paper, we conclude a long line of research on…

We present self-supervised geometric perception (SGP), the first general framework to learn a feature descriptor for correspondence matching without any ground-truth geometric model labels (e.g., camera poses, rigid transformations). Our…

This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the lack of differentiability of the nonlinearity in the state…

Parameter-free stochastic optimization aims to design algorithms that are agnostic to the underlying problem parameters while still achieving convergence rates competitive with optimally tuned methods. While some parameter-free methods do…

We propose a two-scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain computational efficiency. By using a conveniently constructed…

This paper proposes an algorithmic framework for various reconfiguration problems using zero-suppressed binary decision diagrams (ZDDs), a data structure for families of sets. In general, a reconfiguration problem checks if there is a…

When the data are sparse, optimization of hyperparameters of the kernel in Gaussian process regression by the commonly used maximum likelihood estimation (MLE) criterion often leads to overfitting. We show that choosing hyperparameters (in…

The applications of traditional statistical feature selection methods to high-dimension, low sample-size data often struggle and encounter challenging problems, such as overfitting, curse of dimensionality, computational infeasibility, and…

We present a systematic approach to the optimal placement of finitely many sensors in order to infer a finite-dimensional parameter from point evaluations of the solution of an associated parameter-dependent elliptic PDE. The quality of the…

This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…

In a previous work we introduced, in the context of gravitational wave science, an initial study on an automated domain-decomposition approach for reduced basis through hp-greedy refinement. The approach constructs local reduced bases of…

Many real-world problems can be formulated as geometric optimization problems in high dimensions, especially in the fields of machine learning and data mining. Moreover, we often need to take into account of outliers when optimizing the…