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The metric distortion of a randomized social choice function (RSCF) quantifies its worst-case approximation ratio to the optimal social cost when the voters' costs for alternatives are given by distances in a metric space. This notion has…

Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modelling stochastic optimization…

Stochastic estimators are fundamental to large-scale optimization, where population quantities must be inferred from noisy oracle observations. Although influential methods such as momentum, SPIDER, STORM, and PAGE have been highly…

This paper addresses the problem of robust option pricing within the framework of Vectorial Martingale Optimal Transport (VMOT). We investigate the geometry of VMOT solutions for $N$-period market models and demonstrate that, when the…

In this paper, we develop the metric geometry of ranking statistics, proving that the two major permutation distances in the statistics literature -- Kendall tau and Spearman footrule -- extend naturally to incomplete rankings with both…

It is well known that no reasonable voting rule is strategyproof. Moreover, the common Plurality rule is particularly prone to strategic behavior of the voters and empirical studies show that people often vote strategically in practice.…

The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…

There has been growing interest in generalization performance of large multilayer neural networks that can be trained to achieve zero training error, while generalizing well on test data. This regime is known as 'second descent' and it…

Disentangled representation learning offers useful properties such as dimension reduction and interpretability, which are essential to modern deep learning approaches. Although deep learning techniques have been widely applied to…

Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related…

The robust topology optimization formulation that introduces the eroded and dilated versions of the design has gained increasing popularity in recent years, mainly because of its ability to produce designs satisfying a minimum length scale.…

We present results of numerical experiments for neural networks with stochastic gradient-based optimization with adaptive momentum. This widely applied optimization has proved convergence and practical efficiency, but for long-run training…

Based on the framework of multiple instance learning (MIL), tremendous works have promoted the advances of weakly supervised object detection (WSOD). However, most MIL-based methods tend to localize instances to their discriminative parts…

The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well-informed decisions. In this paper, we quantify, for the class of distortion risk measures with…

Most metric learning algorithms, as well as Fisher's Discriminant Analysis (FDA), optimize some cost function of different measures of within-and between-class distances. On the other hand, Support Vector Machines(SVMs) and several Multiple…

Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…

Device variability is a bottleneck for the scalability of semiconductor quantum devices. Increasing device control comes at the cost of a large parameter space that has to be explored in order to find the optimal operating conditions. We…

Support vector machine (SVM) has been one of the most popular learning algorithms, with the central idea of maximizing the minimum margin, i.e., the smallest distance from the instances to the classification boundary. Recent theoretical…

Repeated sampling is a standard way to spend test-time compute, but its benefit is controlled by the latent distribution of correctness across examples, not by one-call accuracy alone. We study the binary correctness layer of repeated LLM…

Swept Volume (SV), the volume displaced by an object when it is moving along a trajectory, is considered a useful metric for motion planning. First, SV has been used to identify collisions along a trajectory, because it directly measures…