Related papers: Multidimensional Sorting: Comparative Statics
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
Sorting is a foundational primitive in modern data processing, influencing the execution speed of high-performance data pipelines. However, the algorithmic landscape is currently bifurcated by a pervasive "Stability Tax": practitioners must…
A common approach to statistical learning with big-data is to randomly split it among $m$ machines and learn the parameter of interest by averaging the $m$ individual estimates. In this paper, focusing on empirical risk minimization, or…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a…
The problem of ranking is a multi-billion dollar problem. In this paper we present an overview of several production quality ranking systems. We show that due to conflicting goals of employing the most effective machine learning models and…
Recognising that real-world optimisation problems have multiple interdependent components can be quite easy. However, providing a generic and formal model for dependencies between components can be a tricky task. In fact, a PMIC can be…
Stochastic dynamic matching problems have recently gained attention in the stochastic-modeling community due to their diverse applications, such as supply-chain management and kidney exchange programs. In this paper, we study a matching…
The presence of a phase transition in a finite system can be deduced, together with its order, from the shape of the distribution of the order parameter. This issue has been extensively studied in multifragmentation experiments, with…
Structural causal models provide a formalism to express causal relations between variables of interest. Models and variables can represent a system at different levels of abstraction, whereby relations may be coarsened and refined according…
Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
We propose a novel framework for analyzing the dynamics of distribution shift in real-world systems that captures the feedback loop between learning algorithms and the distributions on which they are deployed. Prior work largely models…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
Diffusion models have become the de facto standard for modern visual generation, including well-established frameworks such as latent diffusion and flow matching. Recently, modeling high-order dynamics has emerged as a promising frontier in…
We develop an analytically tractable model featuring heterogeneous workers and firms, where labor markets clear through a one-to-many sorting mechanism. Firms determine both the number and composition of their employees, shaping (1) the…
As input data distributions evolve, the predictive performance of machine learning models tends to deteriorate. In the past, predictive performance was considered the key indicator to monitor. However, explanation aspects have come to…
We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the shared information between the two subsystems. If the…
Many allocation problems in multiagent systems rely on agents specifying cardinal preferences. However, allocation mechanisms can be sensitive to small perturbations in cardinal preferences, thus causing agents who make ``small" or…