Related papers: The energy distance for ensemble and scenario redu…
Quantifying the differences between networks is a challenging and ever-present problem in network science. In recent years a multitude of diverse, ad hoc solutions to this problem have been introduced. Here we propose that simple and…
Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum…
This paper presents a novel solution paradigm of general optimization under both exogenous and endogenous uncertainties. This solution paradigm consists of a probability distribution (PD)-free method of obtaining deterministic equivalents…
The Expectation-Maximisation (EM) algorithm is a central tool in statistics and machine learning, widely used for latent-variable models such as Gaussian Mixture Models (GMMs). Despite its ubiquity, EM is typically treated as a…
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…
Recent developments in generative modeling have utilized score-based methods coupled with stochastic differential equations to sample from complex probability distributions. However, these and other performant sampling methods generally…
In this paper, we study the problem of sampling from a distribution under the constraint of differential privacy (DP). Prior works measure the utility of DP sampling with density ratio-based measures such as KL divergence. However, such…
In this paper, we compare the performance of two scenario-based numerical methods to solve stochastic optimal control problems: scenario trees and particles. The problem consists in finding strategies to control a dynamical system perturbed…
Understanding proper distance measures between distributions is at the core of several learning tasks such as generative models, domain adaptation, clustering, etc. In this work, we focus on mixture distributions that arise naturally in…
The unequal representation of different groups in a sample population can lead to discrimination of minority groups when machine learning models make automated decisions. To address these issues, fairness-aware machine learning jointly…
Wasserstein distance is a key metric for quantifying data divergence from a distributional perspective. However, its application in privacy-sensitive environments, where direct sharing of raw data is prohibited, presents significant…
Energy-based models (EBMs) have experienced a resurgence within machine learning in recent years, including as a promising alternative for probabilistic regression. However, energy-based regression requires a proposal distribution to be…
The energy distance is used to test distributional equality, and as a loss function in machine learning. While $D^2(X, Y)=0$ only when $X\sim Y$, the sensitivity to different moments is of practical importance. This work considers $D^2(X,…
This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…
Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…
The multi-period dynamics of energy storage (ES), intermittent renewable generation and uncontrollable power loads, make the optimization of power system operation (PSO) challenging. A multi-period optimal PSO under uncertainty is…
The most efficient MC weights for the calculation of physical, canonical expectation values are not necessarily those of the canonical ensemble. The use of suitably generalized ensembles can lead to a much faster convergence of the…
The rare-event sampling problem has long been the central limiting factor in molecular dynamics (MD), especially in biomolecular simulation. Recently, diffusion models such as BioEmu have emerged as powerful equilibrium samplers that…
The approximation of invariant measures for nonlinear ergodic stochastic differential equations (SDEs) is a central problem in scientific computing, with important applications in stochastic sampling, physics, and ecology. We first propose…
Ensemble techniques in recommender systems have demonstrated accuracy improvements of 10-30%, yet their environmental impact remains unmeasured. While deep learning recommendation algorithms can generate up to 3,297 kg CO2 per paper,…