Related papers: The energy distance for ensemble and scenario redu…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
We ask the following question: what are the relative contributions of the ensemble mean and the ensemble standard deviation to the skill of a site-specific probabilistic temperature forecast? Is it the case that most of the benefit of using…
The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…
Single-cell omics enable the profiles of cells, which contain large numbers of biological features, to be quantified. Cluster analysis, a dimensionality reduction process, is used to reduce the dimensions of the data to make it…
We investigate a state discrimination problem in operationally the most general framework to use a probability, including both classical, quantum theories, and more. In this wide framework, introducing closely related family of ensembles…
This paper proposes a method for generating typical scenarios based on system-level macroscopic characteristics of power system and considering its stability properties. First, considering uncertainties such as renewable energy generation…
Generative Adversarial Nets (GANs) are very successful at modeling distributions from given samples, even in the high-dimensional case. However, their formulation is also known to be hard to optimize and often not stable. While this is…
This paper introduces an innovative interval prediction methodology aimed at addressing the limitations of current evaluation indicators while enhancing prediction accuracy and reliability. To achieve this, new evaluation metrics are…
In data-driven learning and inference tasks, the high cost of acquiring samples from the target distribution often limits performance. A common strategy to mitigate this challenge is to augment the limited target samples with data from a…
We introduce a new statistical quantity the energy to test whether two samples originate from the same distributions. The energy is a simple logarithmic function of the distances of the observations in the variate space. The distribution of…
A Markov decision process (MDP) framework is adopted to represent ensemble control of devices with cyclic energy consumption patterns, e.g., thermostatically controlled loads. Specifically we utilize and develop the class of MDP models…
Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
This paper focuses on a similarity measure, known as the Wasserstein distance, with which to compare images. The Wasserstein distance results from a partial differential equation (PDE) formulation of Monge's optimal transport problem. We…
This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the…
We deal with the problem of energy management in buildings subject to uncertain occupancy. To this end, we formulate this as a finite horizon optimization program and optimize with respect to the windows' blinds position, radiator and…
Considering widely dispersed uncertain renewable energy sources (RESs), scenario-based stochastic optimization is an effective method for the economic dispatch of renewables-rich power systems. However, on classic computers, to simulate RES…
This paper introduces a new way to compact a continuous probability distribution $F$ into a set of representative points called support points. These points are obtained by minimizing the energy distance, a statistical potential measure…
The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…
We revisit Markowitz's mean-variance portfolio selection model by considering a distributionally robust version, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures…