Related papers: Group Averaging for Physics Applications: Accuracy…
Traditional approaches to ensure group fairness in algorithmic decision making aim to equalize ``total'' error rates for different subgroups in the population. In contrast, we argue that the fairness approaches should instead focus only on…
Many supervised learning problems involve high-dimensional data such as images, text, or graphs. In order to make efficient use of data, it is often useful to leverage certain geometric priors in the problem at hand, such as invariance to…
Physical systems obey strict symmetry principles. We expect that machine learning methods that intrinsically respect these symmetries should have higher prediction accuracy and better generalization in prediction of physical dynamics. In…
Cascade SVM (CSVM) can group datasets and train subsets in parallel, which greatly reduces the training time and memory consumption. However, the model accuracy obtained by using this method has some errors compared with direct training. In…
Ensemble models often achieve higher accuracy than single learners, but their ability to maintain small generalization gaps is not always well understood. This study examines how ensembles balance accuracy and overfitting across four…
Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…
Equivariant neural networks are designed to respect symmetries through their architecture, boosting generalization and sample efficiency when those symmetries are present in the data distribution. Real-world data, however, often departs…
To achieve high performance of a machine learning (ML) task, a deep learning-based model must implicitly capture the entire distribution from data. Thus, it requires a huge amount of training samples, and data are expected to fully present…
Given the noisy pairwise measurements among a set of unknown group elements, how to recover them efficiently and robustly? This problem, known as group synchronization, has drawn tremendous attention in the scientific community. In this…
Given the continuous increase in dataset sizes and the complexity of forecasting models, the trade-off between forecast accuracy and computational cost is emerging as an extremely relevant topic, especially in the context of ensemble…
Traditionally model averaging has been viewed as an alternative to model selection with the ultimate goal to incorporate the uncertainty associated with the model selection process in standard errors and confidence intervals by using a…
Symmetry principles underlie and guide scientific theory and research, from Curie's invariance formulation to modern applications across physics, chemistry, and mathematics. Building on a recent matrix Lie group measurement model, this…
Non-parametric tests based on permutation, rotation or sign-flipping are examples of group-invariance tests. These tests test invariance of the null distribution under a set of transformations that has a group structure, in the algebraic…
Covariate balancing is a popular technique for controlling confounding in observational studies. It finds weights for the treatment group which are close to uniform, but make the group's covariate means (approximately) equal to those of the…
The method of model averaging has become an important tool to deal with model uncertainty, for example in situations where a large amount of different theories exist, as are common in economics. Model averaging is a natural and formal…
Ensembles depend on diversity for improved performance. Many ensemble training methods, therefore, attempt to optimize for diversity, which they almost always define in terms of differences in training set predictions. In this paper,…
Machine learning, deep learning, has been accelerating computational physics, which has been used to simulate systems on a lattice. Equivariance is essential to simulate a physical system because it imposes a strong induction bias for the…
Rotation averaging is a synchronization process on single or multiple rotation groups, and is a fundamental problem in many computer vision tasks such as multi-view structure from motion (SfM). Specifically, rotation averaging involves the…
Grouping-based measurement strategies are widely used to reduce measurement complexity in near-term quantum algorithms. While these schemes have typically produced disjoint groups, recently this has been relaxed in what is known as…
This paper is devoted to provide a theoretical underpinning for ensemble forecasting with rapid fluctuations in body forcing and in boundary conditions. Ensemble averaging principles are proved under suitable `mixing' conditions on random…