Recently, Chatterjee (2021) introduced a new rank-based correlation coefficient which can be used to measure the strength of dependence between two random variables. This coefficient has already attracted much attention as it converges to the Dette-Siburg-Stoimenov measure (see Dette et al. (2013)), which equals $0$ if and only if the variables are independent and $1$ if and only if one variable is a function of the other. Further, Chatterjee's coefficient is computable in (near) linear time, which makes it appropriate for large-scale applications. In this paper, we expand the theoretical understanding of Chatterjee's coefficient in two directions: (a) First we consider the problem of testing for independence using Chatterjee's correlation. We obtain its asymptotic distribution under any changing sequence of alternatives converging to the null hypothesis (of independence). We further obtain a general result that gives exact detection thresholds and limiting power for Chatterjee's test of independence under natural nonparametric alternatives converging to the null. As applications of this general result, we prove a $n^{-1/4}$ detection boundary for this test and compute explicitly the limiting local power on the detection boundary for popularly studied alternatives in the literature. (b) We then construct a test for non-trivial levels of dependence using Chatterjee's coefficient. In contrast to testing for independence, we prove that, in this case, Chatterjee's coefficient indeed yields a minimax optimal procedure with a $n^{-1/2}$ detection boundary. Our proof techniques rely on Stein's method of exchangeable pairs, a non-asymptotic projection result, and information theoretic lower bounds.
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Machine Translation (MT) continues to improve in quality and adoption, yet the inadvertent perpetuation of gender bias remains a significant concern. Despite numerous studies into gender bias in translations from gender-neutral languages such as Turkish into more strongly gendered languages like English, there are no benchmarks for evaluating this phenomenon or for assessing mitigation strategies. To address this gap, we introduce GATE X-E, an extension to the GATE (Rarrick et al., 2023) corpus, that consists of human translations from Turkish, Hungarian, Finnish, and Persian into English. Each translation is accompanied by feminine, masculine, and neutral variants for each possible gender interpretation. The dataset, which contains between 1250 and 1850 instances for each of the four language pairs, features natural sentences with a wide range of sentence lengths and domains, challenging translation rewriters on various linguistic phenomena. Additionally, we present an English gender rewriting solution built on GPT-3.5 Turbo and use GATE X-E to evaluate it. We open source our contributions to encourage further research on gender debiasing.
Finite element models of electrical machines allow insights in electrothermal stresses which endanger the insulation system of the machine. This paper presents a thermal finite element model of a 3.7 kW squirrel-cage induction machine. The model resolves the conductors and the surrounding insulation materials in the stator slots. A set of transient thermal scenarios is defined and measured in the machine laboratory. These data are used to assess the finite element model.
The goal of automated summarization techniques (Paice, 1990; Kupiec et al, 1995) is to condense text by focusing on the most critical information. Generative large language models (LLMs) have shown to be robust summarizers, yet traditional metrics struggle to capture resulting performance (Goyal et al, 2022) in more powerful LLMs. In safety-critical domains such as medicine, more rigorous evaluation is required, especially given the potential for LLMs to omit important information in the resulting summary. We propose MED-OMIT, a new omission benchmark for medical summarization. Given a doctor-patient conversation and a generated summary, MED-OMIT categorizes the chat into a set of facts and identifies which are omitted from the summary. We further propose to determine fact importance by simulating the impact of each fact on a downstream clinical task: differential diagnosis (DDx) generation. MED-OMIT leverages LLM prompt-based approaches which categorize the importance of facts and cluster them as supporting or negating evidence to the diagnosis. We evaluate MED-OMIT on a publicly-released dataset of patient-doctor conversations and find that MED-OMIT captures omissions better than alternative metrics.
The problem of optimizing discrete phases in a reconfigurable intelligent surface (RIS) to maximize the received power at a user equipment is addressed. Necessary and sufficient conditions to achieve this maximization are given. These conditions are employed in an algorithm to achieve the maximization. New versions of the algorithm are given that are proven to achieve convergence in N or fewer steps whether the direct link is completely blocked or not, where N is the number of the RIS elements, whereas previously published results achieve this in KN or 2N number of steps where K is the number of discrete phases, e.g., [1], [2]. Thus, for a discrete-phase RIS, the techniques presented in this paper achieve the optimum received power in the smallest number of steps published in the literature. In addition, in each of those N steps, the techniques presented in this paper determine only one or a small number of phase shifts with a simple elementwise update rule, which result in a substantial reduction of computation time, as compared to the algorithms in the literature, e.g., [2], [3].
In exterior calculus on smooth manifolds, the exterior derivative and wedge product are natural with respect to smooth maps between manifolds, that is, these operations commute with pullback. In discrete exterior calculus (DEC), simplicial cochains play the role of discrete forms, the coboundary operator serves as the discrete exterior derivative, and the antisymmetrized cup product provides a discrete wedge product. We show that these discrete operations in DEC are natural with respect to abstract simplicial maps. A second contribution is a new averaging interpretation of the discrete wedge product in DEC. We also show that this wedge product is the same as Wilson's cochain product defined using Whitney and de Rham maps.
Evaluation is essential to understanding the value that digital creativity brings to people's experience, for example in terms of their enjoyment, creativity, and engagement. There is a substantial body of research on how to design and evaluate interactive arts and digital creativity applications. There is also extensive Human-Computer Interaction (HCI) literature on how to evaluate user interfaces and user experiences. However, it can be difficult for artists, practitioners, and researchers to navigate such a broad and disparate collection of materials when considering how to evaluate technology they create that is at the intersection of art and interaction. This chapter provides a guide to designing robust user studies of creative applications at the intersection of art, technology and interaction, which we refer to as Media and Arts Technology (MAT). We break MAT studies down into two main kinds: proof-of-concept and comparative studies. As MAT studies are exploratory in nature, their evaluation requires the collection and analysis of both qualitative data such as free text questionnaire responses, interviews, and observations, and also quantitative data such as questionnaires, number of interactions, and length of time spent interacting. This chapter draws on over 15 years of experience of designing and evaluating novel interactive systems to provide a concrete template on how to structure a study to evaluate MATs that is both rigorous and repeatable, and how to report study results that are publishable and accessible to a wide readership in art and science communities alike.
The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs, as Richard E. Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerically partial differential equations (PDEs) in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. We develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs. The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs into pieces corresponding to different dimensions and randomly samples a subset of these dimensional pieces in each iteration of training PINNs. We prove theoretically the convergence and other desired properties of the proposed method. We demonstrate in various diverse tests that the proposed method can solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schr\"{o}dinger equations in tens of thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach. Notably, we solve nonlinear PDEs with nontrivial, anisotropic, and inseparable solutions in 100,000 effective dimensions in 12 hours on a single GPU using SDGD with PINNs. Since SDGD is a general training methodology of PINNs, it can be applied to any current and future variants of PINNs to scale them up for arbitrary high-dimensional PDEs.
We consider locally checkable labeling LCL problems in the LOCAL model of distributed computing. Since 2016, there has been a substantial body of work examining the possible complexities of LCL problems. For example, it has been established that there are no LCL problems exhibiting deterministic complexities falling between $\omega(\log^* n)$ and $o(\log n)$. This line of inquiry has yielded a wealth of algorithmic techniques and insights that are useful for algorithm designers. While the complexity landscape of LCL problems on general graphs, trees, and paths is now well understood, graph classes beyond these three cases remain largely unexplored. Indeed, recent research trends have shifted towards a fine-grained study of special instances within the domains of paths and trees. In this paper, we generalize the line of research on characterizing the complexity landscape of LCL problems to a much broader range of graph classes. We propose a conjecture that characterizes the complexity landscape of LCL problems for an arbitrary class of graphs that is closed under minors, and we prove a part of the conjecture. Some highlights of our findings are as follows. 1. We establish a simple characterization of the minor-closed graph classes sharing the same deterministic complexity landscape as paths, where $O(1)$, $\Theta(\log^* n)$, and $\Theta(n)$ are the only possible complexity classes. 2. It is natural to conjecture that any minor-closed graph class shares the same complexity landscape as trees if and only if the graph class has bounded treewidth and unbounded pathwidth. We prove the "only if" part of the conjecture. 3. In addition to the well-known complexity landscapes for paths, trees, and general graphs, there are infinitely many different complexity landscapes among minor-closed graph classes.
The fusion of causal models with deep learning introducing increasingly intricate data sets, such as the causal associations within images or between textual components, has surfaced as a focal research area. Nonetheless, the broadening of original causal concepts and theories to such complex, non-statistical data has been met with serious challenges. In response, our study proposes redefinitions of causal data into three distinct categories from the standpoint of causal structure and representation: definite data, semi-definite data, and indefinite data. Definite data chiefly pertains to statistical data used in conventional causal scenarios, while semi-definite data refers to a spectrum of data formats germane to deep learning, including time-series, images, text, and others. Indefinite data is an emergent research sphere inferred from the progression of data forms by us. To comprehensively present these three data paradigms, we elaborate on their formal definitions, differences manifested in datasets, resolution pathways, and development of research. We summarize key tasks and achievements pertaining to definite and semi-definite data from myriad research undertakings, present a roadmap for indefinite data, beginning with its current research conundrums. Lastly, we classify and scrutinize the key datasets presently utilized within these three paradigms.
Recently, Mutual Information (MI) has attracted attention in bounding the generalization error of Deep Neural Networks (DNNs). However, it is intractable to accurately estimate the MI in DNNs, thus most previous works have to relax the MI bound, which in turn weakens the information theoretic explanation for generalization. To address the limitation, this paper introduces a probabilistic representation of DNNs for accurately estimating the MI. Leveraging the proposed MI estimator, we validate the information theoretic explanation for generalization, and derive a tighter generalization bound than the state-of-the-art relaxations.
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