相关论文: Sensitivity indices for output on a Riemannian man…
Sensitivity of linear continuous-time control systems, subject to control and measurement noise, is analyzed by deriving the lower bounds of Bode-like integrals via an information-theoretic approach. Bode integrals of four different…
Scatterometry is a fast, indirect and nondestructive optical method for the quality control in the production of lithography masks. Geometry parameters of line gratings are obtained from diffracted light intensities by solving an inverse…
Motivated by the goals of dataset pruning and defect identification, a growing body of methods have been developed to score individual examples within a dataset. These methods, which we call "example difficulty scores", are typically used…
Deep learning-based image manipulation localization (IML) methods have achieved remarkable performance in recent years, but typically rely on large-scale pixel-level annotated datasets. To address the challenge of acquiring high-quality…
We study the problem of learning multi-index models (MIMs), where the label depends on the input $\boldsymbol{x} \in \mathbb{R}^d$ only through an unknown $\mathsf{s}$-dimensional projection $\boldsymbol{W}_*^\mathsf{T} \boldsymbol{x} \in…
Semiparametric discrete choice models are widely used in a variety of practical applications. While these models are point identified in the presence of continuous covariates, they can become partially identified when covariates are…
Industrial sensor networks produce complex signals with nonlinear structure and shifting distributions. We propose RIE-SenseNet, a novel geometry-aware Transformer model that embeds sensor data in a Riemannian manifold to tackle these…
This paper proposes an empirical method to implement the recentered influence function (RIF) regression of Firpo, Fortin and Lemieux (2009), a relevant method to study the effect of covariates on many statistics beyond the mean. In…
In this paper we treat statistical inference for an intrinsic wavelet estimator of curves of symmetric positive definite (SPD) matrices in a log-Euclidean manifold. This estimator preserves positive-definiteness and enjoys…
Information coefficient (IC) is a widely used metric for measuring investment managers' skills in selecting stocks. However, its adequacy and effectiveness for evaluating stock selection models has not been clearly understood, as IC from a…
Symmetric positive definite (SPD) matrix has been demonstrated to be an effective feature descriptor in many scientific areas, as it can encode spatiotemporal statistics of the data adequately on a curved Riemannian manifold, i.e., SPD…
The sparse identification of nonlinear dynamics (SINDy) has been established as an effective method to learn interpretable models of dynamical systems from data. However, for high-dimensional slow-fast dynamical systems, the regression…
Sensitivity analysis measures the influence of a Bayesian network's parameters on a quantity of interest defined by the network, such as the probability of a variable taking a specific value. Various sensitivity measures have been defined…
Quantifying uncertainty in predictive simulations for real-world problems is of paramount importance - and far from trivial, mainly due to the large number of stochastic parameters and significant computational requirements. Adaptive sparse…
Following up on the success of the analysis of variance (ANOVA) decomposition and the Sobol indices (SI) for global sensitivity analysis, various related quantities of interest have been defined in the literature including the effective and…
We introduce an intrinsic estimator for the scalar curvature of a data set presented as a finite metric space. Our estimator depends only on the metric structure of the data and not on an embedding in $\mathbb{R}^n$. We show that the…
Drawing parallels with the way biological networks are studied, we adapt the treatment--control paradigm to explainable artificial intelligence research and enrich it through multi-parametric input alterations. In this study, we propose a…
A general approach to provide approximate parameterizations of the "small" scales by the "large" ones, is developed for stochastic partial differential equations driven by linear multiplicative noise. This is accomplished via the concept of…
Network estimation from multi-variate point process or time series data is a problem of fundamental importance. Prior work has focused on parametric approaches that require a known parametric model, which makes estimation procedures less…
To study and develop wall-functions for low-Reynolds-number models, a model linear equation is introduced. This equation simulates major mathematical peculiarities of the low-Reynolds-number model including a near wall sub-layer and…