相关论文: Extremal Depth for Functional Data and Application…

Deep Learning is becoming increasingly relevant in Embedded and Internet-of-things applications. However, deploying models on embedded devices poses a challenge due to their resource limitations. This can impact the model's inference…

Data depth functions are a generalization of one-dimensional order statistics and medians to real spaces of dimension greater than one; in particular, a data depth function quantifies the centrality of a point with respect to a data set or…

Recent feature matching methods have achieved remarkable performance but lack efficiency consideration. In this paper, we revisit the mainstream detector-free matching pipeline and improve all its stages considering both accuracy and…

Designing efficient and accurate numerical solvers for high-dimensional partial differential equations (PDEs) remains a challenging and important topic in computational science and engineering, mainly due to the "curse of dimensionality" in…

This paper concerns estimation and inference for treatment effects in deep tails of the counterfactual distribution of unobservable potential outcomes corresponding to a continuously valued treatment. We consider two measures for the deep…

Estimating the intrinsic dimensionality (ID) of data is a fundamental problem in machine learning and computer vision, providing insight into the true degrees of freedom underlying high-dimensional observations. Existing methods often rely…

We develop a novel EDMD-type algorithm that captures the spectrum of the Koopman operator defined on a reproducing kernel Hilbert space of analytic functions. This method, which we call analytic EDMD, relies on an orthogonal projection on…

We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpose of this analysis is twofold: first, we prove that…

For hypothesis testing of functional parameters, given a functional statistic $T_n$ and a functional depth $D$ with respect to the distribution $P_n$ of $T_n$, we propose the depth value $DT_n \equiv D(T_n;P_n)$ as a test statistic, which…

Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…

This paper introduces the sparse functional boxplot and the intensity sparse functional boxplot as practical exploratory tools. Besides being available for complete functional data, they can be used in sparse univariate and multivariate…

In this paper, we present a novel end-to-end network architecture to estimate fundamental matrix directly from stereo images. To establish a complete working pipeline, different deep neural networks in charge of finding correspondences in…

This article proposes a new graphical tool, the magnitude-shape (MS) plot, for visualizing both the magnitude and shape outlyingness of multivariate functional data. The proposed tool builds on the recent notion of functional directional…

Functional data analysis, FDA, is now a well established discipline of statistics, with its core concepts and perspectives in place. Despite this, there are still fundamental statistical questions which have received relatively little…

Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…

Estimation of extreme conditional quantiles is often required for risk assessment of natural hazards in climate and geo-environmental sciences and for quantitative risk management in statistical finance, econometrics, and actuarial…

This paper proposes an extension of Random Projection Depth (RPD) to cope with multiple modalities and non-convexity on data clouds. In the framework of the proposed method, the RPD is computed in a reproducing kernel Hilbert space. With…

The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…

The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine…

Data redundancy is ubiquitous in the inputs and intermediate results of Deep Neural Networks (DNN). It offers many significant opportunities for improving DNN performance and efficiency and has been explored in a large body of work. These…