Related papers: Deep Fr\'echet Regression
Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of…
Non-Euclidean data is frequently encountered across different fields, yet there is limited literature that addresses the fundamental challenge of training neural networks with manifold representations as outputs. We introduce the trick…
This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…
We study the properties of nonparametric least squares regression using deep neural networks. We derive non-asymptotic upper bounds for the prediction error of the empirical risk minimizer of feedforward deep neural regression. Our error…
We focus on nonlinear Function-on-Scalar regression, where the predictors are scalar variables, and the responses are functional data. Most existing studies approximate the hidden nonlinear relationships using linear combinations of basis…
Distribution-as-response regression problems are gaining wider attention, especially within biomedical settings where observation-rich patient specific data sets are available, such as feature densities in CT scans (Petersen et al., 2021)…
Network data are increasingly available in various research fields, motivating statistical analysis for populations of networks where a network as a whole is viewed as a data point. Due to the non-Euclidean nature of networks, basic…
Many modern applications involve predicting structured, non-Euclidean outputs such as probability distributions, networks, and symmetric positive-definite matrices. These outputs are naturally modeled as elements of general metric spaces,…
Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this paper, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…
Fr\'echet regression has emerged as a useful tool for modeling non-Euclidean response variables associated with Euclidean covariates. In this work, we propose a global Fr\'echet regression estimation method that incorporates low-rank…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
This paper proposes a nonparametric multivariate density forecast model based on deep learning. It not only offers the whole marginal distribution of each random variable in forecasting targets, but also reveals the future correlation…
We study harmonic map regression, a nonparametric estimator for manifold-valued responses, that penalizes the empirical Fr\'echet risk by the Dirichlet energy. By connecting penalized regression to the theory of harmonic maps, the estimator…
This paper considers improved forecasting in possibly nonlinear dynamic settings, with high-dimension predictors ("big data" environments). To overcome the curse of dimensionality and manage data and model complexity, we examine shrinkage…
Deep neural networks tend to underestimate uncertainty and produce overly confident predictions. Recently proposed solutions, such as MC Dropout and SDENet, require complex training and/or auxiliary out-of-distribution data. We propose a…
Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper,…
Recent advances in deep learning have achieved impressive gains in classification accuracy on a variety of types of data, including images and text. Despite these gains, however, concerns have been raised about the calibration, robustness,…
This paper proposes a new high dimensional regression method by merging Gaussian process regression into a variational autoencoder framework. In contrast to other regression methods, the proposed method focuses on the case where output…
This paper revisits an adaptation of the random forest algorithm for Fr\'echet regression, addressing the challenge of regression in the context of random objects in metric spaces. Recognizing the limitations of previous approaches, we…