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Related papers: Deep Learning with Functional Inputs

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This paper proposes a multivariate nonlinear function-on-function regression model, which allows both the response and the covariates can be multi-dimensional functions. The model is built upon the multivariate functional reproducing kernel…

Methodology · Statistics 2024-06-28 Xu Haijie , Zhang Chen

Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regressions remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more…

Statistics Theory · Mathematics 2021-06-14 Qixian Zhong , Jane-Ling Wang

Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…

Computation · Statistics 2018-05-28 Minh-Ngoc Tran , Nghia Nguyen , David Nott , Robert Kohn

Functional data, representing curves or trajectories, are ubiquitous in fields like biomedicine and motion analysis. A fundamental challenge is phase variability -- temporal misalignments that obscure underlying patterns and degrade model…

Computer Vision and Pattern Recognition · Computer Science 2025-09-30 Siyuan Jiang , Yihan Hu , Wenjie Li , Pengcheng Zeng

Multi-scale deep CNNs have been used successfully for problems mapping each pixel to a label, such as depth estimation and semantic segmentation. It has also been shown that such architectures are reusable and can be used for multiple…

Computer Vision and Pattern Recognition · Computer Science 2016-09-21 Arsalan Mousavian , Hamed Pirsiavash , Jana Kosecka

We propose an empirical approach centered on the spectral dynamics of weights -- the behavior of singular values and vectors during optimization -- to unify and clarify several phenomena in deep learning. We identify a consistent bias in…

In conventional formulations of multilayer feedforward neural networks, the individual layers are customarily defined by explicit functions. In this paper we demonstrate that defining individual layers in a neural network \emph{implicitly}…

Computer Vision and Pattern Recognition · Computer Science 2020-06-04 Qianggong Zhang , Yanyang Gu , Michalkiewicz Mateusz , Mahsa Baktashmotlagh , Anders Eriksson

Understanding the functional principles of information processing in deep neural networks continues to be a challenge, in particular for networks with trained and thus non-random weights. To address this issue, we study the mapping between…

Disordered Systems and Neural Networks · Physics 2023-04-05 Kirsten Fischer , Alexandre René , Christian Keup , Moritz Layer , David Dahmen , Moritz Helias

Functional Distributional Semantics is a recently proposed framework for learning distributional semantics that provides linguistic interpretability. It models the meaning of a word as a binary classifier rather than a numerical vector. In…

Computation and Language · Computer Science 2022-04-25 Yinhong Liu , Guy Emerson

Effective training of deep neural networks can be challenging, and there remain many open questions on how to best learn these models. Recently developed methods to improve neural network training examine teaching: providing learned…

Machine Learning · Computer Science 2021-03-15 Aniruddh Raghu , Maithra Raghu , Simon Kornblith , David Duvenaud , Geoffrey Hinton

We approach structured output prediction by optimizing a deep value network (DVN) to precisely estimate the task loss on different output configurations for a given input. Once the model is trained, we perform inference by gradient descent…

Machine Learning · Computer Science 2017-08-09 Michael Gygli , Mohammad Norouzi , Anelia Angelova

Function approximation from input and output data pairs constitutes a fundamental problem in supervised learning. Deep neural networks are currently the most popular method for learning to mimic the input-output relationship of a general…

Machine Learning · Computer Science 2019-12-09 Nikos Kargas , Nicholas D. Sidiropoulos

This paper studies a very flexible model that can be used widely to analyze the relation between a response and multiple covariates. The model is nonparametric, yet renders easy interpretation for the effects of the covariates. The model…

Statistics Theory · Mathematics 2012-10-18 Young K. Lee , Enno Mammen , Byeong U. Park

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…

Machine Learning · Computer Science 2019-01-15 Giuseppe Marra , Francesco Giannini , Michelangelo Diligenti , Marco Gori

There are relatively few works dealing with conformal prediction for multi-task learning issues, and this is particularly true for multi-target regression. This paper focuses on the problem of providing valid (i.e., frequency calibrated)…

Machine Learning · Computer Science 2021-01-29 Soundouss Messoudi , Sébastien Destercke , Sylvain Rousseau

Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…

Machine Learning · Statistics 2023-10-11 Nick Polson , Vadim Sokolov

The functional linear model is a popular tool to investigate the relationship between a scalar/functional response variable and a scalar/functional covariate. We generalize this model to a functional linear mixed-effects model when repeated…

Methodology · Statistics 2016-01-07 Baisen Liu , Jiguo Cao

In recent years, Deep Learning has been successfully applied to multimodal learning problems, with the aim of learning useful joint representations in data fusion applications. When the available modalities consist of time series data such…

Computer Vision and Pattern Recognition · Computer Science 2017-04-12 Xitong Yang , Palghat Ramesh , Radha Chitta , Sriganesh Madhvanath , Edgar A. Bernal , Jiebo Luo

Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…

Numerical Analysis · Mathematics 2021-03-25 Remco van der Meer , Cornelis Oosterlee , Anastasia Borovykh

Accurate prediction of crop yield is critical for supporting food security, agricultural planning, and economic decision-making. However, yield forecasting remains a significant challenge due to the complex and nonlinear relationships…

Applications · Statistics 2026-04-09 Yeonjoo Park , Bo Li , Yehua Li