Related papers: Modern Non-Linear Function-on-Function Regression
We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two…
We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…
Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…
It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of…
The regression of a functional response on a set of scalar predictors can be a challenging task, especially if there is a large number of predictors, or the relationship between those predictors and the response is nonlinear. In this work,…
Semi-structured networks (SSNs) merge the structures familiar from additive models with deep neural networks, allowing the modeling of interpretable partial feature effects while capturing higher-order non-linearities at the same time. A…
Using representations of functional data can be more convenient and beneficial in subsequent statistical models than direct observations. These representations, in a lower-dimensional space, extract and compress information from individual…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
Function regression/approximation is a fundamental application of machine learning. Neural networks (NNs) can be easily trained for function regression using a sufficient number of neurons and epochs. The forward-forward learning algorithm…
We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…
Feedforward neural networks (FNNs) can be viewed as non-linear regression models, where covariates enter the model through a combination of weighted summations and non-linear functions. Although these models have some similarities to the…
Recently, deep learning has been widely applied in functional data analysis (FDA) with notable empirical success. However, the infinite dimensionality of functional data necessitates an effective dimension reduction approach for functional…
Modern sensing and metrology systems now stream terabytes of heterogeneous, high-dimensional (HD) data profiles, images, and dense point clouds, whose natural representation is multi-way tensors. Understanding such data requires regression…
We present an explicit construction for feedforward neural network (FNN), which provides a piecewise constant approximation for multivariate functions. The proposed FNN has two hidden layers, where the weights and thresholds are explicitly…
Deep neural networks (DNNs) are so over-parametrized that recent research has found them to already contain a subnetwork with high accuracy at their randomly initialized state. Finding these subnetworks is a viable alternative training…
Functional linear regression is a widely used approach to model functional responses with respect to functional inputs. However, classical functional linear regression models can be severely affected by outliers. We therefore introduce a…
The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…
In this paper, we show how convolutional neural networks (CNN) can be used in regression and classification learning problems of noisy and non-noisy functional data. The main idea is to transform the functional data into a 28 by 28 image.…
Convolutional Neural Networks (CNNs) have been widely applied. But as the CNNs grow, the number of arithmetic operations and memory footprint also increase. Furthermore, typical non-linear activation functions do not allow associativity of…
In this paper, feedforward neural networks are presented that have nonlinear weight functions based on look--up tables, that are specially smoothed in a regularization called the diffusion. The idea of such a type of networks is based on…