Related papers: A Non-linear Function-on-Function Model for Regres…

Time series classification problems have drawn increasing attention in the machine learning and statistical community. Closely related is the field of functional data analysis (FDA): it refers to the range of problems that deal with the…

Time Series Forecasting has been an active area of research due to its many applications ranging from network usage prediction, resource allocation, anomaly detection, and predictive maintenance. Numerous publications published in the last…

Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical…

Functional data often arise from measurements on fine time grids and are obtained by separating an almost continuous time record into natural consecutive intervals, for example, days. The functions thus obtained form a functional time…

The classical approach to non-linear regression in physics, is to take a mathematical model describing the functional dependence of the dependent variable from a set of independent variables, and then, using non-linear fitting algorithms,…

As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…

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…

Function-on-function regression has been a topic of substantial interest due to its broad applicability, where the relation between functional predictor and response is concerned. In this article, we propose a new framework for modeling the…

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…

Recent work has shown the efficiency of deep learning models such as Fully Convolutional Networks (FCN) or Recurrent Neural Networks (RNN) to deal with Time Series Regression (TSR) problems. These models sometimes need a lot of data to be…

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology…

Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…

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…

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…

Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…

In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to…

The availability of large amounts of time series data, paired with the performance of deep-learning algorithms on a broad class of problems, has recently led to significant interest in the use of sequence-to-sequence models for time series…

Forecasting based on financial time-series is a challenging task since most real-world data exhibits nonstationary property and nonlinear dependencies. In addition, different data modalities often embed different nonlinear relationships…

Despite their simplicity, linear models perform well at time series forecasting, even when pitted against deeper and more expensive models. A number of variations to the linear model have been proposed, often including some form of feature…

Scalar-on-function linear models are commonly used to regress functional predictors on a scalar response. However, functional models are more difficult to estimate and interpret than traditional linear models, and may be unnecessarily…