Related papers: Functional continuum regression
A new partial functional linear regression model for panel data with time varying parameters is introduced. The parameter vector of the multivariate model component is allowed to be completely time varying while the function-valued…
Data analyses based on linear methods constitute the simplest, most robust, and transparent approaches to the automatic processing of large amounts of data for building supervised or unsupervised machine learning models. Principal…
We study principal component analysis (PCA) for mean zero i.i.d. Gaussian observations $X_1,\dots, X_n$ in a separable Hilbert space $\mathbb{H}$ with unknown covariance operator $\Sigma.$ The complexity of the problem is characterized by…
Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
This paper proposes distributed estimation procedures for three scalar-on-function regression models: the functional linear model (FLM), the functional non-parametric model (FNPM), and the functional partial linear model (FPLM). The…
Machine learning (ML) has seen promising developments in materials science, yet its efficacy largely depends on detailed crystal structural data, which are often complex and hard to obtain, limiting their applicability in real-world…
The functional linear regression model with points of impact is a recent augmentation of the classical functional linear model with many practically important applications. In this work, however, we demonstrate that the existing data-driven…
In practice functional data are sampled on a discrete set of observation points and often susceptible to noise. We consider in this paper the setting where such data are used as explanatory variables in a regression problem. If the primary…
The main objective of Prognostics and Health Management is to estimate the Remaining Useful Lifetime (RUL), namely, the time that a system or a piece of equipment is still in working order before starting to function incorrectly. In recent…
This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…
Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…
For the challenging semantic image segmentation task the most efficient models have traditionally combined the structured modelling capabilities of Conditional Random Fields (CRFs) with the feature extraction power of CNNs. In more recent…
We propose in this work to derive a CLT in the functional linear regression model to get confidence sets for prediction based on functional linear regression. The main difficulty is due to the fact that estimation of the functional…
The quantitative structure-activity relationship (QSAR) regression model is a commonly used technique for predicting biological activities of compounds using their molecular descriptors. Predictions from QSAR models can help, for example,…
Reduced rank regression (RRR) is a widely employed model for investigating the linear association between multiple response variables and a set of predictors. While RRR has been extensively explored in various works, the focus has…
Functional data analysis is a growing research field as more and more practical applications involve functional data. In this paper, we focus on the problem of regression and classification with functional predictors: the model suggested…
Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…
This paper develops a simple method to construct confidence bands, centered at a principal component analysis (PCA) based estimator, for the slope function in a functional linear regression model with a scalar response variable and a…
We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression…
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…