Related papers: Supervised Principal Component Regression for Func…
Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the…
Nonparametric regression imputation is commonly used in missing data analysis. However, it suffers from the ``curse of dimension". The problem can be alleviated by the explosive sample size in the era of big data, while the large-scale data…
We analyse the prediction error of principal component regression (PCR) and prove non-asymptotic upper bounds for the corresponding squared risk. Under mild assumptions, we show that PCR performs as well as the oracle method obtained by…
We consider the functional regression model with multivariate response and functional predictors. Compared to fitting each individual response variable separately, taking advantage of the correlation between the response variables can…
We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially…
This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…
Motivated by the analysis of high-dimensional neuroimaging signals located over the cortical surface, we introduce a novel Principal Component Analysis technique that can handle functional data located over a two-dimensional manifold. For…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…
Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…
Reduced-rank regression estimates regression coefficients by imposing a low-rank constraint on the matrix of regression coefficients, thereby accounting for correlations among response variables. To further improve predictive accuracy and…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
Principal Components Analysis is a widely used technique for dimension reduction and characterization of variability in multivariate populations. Our interest lies in studying when and why the rotation to principal components can be used…
A reduced-rank mixed effects model is developed for robust modeling of sparsely observed paired functional data. In this model, the curves for each functional variable are summarized using a few functional principal components, and the…
In many applications, particularly in the natural sciences, the available high-dimensional set of features may contain variables that are not correlated with the response under consideration. Such irrelevant features can, in certain cases,…
We propose a new fast generalized functional principal components analysis (fast-GFPCA) algorithm for dimension reduction of non-Gaussian functional data. The method consists of: (1) binning the data within the functional domain; (2)…
In this paper, we consider a generalized multivariate regression problem where the responses are monotonic functions of linear transformations of predictors. We propose a semi-parametric algorithm based on the ordering of the responses…
In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…