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Functional data analysis (FDA) methods have computational and theoretical appeals for some high dimensional data, but lack the scalability to modern large sample datasets. To tackle the challenge, we develop randomized algorithms for two…
We develop a unified operator framework for scalar, multivariate, and functional regression based on integral operators defined with respect to general measures. Within this framework, classical regression models, including…
A central problem in unsupervised deep learning is how to find useful representations of high-dimensional data, sometimes called "disentanglement". Most approaches are heuristic and lack a proper theoretical foundation. In linear…
Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the…
One approach to analyzing the dynamics of a physical system is to search for long-lived patterns in its motions. This approach has been particularly successful for molecular dynamics data, where slowly decorrelating patterns can indicate…
This work aims at performing Functional Principal Components Analysis (FPCA) with Horvitz-Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA…
In many applied fields incomplete covariate vectors are commonly encountered. It is well known that this can be problematic when making inference on model parameters, but its impact on prediction performance is less understood. We develop a…
Classification (supervised-learning) of multivariate functional data is considered when the elements of the random functional vector of interest are defined on different domains. In this setting, PLS classification and tree PLS-based…
A new classification method for functional data is proposed in this paper. This work is motivated by the need to identify features that discriminate between neurological conditions on which local field potentials (LFPs) were recorded.…
Representing nonlinear dynamical systems using the Koopman Operator and its spectrum has distinct advantages in terms of linear interpretability of the model as well as in analysis and control synthesis through the use of well-studied…
Functional data analysis is concerned with the analysis of infinite-dimensional data functions. Functional principal component analysis (FPCA) is a key method to obtain finite-dimensional summaries. Consistency of FPCA has been…
Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…
A frequent task in exploratory data analysis consists in examining pairwise dependencies between data variables. Popular approaches include visualizing correlation or scatter plot matrices. However, both methods can be misleading. The…
In distributed-parameter inverse problems in computational mechanics, spatially varying fields are inferred from noisy, indirect, and heterogeneous observations. The relevant identifiability question concerns which spatial perturbation…
Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…
Explicit evaluations of matrix-variate gamma and beta integrals in the complex domain by using conventional procedures is extremely difficult. Such an evaluation will reveal the structure of these matrix-variate integrals. In this article,…
We consider functional data which have only been observed on a subset of their domain. This paper aims to develop statistical tests to determine whether the function and the domain over which it is observed are independent. The assumption…
Disentangling complex data to its latent factors of variation is a fundamental task in representation learning. Existing work on sequential disentanglement mostly provides two factor representations, i.e., it separates the data to…
Independent Component Analysis (ICA) is a technique for unsupervised exploration of multi-channel data that is widely used in observational sciences. In its classic form, ICA relies on modeling the data as linear mixtures of non-Gaussian…
Learning causal relationships among a set of variables, as encoded by a directed acyclic graph, from observational data is complicated by the presence of unobserved confounders. Instrumental variables (IVs) are a popular remedy for this…