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Multi-dimensional functional data arises in numerous modern scientific experimental and observational studies. In this paper we focus on longitudinal functional data, a structured form of multidimensional functional data. Operating within a…

We propose a Bayesian modeling framework for jointly analyzing multiple functional responses of different types (e.g. binary and continuous data). Our approach is based on a multivariate latent Gaussian process and models the dependence…

Inferring causal relationships from observed data is an important task, yet it becomes challenging when the data is subject to various external interferences. Most of these interferences are the additional effects of external factors on…

Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which $p$,…

Successful modeling of degradation performance data is essential for accurate reliability assessment and failure predictions of highly reliable product units. The degradation performance measurements over time are highly heterogeneous. Such…

Modeling how individuals evolve over time is a fundamental problem in the natural and social sciences. However, existing datasets are often cross-sectional with each individual observed only once, making it impossible to apply traditional…

Understanding the dynamics of time series data typically requires identifying the unique latent factors for data generation, \textit{a.k.a.}, latent processes identification. Driven by the independent assumption, existing works have made…

We propose a novel approximate factor model tailored for analyzing time-dependent curve data. Our model decomposes such data into two distinct components: a low-dimensional predictable factor component and an unpredictable error term. These…

A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the…

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…

The problem of complex data analysis is a central topic of modern statistical science and learning systems and is becoming of broader interest with the increasing prevalence of high-dimensional data. The challenge is to develop statistical…

We developed a single factor model with measure-specific sample weights for multivariate data with multiple observed indicators clustered within a higher level subject. The factor is therefore a latent variable shared by multiple indicators…

Disentangled representations, where the higher level data generative factors are reflected in disjoint latent dimensions, offer several benefits such as ease of deriving invariant representations, transferability to other tasks,…

Complex, multivariable systems are often analyzed by grouping their constituent units into components, sometimes referred to as latent features, which afford physical or biological interpretation. However, a priori many different types of…

In this paper, we aim to improve multivariate anomaly detection (AD) by modeling the \textit{time-varying non-linear spatio-temporal correlations} found in multivariate time series data . In multivariate time series data, an anomaly may be…

A novel approach to perform unsupervised sequential learning for functional data is proposed. Our goal is to extract reference shapes (referred to as templates) from noisy, deformed and censored realizations of curves and images. Our model…

Learning controllable and generalizable representation of multivariate data with desired structural properties remains a fundamental problem in machine learning. In this paper, we present a novel framework for learning generative models…

We consider functional data which are measured on a discrete set of observation points. Often such data are measured with additional noise. We explore in this paper the factor structure underlying this type of data. We show that the latent…

This article focuses on covariance estimation for multi-study data. Popular approaches employ factor-analytic terms with shared and study-specific loadings that decompose the variance into (i) a shared low-rank component, (ii)…

Functional data, representing curves or trajectories, are ubiquitous in fields like biomedicine and motion analysis. A fundamental challenge is phase variability -- temporal misalignments that obscure underlying patterns and degrade model…