Related papers: Structured Functional Principal Component Analysis
A key goal of unsupervised learning is to go beyond density estimation and sample generation to reveal the structure inherent within observed data. Such structure can be expressed in the pattern of interactions between explanatory latent…
As one of the most powerful tools for examining the association between functional covariates and a response, the functional regression model has been widely adopted in various interdisciplinary studies. Usually, a limited number of…
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…
Neuronal systems need to process temporal signals. We here show how higher-order temporal (co-)fluctuations can be employed to represent and process information. Concretely, we demonstrate that a simple biologically inspired feedforward…
Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or…
Sensory perception originates from the responses of sensory neurons, which react to a collection of sensory signals linked to various physical attributes of a singular perceptual object. Unraveling how the brain extracts perceptual…
This paper addresses the fundamental task of estimating covariance matrix functions for high-dimensional functional data/functional time series. We consider two functional factor structures encompassing either functional factors with scalar…
Statistical morphological inflectors are typically trained on fully supervised, type-level data. One remaining open research question is the following: How can we effectively exploit raw, token-level data to improve their performance? To…
Models of neural networks have proven their utility in the development of learning algorithms in computer science and in the theoretical study of brain dynamics in computational neuroscience. We propose in this paper a spatial neural…
Many studies collect functional data from multiple subjects that have both multilevel and multivariate structures. An example of such data comes from popular neuroscience experiments where participants' brain activity is recorded using…
It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of…
Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…
Latent factor models are widely used to measure unobserved latent traits in social and behavioral sciences, including psychology, education, and marketing. When used in a confirmatory manner, design information is incorporated, yielding…
The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of ``functional data analysis,'' it has often been assumed that a sample of random functions is observed…
Sparse functional/longitudinal data have attracted widespread interest due to the prevalence of such data in social and life sciences. A prominent scenario where such data are routinely encountered are accelerated longitudinal studies,…
Structural and functional neuroimaging modalities provide complementary windows into brain organization: structural imaging characterizes neural tissue anatomy and microstructure, while functional imaging captures dynamic patterns of neural…
Attention networks have proven to be an effective approach for embedding categorical inference within a deep neural network. However, for many tasks we may want to model richer structural dependencies without abandoning end-to-end training.…
We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…
Machine learning is rapidly making its path into natural sciences, including high-energy physics. We present the first study that infers, directly from experimental data, a functional form of fragmentation functions. The latter represent a…
Statistical and structural modeling represent two distinct approaches to data analysis. In this paper, we propose a set of novel methods for combining statistical and structural models for improved prediction and causal inference. Our first…