Related papers: Functional Moments Regression
Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…
Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure…
Dynamic functional connectivity, as measured by the time-varying covariance of neurological signals, is believed to play an important role in many aspects of cognition. While many methods have been proposed, reliably establishing the…
Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice,…
Functional concurrent, or varying-coefficient, regression models are commonly used in biomedical and clinical settings to investigate how the relation between an outcome and observed covariate varies as a function of another covariate. In…
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…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
Geostatistics is a branch of statistics concerned with stochastic processes over continuous domains, with Gaussian processes (GPs) providing a flexible and principled modelling framework. However, the high computational cost of simulating…
Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs,…
Dynamic prediction of causal effects under different treatment regimes conditional on an individual's characteristics and longitudinal history is an essential problem in precision medicine. This is challenging in practice because outcomes…
Bayesian inference for survival regression modeling offers numerous advantages, especially for decision-making and external data borrowing, but demands the specification of the baseline hazard function, which may be a challenging task. We…
Shape restrictions have played a central role in economics as both testable implications of theory and sufficient conditions for obtaining informative counterfactual predictions. In this paper we provide a general procedure for inference…
Estimation and inference with modern longitudinal data from wearable devices, which consist of biological signals at high-frequency time points, is burdened by massive computational costs. We propose a distributed estimation and inference…
We propose simple inferential approaches for the fixed effects in complex functional mixed effects models. We estimate the fixed effects under the independence of functional residuals assumption and then bootstrap independent units (e.g.…
The analysis of complex computer simulations, often involving functional data, presents unique statistical challenges. Conventional regression methods, such as function-on-function regression, typically associate functional outcomes with…
Sparse variational Gaussian process (GP) approximations based on inducing points have become the de facto standard for scaling GPs to large datasets, owing to their theoretical elegance, computational efficiency, and ease of implementation.…
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the…
Longitudinal binary or count functional data are common in neuroscience, but are often too large to analyze with existing functional regression methods. We propose one-step penalized generalized estimating equations that supports…
We propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is…
This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to…