Related papers: A hidden process regression model for functional d…

We develop and apply an approach for analyzing multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function, forcing the individual curve to switch from one function…

Using supervised machine learning approaches to recognize human activities from on-body wearable accelerometers generally requires a large amount of labelled data. When ground truth information is not available, too expensive, time…

Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…

Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are…

The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction accuracy or the so-called Area Under the Curve (AUC). Minimizing the reciprocals of these measures are the goals of…

Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…

Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…

Complex systems in science and engineering sometimes exhibit behavior that changes across different regimes. Traditional global models struggle to capture the full range of this complex behavior, limiting their ability to accurately…

In massive data analysis, training and testing data often come from very different sources, and their probability distributions are not necessarily identical. A feature example is nonparametric classification in posterior drift model where…

We consider the use of extreme learning machines (ELM) for computational partial differential equations (PDE). In ELM the hidden-layer coefficients in the neural network are assigned to random values generated on $[-R_m,R_m]$ and fixed,…

Point process modeling is gaining increasing attention, as point process type data are emerging in numerous scientific applications. In this article, motivated by a neuronal spike trains study, we propose a novel point process regression…

We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…

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…

Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…

As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…

We introduce a novel function-on-function linear quantile regression model to characterize the entire conditional distribution of a functional response for a given functional predictor. Tensor cubic $B$-splines expansion is used to…

Samples of curves, or functional data, usually present phase variability in addition to amplitude variability. Existing functional regression methods do not handle phase variability in an efficient way. In this paper we propose a functional…

The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…

This article addresses the problem of classification method based on both labeled and unlabeled data, where we assume that a density function for labeled data is different from that for unlabeled data. We propose a semi-supervised logistic…

When observations are curves over some natural time interval, the field of functional data analysis comes into play. Functional linear processes account for temporal dependence in the data. The prediction problem for functional linear…