Related papers: BFDA: A Matlab Toolbox for Bayesian Functional Dat…

We propose a Bayesian approach to estimating parameters in multiclass functional models. Unordered multinomial probit, ordered multinomial probit and multinomial logistic models are considered. We use finite random series priors based on a…

The Bayesian approach to feature extraction, known as factor analysis (FA), has been widely studied in machine learning to obtain a latent representation of the data. An adequate selection of the probabilities and priors of these bayesian…

We propose an interdisciplinary framework that combines Bayesian predictive inference, a well-established tool in Machine Learning, with Formal Methods rooted in the computer science community. Bayesian predictive inference allows for…

Bayesian deep learning approaches assume model parameters to be latent random variables and infer posterior distributions to quantify uncertainty, increase safety and trust, and prevent overconfident and unpredictable behavior. However,…

We develop a weighted Bayesian Bootstrap (WBB) for machine learning and statistics. WBB provides uncertainty quantification by sampling from a high dimensional posterior distribution. WBB is computationally fast and scalable using only…

Sparse functional data frequently arise in real-world applications, posing significant challenges for accurate classification. To address this, we propose a novel classification method that integrates functional principal component analysis…

There is a considerable body of work on data cleaning which employs various principles to rectify erroneous data and transform a dirty dataset into a cleaner one. One of prevalent approaches is probabilistic methods, including Bayesian…

The paper introduces a general framework for statistical analysis of functional time series from a Bayesian perspective. The proposed approach, based on an extension of the popular dynamic linear model to Banach-space valued observations…

The fine-tuning of pre-trained language models has resulted in the widespread availability of task-specific models. Model merging offers an efficient way to create multi-task models by combining these fine-tuned models at the parameter…

Task functional magnetic resonance imaging (fMRI) is a type of neuroimaging data used to identify areas of the brain that activate during specific tasks or stimuli. These data are conventionally modeled using a massive univariate approach…

Due to developments in instruments and computers, functional observations are increasingly popular. However, effective methodologies for flexibly estimating the underlying trends with valid uncertainty quantification for a sequence of…

The functional delta-method provides a convenient tool for deriving the asymptotic distribution of a plug-in estimator of a statistical functional from the asymptotic distribution of the respective empirical process. Moreover, it provides a…

We propose an approximation to the forward-filter-backward-sampler (FFBS) algorithm for large-scale spatio-temporal smoothing. FFBS is commonly used in Bayesian statistics when working with linear Gaussian state-space models, but it…

We propose a fast inference method for Bayesian nonlinear support vector machines that leverages stochastic variational inference and inducing points. Our experiments show that the proposed method is faster than competing Bayesian…

Let $\mathbf{x}_j = \mathbf{\theta} + \mathbf{\epsilon}_j$, $j=1,\dots,n$ be i.i.d. copies of a Gaussian random vector $\mathbf{x}\sim\mathcal{N}(\mathbf{\theta},\mathbf{\Sigma})$ with unknown mean $\mathbf{\theta} \in \mathbb{R}^d$ and…

We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…

We propose modeling raw functional data as a mixture of a smooth function and a high-dimensional factor component. The conventional approach to retrieving the smooth function from the raw data is through various smoothing techniques.…

The Full Bayesian Significance Test (FBST) possesses many desirable aspects, such as dismissing the need for hypotheses to have positive prior probability and providing a measure of evidence against $H_0$. Still, few attempts have been made…

Large-scale longitudinal molecular profiling is now firmly established in biomedical research, prompted by the need to uncover coordinated biomarker trajectories reflecting the dynamics of underlying biological mechanisms and characterise…

Functional Principal Components Analysis (FPCA) provides a parsimonious, semi-parametric model for multivariate, sparsely-observed functional data. Frequentist FPCA approaches estimate principal components (PCs) from the data, then…