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The Poisson log-normal model is a latent variable model that provides a generic framework for the analysis of multivariate count data. Inferring its parameters can be a daunting task since the conditional distribution of the latent…
A lower bound on the minimum mean-squared error (MSE) in a Bayesian estimation problem is proposed in this paper. This bound utilizes a well-known connection to the deterministic estimation setting. Using the prior distribution, the bias…
Calculating the expected information gain in optimal Bayesian experimental design typically relies on nested Monte Carlo sampling. When the model also contains nuisance parameters, which are parameters that contribute to the overall…
In this paper, online linear regression in environments corrupted by non-Gaussian noise (especially heavy-tailed noise) is addressed. In such environments, the error between the system output and the label also does not follow a Gaussian…
In recent years, partially observable functional data has gained significant attention in practical applications and has become the focus of increasing interest in the literature. In this thesis, we build upon the concept of data…
Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian…
A Bayesian method of moments/instrumental variable (BMOM/IV) approach is developed and applied in the analysis of the important mean and multiple regression models. Given a single set of data, it is shown how to obtain posterior and…
We analyze the best achievable performance of Bayesian learning under generative models by defining and upper-bounding the minimum excess risk (MER): the gap between the minimum expected loss attainable by learning from data and the minimum…
Bayesian Optimization (BO) methods are useful for optimizing functions that are expen- sive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the…
We study Bayesian optimization (BO) in high-dimensional and non-stationary scenarios. Existing algorithms for such scenarios typically require extensive hyperparameter tuning, which limits their practical effectiveness. We propose a…
The recently proposed statistical finite element (statFEM) approach synthesises measurement data with finite element models and allows for making predictions about the unknown true system response. We provide a probabilistic error analysis…
In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…
Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…
Mixtures-of-Experts models and their maximum likelihood estimation (MLE) via the EM algorithm have been thoroughly studied in the statistics and machine learning literature. They are subject of a growing investigation in the context of…
For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…
To handle with inverse problems, two probabilistic approaches have been proposed: the maximum entropy on the mean (MEM) and the Bayesian estimation (BAYES). The main object of this presentation is to compare these two approaches which are…
Our investigation concerns the estimation of predictive densities and a study of efficiency as measured by the frequentist risk of such predictive densities with integrated $L_2$ and $L_1$ losses. Our findings relate to a $p-$variate…
We study minimal attention-only transformers under all-token corruption and show they admit a two-stage empirical Bayes interpretation. A single attention step computes a kernel-weighted posterior mean with respect to the empirical…
Bayesian optimization (BO) is a popular algorithm for solving challenging optimization tasks. It is designed for problems where the objective function is expensive to evaluate, perhaps not available in exact form, without gradient…
We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…