Related papers: Goal-oriented adaptive sampling under random field…
In ecology we may find scenarios where the same phenomenon (species occurrence, species abundance, etc.) is observed using two different types of samplers. For instance, species data can be collected from scientific sampling with a…
Online reinforcement learning and other adaptive sampling algorithms are increasingly used in digital intervention experiments to optimize treatment delivery for users over time. In this work, we focus on longitudinal user data collected by…
Score-based generative models have demonstrated significant practical success in data-generating tasks. The models establish a diffusion process that perturbs the ground truth data to Gaussian noise and then learn the reverse process to…
Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…
The aim of this paper is twofold. First, three theoretical principles are formalized: randomization, overrepresentation and restriction. We develop these principles and give a rationale for their use in choosing the sampling design in a…
A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of…
We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of observations. Motivated by this problem, in this contribution we first investigate the extremes of Gaussian fields…
Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified…
We study non-Gaussian random fields constructed by the selection normal distribution, and we term them selection Gaussian random fields. The selection Gaussian random field can capture skewness, multi-modality, and to some extend heavy…
Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA).…
Sampling is a common strategy for generating text from probabilistic models, yet standard ancestral sampling often results in text that is incoherent or ungrammatical. To alleviate this issue, various modifications to a model's sampling…
Recent developments in generative modeling have utilized score-based methods coupled with stochastic differential equations to sample from complex probability distributions. However, these and other performant sampling methods generally…
To facilitate effective decision-making, precipitation datasets should include uncertainty estimates. Quantile regression with machine learning has been proposed for issuing such estimates. Distributional regression offers distinct…
Generative models have fundamentally reshaped the landscape of decision-making, reframing the problem from pure scalar reward maximization to high-fidelity trajectory generation and distribution matching. This paradigm shift addresses…
Many existing approaches for generating predictions in settings with distribution shift model distribution shifts as adversarial or low-rank in suitable representations. In various real-world settings, however, we might expect shifts to…
Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
Aleatoric uncertainty quantification seeks for distributional knowledge of random responses, which is important for reliability analysis and robustness improvement in machine learning applications. Previous research on aleatoric uncertainty…
Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…
This thesis contributes to the mathematical foundation of domain adaptation as emerging field in machine learning. In contrast to classical statistical learning, the framework of domain adaptation takes into account deviations between…