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A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…
Recent advances in engineering technologies have enabled the collection of a large number of longitudinal features. This wealth of information presents unique opportunities for researchers to investigate the complex nature of diseases and…
A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in…
Graphical interaction models have become an important tool for analysing multivariate time series. In these models, the interrelationships among the components of a time series are described by undirected graphs in which the vertices depict…
High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear…
Generalized additive models for location, scale and shape (GAMLSS) are a popular extension to mean regression models where each parameter of an arbitrary distribution is modelled through covariates. While such models have been developed for…
Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model representing the conditional relationships between the functional variables. However, in many…
Clinical research often focuses on complex traits in which many variables play a role in mechanisms driving, or curing, diseases. Clinical prediction is hard when data is high-dimensional, but additional information, like domain knowledge…
Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and…
Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or…
This paper presents the first application of Gaussian Mixture Copula Models to the statistical modeling of driving scenarios for the safety validation of automated driving systems. Knowledge of the joint probability distribution of scenario…
We extend the synthetic theories of discrete and Gaussian categorical probability by introducing a diagrammatic calculus for reasoning about hybrid probabilistic models in which continuous random variables, conditioned on discrete ones,…
Multimodal data are now prevailing in scientific research. A central question in multimodal integrative analysis is to understand how two data modalities associate and interact with each other given another modality or demographic…
Factor analysis for high-dimensional data is a canonical problem in statistics and has a wide range of applications. However, there is currently no factor model tailored to effectively analyze high-dimensional count responses with…
In genome-wide prediction, independence of marker allele substitution effects is typically assumed; however, since early stages of this technology it has been known that nature points to correlated effects. In statistics, graphical models…
We present a probabilistic model for natural images which is based on Gaussian scale mixtures and a simple multiscale representation. In contrast to the dominant approach to modeling whole images focusing on Markov random fields, we…
We consider the problem of learning causal models from observational data generated by linear non-Gaussian acyclic causal models with latent variables. Without considering the effect of latent variables, one usually infers wrong causal…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
Properties of data are frequently seen to vary depending on the sampled situations, which usually changes along a time evolution or owing to environmental effects. One way to analyze such data is to find invariances, or representative…