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Inference and inverse problems are closely related concepts, both fundamentally involving the deduction of unknown causes or parameters from observed data. Bayesian inference, a powerful class of methods, is often employed to solve a…
The ability to accurately model random fields plays a critical role in science and engineering for problems involving uncertain, spatially-varying quantities such as heterogeneous material properties and turbulent flows. Deep generative…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
In variational autoencoders, the prior on the latent codes $z$ is often treated as an afterthought, but the prior shapes the kind of latent representation that the model learns. If the goal is to learn a representation that is interpretable…
Latent variables (LVs) play a crucial role in encoder-decoder models by enabling effective data compression, prediction, and generation. Although their theoretical properties, such as generalization, have been extensively studied in…
Variational AutoEncoders (VAEs) are powerful generative models that merge elements from statistics and information theory with the flexibility offered by deep neural networks to efficiently solve the generation problem for high dimensional…
Variational Autoencoders (VAEs) are powerful in data representation inference, but it cannot learn relations between features with its vanilla form and common variations. The ability to capture relations within data can provide the much…
One of the core facets of Bayesianism is in the updating of prior beliefs in light of new evidence$\text{ -- }$so how can we maintain a Bayesian approach if we have no prior beliefs in the first place? This is one of the central challenges…
In this tutorial, we explore Variational Autoencoders (VAEs), an essential framework for unsupervised learning, particularly suited for high-dimensional datasets such as neuroimaging. By integrating deep learning with Bayesian inference,…
Variational autoencdoers (VAE) are a popular approach to generative modelling. However, exploiting the capabilities of VAEs in practice can be difficult. Recent work on regularised and entropic autoencoders have begun to explore the…
In recent years, extending variational autoencoder's framework to learn disentangled representations has received much attention. We address this problem by proposing a framework capable of disentangling class-related and class-independent…
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…
We study the problem of self-supervised structured representation learning using autoencoders for downstream tasks such as generative modeling. Unlike most methods which rely on matching an arbitrary, relatively unstructured, prior…
Variational Autoencoders (VAEs) typically rely on a probabilistic decoder with a predefined likelihood, most commonly an isotropic Gaussian, to model the data conditional on latent variables. While convenient for optimization, this choice…
The manifold hypothesis states that many kinds of high-dimensional data are concentrated near a low-dimensional manifold. If the topology of this data manifold is non-trivial, a continuous encoder network cannot embed it in a one-to-one…
In just three years, Variational Autoencoders (VAEs) have emerged as one of the most popular approaches to unsupervised learning of complicated distributions. VAEs are appealing because they are built on top of standard function…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
In the following short article we adapt a new and popular machine learning model for inference on medical data sets. Our method is based on the Variational AutoEncoder (VAE) framework that we adapt to survival analysis on small data sets…
We propose a novel amortized variational inference scheme for an empirical Bayes meta-learning model, where model parameters are treated as latent variables. We learn the prior distribution over model parameters conditioned on limited…
Bayesian networks faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents…