Related papers: The Lie-Group Bayesian Learning Rule

Bayesian latent space models offer a principled approach to network representation, but rely on correct specification of both geometry and link function. Real-world networks often violate these assumptions, exhibiting geometric mismatch and…

We present several theoretical contributions which allow Lie groups to be fit to high dimensional datasets. Transformation operators are represented in their eigen-basis, reducing the computational complexity of parameter estimation to that…

Recent advances in deep learning have led to a paradigm shift in the field of reversible steganography. A fundamental pillar of reversible steganography is predictive modelling which can be realised via deep neural networks. However,…

Advances in quantum computing over the last two decades have required sophisticated mathematical frameworks to deepen the understanding of quantum algorithms. In this review, we introduce the theory of Lie groups and their algebras to…

Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainty by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have focused…

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…

Discovering a unique causal structure is difficult due to both inherent identifiability issues, and the consequences of finite data. As such, uncertainty over causal structures, such as those obtained from a Bayesian posterior, are often…

Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward:…

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…

High dimensional categorical data are routinely collected in biomedical and social sciences. It is of great importance to build interpretable parsimonious models that perform dimension reduction and uncover meaningful latent structures from…

Bayesian reinforcement learning (BRL) is a method that merges principles from Bayesian statistics and reinforcement learning to make optimal decisions in uncertain environments. As a model-based RL method, it has two key components: (1)…

Structure learning algorithms that learn the graph of a Bayesian network from observational data often do so by assuming the data correctly reflect the true distribution of the variables. However, this assumption does not hold in the…

Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data…

After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…

Change-plane regression identifies subpopulations through an interpretable linear threshold rule, but likelihood-based inference for the hard-threshold boundary is nonregular: objectives are non-smooth, the boundary is weakly identified…

We investigate the parameterized complexity of Bayesian Network Structure Learning (BNSL), a classical problem that has received significant attention in empirical but also purely theoretical studies. We follow up on previous works that…

Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational…

In this work, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an…

In this thesis, we introduce Bayesian filtering as a principled framework for tackling diverse sequential machine learning problems, including online (continual) learning, prequential (one-step-ahead) forecasting, and contextual bandits. To…

We view disentanglement learning as discovering an underlying structure that equivariantly reflects the factorized variations shown in data. Traditionally, such a structure is fixed to be a vector space with data variations represented by…