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The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…

Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…

Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…

Utilizing covariate information has been a powerful approach to improve the efficiency and accuracy for causal inference, which support massive amount of randomized experiments run on data-driven enterprises. However, state-of-art…

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…

Probabilistic Circuits (PCs) are a general and unified computational framework for tractable probabilistic models that support efficient computation of various inference tasks (e.g., computing marginal probabilities). Towards enabling such…

Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…

This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…

We show an alternative way of representing a Bayesian belief network by sensitivities and probability distributions. This representation is equivalent to the traditional representation by conditional probabilities, but makes dependencies…

Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…

Bayesian neural networks and deep ensembles represent two modern paradigms of uncertainty quantification in deep learning. Yet these approaches struggle to scale mainly due to memory inefficiency issues, since they require parameter storage…

We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives…

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

Several approximate inference methods have been proposed for deep discrete latent variable models. However, non-parametric methods which have previously been successfully employed for classical sparse coding models have largely been…

A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves…

We show that ensembles of deep neural networks, called deep ensembles, can be used to perform quantum parameter estimation while also providing a means for quantifying uncertainty in parameter estimates, which is a key advantage of using…

Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…

We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…