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Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic…

Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting…

Quantifying uncertainty in medical image segmentation applications is essential, as it is often connected to vital decision-making. Compelling attempts have been made in quantifying the uncertainty in image segmentation architectures, e.g.…

Analyzing and interpreting time-dependent stochastic data requires accurate and robust density estimation. In this paper we extend the concept of normalizing flows to so-called temporal Normalizing Flows (tNFs) to estimate time dependent…

The mean-field theory for two-layer neural networks considers infinitely wide networks that are linearly parameterized by a probability measure over the parameter space. This nonparametric perspective has significantly advanced both the…

Density estimation, which estimates the distribution of data, is an important category of probabilistic machine learning. A family of density estimators is mixture models, such as Gaussian Mixture Model (GMM) by expectation maximization.…

Flow models have rapidly become the go-to method for training and deploying large-scale generators, owing their success to inference-time flexibility via adjustable integration steps. A crucial ingredient in flow training is the choice of…

This paper introduces the multivariate beta mixture model (MBMM), a new probabilistic model for soft clustering. MBMM adapts to diverse cluster shapes because of the flexible probability density function of the multivariate beta…

The mixture of factor analyzers (MFA) model provides a powerful tool for analyzing high-dimensional data as it can reduce the number of free parameters through its factor-analytic representation of the component covariance matrices. This…

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential…

Mixture Density Networks (MDNs) can be used to generate probability density functions of model parameters $\boldsymbol{\theta}$ given a set of observables $\mathbf{x}$. In some applications, training data are available only for discrete…

Scientific machine learning (SciML) increasingly requires models that capture multimodal conditional uncertainty arising from ill-posed inverse problems, multistability, and chaotic dynamics. While recent work has favored highly expressive…

We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…

Building on the recent trend of new deep generative models known as Normalizing Flows (NF), simulation-based inference (SBI) algorithms can now efficiently accommodate arbitrary complex and high-dimensional data distributions. The…

Variational inference (VI) is a technique to approximate difficult to compute posteriors by optimization. In contrast to MCMC, VI scales to many observations. In the case of complex posteriors, however, state-of-the-art VI approaches often…

Generative models, particularly normalizing flows, have shown exceptional performance in learning probability distributions across various domains of physics, including statistical mechanics, collider physics, and lattice field theory. In…

As deep neural networks continue to revolutionize various application domains, there is increasing interest in making these powerful models more understandable and interpretable, and narrowing down the causes of good and bad predictions. We…

Deep generative models complement Markov-chain-Monte-Carlo methods for efficiently sampling from high-dimensional distributions. Among these methods, explicit generators, such as Normalising Flows (NFs), in combination with the Metropolis…

Normalizing Flows (NFs) are a class of generative models distinguished by a mathematically invertible architecture, where the forward pass transforms data into a latent space for density estimation, and the reverse pass generates new…

Machine Learning (ML) models in Robotic Assembly Sequence Planning (RASP) need to be introspective on the predicted solutions, i.e. whether they are feasible or not, to circumvent potential efficiency degradation. Previous works need both…