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We develop deep Poisson-gamma dynamical systems (DPGDS) to model sequentially observed multivariate count data, improving previously proposed models by not only mining deep hierarchical latent structure from the data, but also capturing…

The latent space of diffusion model mostly still remains unexplored, despite its great success and potential in the field of generative modeling. In fact, the latent space of existing diffusion models are entangled, with a distorted mapping…

Noting the importance of the latent variables in inference and learning, we propose a novel framework for autoencoders based on the homeomorphic transformation of latent variables, which could reduce the distance between vectors in the…

Neural processes (NPs) constitute a family of variational approximate models for stochastic processes with promising properties in computational efficiency and uncertainty quantification. These processes use neural networks with latent…

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

Group-invariant probability distributions appear in many data-generative models in machine learning, such as graphs, point clouds, and images. In practice, one often needs to estimate divergences between such distributions. In this work, we…

We consider the problem of parameter estimation using weakly supervised datasets, where a training sample consists of the input and a partially specified annotation, which we refer to as the output. The missing information in the annotation…

We introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo…

We introduce a generalized additive model for location, scale, and shape (GAMLSS) next of kin aiming at distribution-free and parsimonious regression modelling for arbitrary outcomes. We replace the strict parametric distribution…

In order to plan a safe maneuver an autonomous vehicle must accurately perceive its environment, and understand the interactions among traffic participants. In this paper, we aim to learn scene-consistent motion forecasts of complex urban…

Assumptions about invariances or symmetries in data can significantly increase the predictive power of statistical models. Many commonly used models in machine learning are constraint to respect certain symmetries in the data, such as…

Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…

This article presents a novel approach to construct Intrinsic Gaussian Processes for regression on unknown manifolds with probabilistic metrics (GPUM) in point clouds. In many real world applications, one often encounters high dimensional…

Quantitatively assessing relationships between latent variables and observed variables is important for understanding and developing generative models and representation learning. In this paper, we propose latent-observed dissimilarity…

Latent dynamical models are commonly used to learn the distribution of a latent dynamical process that represents a sequence of noisy data samples. However, producing samples from such models with high fidelity is challenging due to the…

We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…

Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…