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We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…

We propose a geometric latent-subspace framework for generative modeling of discrete data. Specifically, we introduce latent subspaces in the exponential parameter space of product manifolds of categorical distributions as a novel method…

We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary last layer, they can model manifold- and scalar-valued…

Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…

We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…

Gaussian process latent variable models (GPLVM) are a flexible and non-linear approach to dimensionality reduction, extending classical Gaussian processes to an unsupervised learning context. The Bayesian incarnation of the GPLVM Titsias…

A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…

Gaussian Process Latent Variable Models (GPLVMs) have become increasingly popular for unsupervised tasks such as dimensionality reduction and missing data recovery due to their flexibility and non-linear nature. An importance-weighted…

The paper proposes an identification procedure for autoregressive gaussian stationary stochastic processes wherein the manifest (or observed) variables are mostly related through a limited number of latent (or hidden) variables. The method…

Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally.…

Forecasting tasks using large datasets gathering thousands of heterogeneous time series is a crucial statistical problem in numerous sectors. The main challenge is to model a rich variety of time series, leverage any available external…

Riemannian geometry provides us with powerful tools to explore the latent space of generative models while preserving the underlying structure of the data. The latent space can be equipped it with a Riemannian metric, pulled back from the…

We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical…

We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic…

Multivariate categorical data occur in many applications of machine learning. One of the main difficulties with these vectors of categorical variables is sparsity. The number of possible observations grows exponentially with vector length,…

Latent tree graphical models are widely used in computational biology, signal and image processing, and network tomography. Here we design a new efficient, estimation procedure for latent tree models, including Gaussian and discrete,…

Generalising well in supervised learning tasks relies on correctly extrapolating the training data to a large region of the input space. One way to achieve this is to constrain the predictions to be invariant to transformations on the input…

Statistical models often assume that data are generated near a structured, smooth, or low-dimensional set. A common approach is to use Bayesian latent variable models, in which each observation is associated with a latent coordinate on the…

Analysis of heterogeneous patterns in complex spatio-temporal data finds usage across various domains in applied science and engineering, including training autonomous vehicles to navigate in complex traffic scenarios. Motivated by…