Related papers: A Bayesian Gaussian Process-Based Latent Discrimin…

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…

Variational Autoencoder based Bayesian Optimization (VAE-BO) has demonstrated its excellent performance in addressing high-dimensional structured optimization problems. However, current mainstream methods overlook the potential of utilizing…

Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back…

Studying the complex interactions between different brain regions is crucial in neuroscience. Various statistical methods have explored the latent communication across multiple brain regions. Two main categories are the Gaussian Process…

We introduce a class of scalable Bayesian hierarchical models for the analysis of massive geostatistical datasets. The underlying idea combines ideas on high-dimensional geostatistics by partitioning the spatial domain and modeling the…

Classification is a vital tool that is important for modelling many complex numerical models. A model or system may be such that, for certain areas of input space, the output either does not exist, or is not in a quantifiable form. Here, we…

In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as…

Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent…

Datasets that exhibit non-Gaussian characteristics are common in many fields, while the current modeling framework and available software for non-Gaussian models is limited. We introduce Linear Latent Non-Gaussian Models (LLnGMs), a unified…

Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the…

Anomalies are samples that significantly deviate from the rest of the data and their detection plays a major role in building machine learning models that can be reliably used in applications such as data-driven design and novelty…

The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do…

Memory units have been widely used to enrich the capabilities of deep networks on capturing long-term dependencies in reasoning and prediction tasks, but little investigation exists on deep generative models (DGMs) which are good at…

In this paper we present a fully Bayesian latent variable model which exploits conditional nonlinear(in)-dependence structures to learn an efficient latent representation. The latent space is factorized to represent shared and private…

Unsupervised anomaly detection aims to identify anomalous samples from highly complex and unstructured data, which is pervasive in both fundamental research and industrial applications. However, most existing methods neglect the complex…

Deep Gaussian processes (DGPs) are popular surrogate models for complex nonstationary computer experiments. DGPs use one or more latent Gaussian processes (GPs) to warp the input space into a plausibly stationary regime, then use typical GP…

We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution…

Longitudinal data are important in numerous fields, such as healthcare, sociology and seismology, but real-world datasets present notable challenges for practitioners because they can be high-dimensional, contain structured missingness…

In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then…

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,…