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Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…
This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process,…
The hierarchical Dirichlet process (HDP) has become an important Bayesian nonparametric model for grouped data, such as document collections. The HDP is used to construct a flexible mixed-membership model where the number of components is…
Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…
In this paper, we propose a new framework for designing fast parallel algorithms for fundamental statistical subset selection tasks that include feature selection and experimental design. Such tasks are known to be weakly submodular and are…
MultiBUGS (https://www.multibugs.org) is a new version of the general-purpose Bayesian modelling software BUGS that implements a generic algorithm for parallelising Markov chain Monte Carlo (MCMC) algorithms to speed up posterior inference…
We consider the estimation of Dirichlet Process Mixture Models (DPMMs) in distributed environments, where data are distributed across multiple computing nodes. A key advantage of Bayesian nonparametric models such as DPMMs is that they…
We use the Sum of Squares method to develop new efficient algorithms for learning well-separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that substantially improve upon the statistical guarantees achieved…
Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…
Gaussian processes (GPs) are generally regarded as the gold standard surrogate model for emulating computationally expensive computer-based simulators. However, the problem of training GPs as accurately as possible with a minimum number of…
In their standard form Gaussian processes (GPs) provide a powerful non-parametric framework for regression and classificaton tasks. Their one limiting property is their $\mathcal{O}(N^{3})$ scaling where $N$ is the number of training data…
Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of automatic relevance determination kernels, but in high-dimensional datasets this approach can be unreliable. A more…
This work presents a fast and scalable algorithm for incremental learning of Gaussian mixture models. By performing rank-one updates on its precision matrices and determinants, its asymptotic time complexity is of \BigO{NKD^2} for $N$ data…
Modern statistical applications involving large data sets have focused attention on statistical methodologies which are both efficient computationally and able to deal with the screening of large numbers of different candidate models. Here…
Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…
Image segmentation is a fundamental step for the interpretation of Remote Sensing Images. Clustering or segmentation methods usually precede the classification task and are used as support tools for manual labeling. The most common…
Mixtures of experts have become an indispensable tool for flexible modelling in a supervised learning context, allowing not only the mean function but the entire density of the output to change with the inputs. Sparse Gaussian processes…
Finite mixture models, typically Gaussian mixtures, are well known and widely used as model-based clustering. In practical situations, there are many non-Gaussian data that are heavy-tailed and/or asymmetric. Normal inverse Gaussian (NIG)…
Bayesian nonparametric mixture models are common for modeling complex data. While these models are well-suited for density estimation, recent results proved posterior inconsistency of the number of clusters when the true number of…
Combining data has become an indispensable tool for managing the current diversity and abundance of data. But, as data complexity and data volume swell, the computational demands of previously proposed models for combining data escalate…