Related papers: Adaptive Seeding for Gaussian Mixture Models
Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This paper gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior…
Clustering is a fundamental tool in statistical machine learning in the presence of heterogeneous data. Most recent results focus primarily on optimal mislabeling guarantees when data are distributed around centroids with sub-Gaussian…
We present a computationally-efficient strategy to initialise the hyperparameters of a Gaussian process (GP) avoiding the computation of the likelihood function. Our strategy can be used as a pretraining stage to find initial conditions for…
Selection of initial seeds greatly affects the quality of the clusters and in k-means type algorithms. Most of the seed selection methods result different results in different independent runs. We propose a single, optimal, outlier…
We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of…
Gaussian process (GP) models have received increasing attention in recent years due to their superb prediction accuracy and modeling flexibility. To address the computational burdens of GP models for large-scale datasets, distributed…
Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…
Mixtures of generalized normal distributions (MGND) have gained popularity for modelling datasets with complex statistical behaviours. However, the estimation of the shape parameter within the maximum likelihood framework is quite complex,…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
Training large-scale mixture of experts models efficiently on modern hardware requires assigning datapoints in a batch to different experts, each with a limited capacity. Recently proposed assignment procedures lack a probabilistic…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian…
Mixtures of experts probabilistically divide the input space into regions, where the assumptions of each expert, or conditional model, need only hold locally. Combined with Gaussian process (GP) experts, this results in a powerful and…
Variational inference, as an alternative to Markov chain Monte Carlo sampling, has played a transformative role in enabling scalable computation for complex Bayesian models. Nevertheless, existing approaches often depend on either rigid…
We consider maximum likelihood estimation for Gaussian Mixture Models (Gmms). This task is almost invariably solved (in theory and practice) via the Expectation Maximization (EM) algorithm. EM owes its success to various factors, of which…
Traffic forecasting is a challenging spatio-temporal modeling task and a critical component of urban transportation management. Current studies mainly focus on deterministic predictions, with limited considerations on the uncertainty and…
Gaussian Process Regression (GPR) is a Bayesian method for inferring profiles based on input data. The technique is increasing in popularity in the fusion community due to its many advantages over traditional fitting techniques including…
We develop and analyze a method for stochastic simulation optimization based on Gaussian process models within a trust-region framework. We focus on settings where the variance of the objective function is large, making accurate estimation…
Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
In this paper, we study the problem of learning one-dimensional Gaussian mixture models (GMMs) with a specific focus on estimating both the model order and the mixing distribution from independent and identically distributed (i.i.d.)…