Related papers: One-Pass Sparsified Gaussian Mixtures
The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension,…
Diffusion models are distinguished by their exceptional generative performance, particularly in producing high-quality samples through iterative denoising. While current theory suggests that the number of denoising steps required for…
Superpixel segmentation algorithms are to partition an image into perceptually coherence atomic regions by assigning every pixel a superpixel label. Those algorithms have been wildly used as a preprocessing step in computer vision works, as…
A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific…
Gaussian mixture models (GMMs) are fundamental tools in statistical and data sciences. We study the moments of multivariate Gaussians and GMMs. The $d$-th moment of an $n$-dimensional random variable is a symmetric $d$-way tensor of size…
This letter presents a continuous probabilistic modeling methodology for spatial point cloud data using finite Gaussian Mixture Models (GMMs) where the number of components are adapted based on the scene complexity. Few hierarchical and…
Machine learning systems operate under the assumption that training and test data are sampled from a fixed probability distribution. However, this assumptions is rarely verified in practice, as the conditions upon which data was acquired…
A simple model to study subspace clustering is the high-dimensional $k$-Gaussian mixture model where the cluster means are sparse vectors. Here we provide an exact asymptotic characterization of the statistically optimal reconstruction…
Learning a Gaussian Mixture Model (GMM) is hard when the number of parameters is too large given the amount of available data. As a remedy, we propose restricting the GMM to a Gaussian Markov Random Field Mixture Model (GMRF-MM), as well as…
The parsimonious Gaussian mixture models, which exploit an eigenvalue decomposition of the group covariance matrices of the Gaussian mixture, have shown their success in particular in cluster analysis. Their estimation is in general…
Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
This paper is about variable selection, clustering and estimation in an unsupervised high-dimensional setting. Our approach is based on fitting constrained Gaussian mixture models, where we learn the number of clusters $K$ and the set of…
We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…
Spatial generalized linear mixed models (SGLMMs) are popular and flexible models for non-Gaussian spatial data. They are useful for spatial interpolations as well as for fitting regression models that account for spatial dependence, and are…
In this paper, we first propose a Bayesian neighborhood selection method to estimate Gaussian Graphical Models (GGMs). We show the graph selection consistency of this method in the sense that the posterior probability of the true model…
We investigate a Gaussian mixture model (GMM) with component means constrained in a pre-selected subspace. Applications to classification and clustering are explored. An EM-type estimation algorithm is derived. We prove that the subspace…
In this paper we propose a mixture model, SparseMix, for clustering of sparse high dimensional binary data, which connects model-based with centroid-based clustering. Every group is described by a representative and a probability…
We present the Gaussian process dynamical mixture model (GPDMM) and show its utility in single-example learning of human motion data. The Gaussian process dynamical model (GPDM) is a form of the Gaussian process latent variable model…
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…