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Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…
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 study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
Mixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering - at the same time - dimension reduction and model-based clustering. Unfortunately, the high prevalence of spurious solutions and…
We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…
In the mixture modeling frame, this paper presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. Firstly, it allows for possible nonlinear dependencies in the…
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…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
Spatial statistical models are commonly used in geographical scenarios to ensure spatial variation is captured effectively. However, spatial models and cluster algorithms can be complicated and expensive. This paper pursues three main…
In recent years, data dimensionality has increasingly become a concern, leading to many parameter and dimension reduction techniques being proposed in the literature. A parameter-wise co-clustering model, for data modelled via continuous…
We propose efficient computational methods to fit multivariate Gaussian additive models, where the mean vector and the covariance matrix are allowed to vary with covariates, in an empirical Bayes framework. To guarantee the…
Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covariance matrices in high-dimensional spaces, spherical GMMs…
We develop here a semiparametric Gaussian mixture model (SGMM) for unsupervised learning with valuable spatial information taken into consideration. Specifically, we assume for each instance a random location. Then, conditional on this…
We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Uncertainty is an inherent characteristic of biological and geospatial data which is almost made by measurement error in the observed values of the quantity of interest. Ignoring measurement error can lead to biased estimates and inflated…
This paper is concerned with an important issue in finite mixture modelling, the selection of the number of mixing components. We propose a new penalized likelihood method for model selection of finite multivariate Gaussian mixture models.…
With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…
While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings…
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.)…