Related papers: Scale-Based Gaussian Coverings: Combining Intra an…
Finite mixture such as the Gaussian mixture is a flexible and powerful probabilistic modeling tool for representing the multimodal distribution widely involved in many estimation and learning problems. The core of it is representing the…
Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…
We develop a simple framework for implementing a type of path integral "surgery" via correlated averaging over codimension-one defects/extended operators. This technique is used to construct replica manifolds by effectively cutting and…
Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…
In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex…
We introduce a novel approach to improve unsupervised hashing. Specifically, we propose a very efficient embedding method: Gaussian Mixture Model embedding (Gemb). The proposed method, using Gaussian Mixture Model, embeds feature vector…
One of the most popular algorithms for clustering in Euclidean space is the $k$-means algorithm; $k$-means is difficult to analyze mathematically, and few theoretical guarantees are known about it, particularly when the data is {\em…
Gaussian Splatting (GS), a recent technique for converting discrete points into continuous spatial representations, has shown promising results in 3D scene modeling and 2D image super-resolution. In this paper, we explore its untapped…
This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of clusters of the involved covariance matrices according to a criterion, such as sharing Principal…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…
When fitting Gaussian Mixture Models to 3D geometry, the model is typically fit to point clouds, even when the shapes were obtained as 3D meshes. Here we present a formulation for fitting Gaussian Mixture Models (GMMs) directly to a…
Coincidence probabilities, which yield Renyi entropies, are investigated in a generalized Gaussian model, which includes interparticle correlations
Humans are exposed to complex mixtures of environmental pollutants rather than single chemicals, necessitating methods to quantify the health effects of such mixtures. Research on environmental mixtures provides insights into realistic…
Gaussian mixture models are widely used to model data generated from multiple latent sources. Despite its popularity, most theoretical research assumes that the labels are either independent and identically distributed, or follows a Markov…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
The clustering of bounded data presents unique challenges in statistical analysis due to the constraints imposed on the data values. This paper introduces a novel method for model-based clustering specifically designed for bounded data.…
In the estimation of the causal effect under linear Structural Causal Models (SCMs), it is common practice to first identify the causal structure, estimate the probability distributions, and then calculate the causal effect. However, if the…
Principal Component Analysis (PCA), a classical dimensionality reduction technique, and 2D Gaussian representation, an adaptation of 3D Gaussian Splatting for image representation, offer distinct approaches to modeling visual data. We…
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…