Related papers: Field Formulation of Parzen Data Analysis
Traditional interpolation techniques for particle tracking include binning and convolutional formulas that use pre-determined (i.e., closed-form, parameteric) kernels. In many instances, the particles are introduced as point sources in time…
Critical points of a scalar quantitiy are either extremal points or saddle points. The character of the critical points is determined by the sign distribution of the eigenvalues of the Hessian matrix. For a two-dimensional homogeneous and…
Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and…
Score estimation is the backbone of score-based generative models (SGMs), especially denoising diffusion probabilistic models (DDPMs). A key result in this area shows that with accurate score estimates, SGMs can efficiently generate samples…
Machine learning techniques can reveal hidden structure in large data amounts and can potentially extent or even replace analytical scientific methods. In nanophotonics, modes can increase the light yield from emitters located inside the…
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…
Primordial non-Gaussianity introduces a scale-dependent variation in the clustering of density peaks corresponding to rare objects. This variation, parametrized by the bias, is investigated on scales where a linear perturbation theory is…
In the framework of the grand-canonical ensemble of statistical mechanics, we give an exact diagrammatic representation of the density profiles in a classical multicomponent plasma near a dielectric wall. By a reorganization of Mayer…
The dependence of galaxy clustering on local density provides an effective method for extracting non-Gaussian information from galaxy surveys. The two-point correlation function (2PCF) provides a complete statistical description of a…
In this article, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend…
We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of…
Diffusion in rugged free-energy landscapes is central to diverse problems in chemical physics, biomolecular dynamics, polymer transport and numerous disordered systems. Zwanzig's well-known classic mean-field theory predicts that roughness…
This work presents a formalism for deriving likelihoods of the cosmological density field directly from first principles within Perturbation Theory (PT). By assuming a perturbative expansion around the Gaussian initial density field and…
The interest in variable selection for clustering has increased recently due to the growing need in clustering high-dimensional data. Variable selection allows in particular to ease both the clustering and the interpretation of the results.…
We connect shift-invariant characteristic kernels to infinitely divisible distributions on $\mathbb{R}^{d}$. Characteristic kernels play an important role in machine learning applications with their kernel means to distinguish any two…
Spectral clustering is a powerful technique for clustering high-dimensional data, utilizing graph-based representations to detect complex, non-linear structures and non-convex clusters. The construction of a similarity graph is essential…
In this article we construct a maximal set of kernels for a multi-parameter linear scale-space that allow us to construct trees for classification and recognition of one-dimensional continuous signals similar the Gaussian linear scale-space…
One of the key advantages of 3D rendering is its ability to simulate intricate scenes accurately. One of the most widely used methods for this purpose is Gaussian Splatting, a novel approach that is known for its rapid training and…
Gaussian mixture block models are distributions over graphs that strive to model modern networks: to generate a graph from such a model, we associate each vertex $i$ with a latent feature vector $u_i \in \mathbb{R}^d$ sampled from a mixture…
We consider a random geometric graph with vertices sampled from a probability measure supported on $\mathbb R^d$, and study its connectivity. We show the graph is typically disconnected, unless the sampling density has superexponential…