Related papers: Hilbert Space Embedding for Dirichlet Process Mixt…
This paper focuses on the problem of hierarchical non-overlapping clustering of a dataset. In such a clustering, each data item is associated with exactly one leaf node and each internal node is associated with all the data items stored in…
Weaving Hilbert space frames have been introduced recently by Bemrose et al. to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle, so we obtain new…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
We study embeddings between reproducing kernel Hilbert spaces $H(K)$ of functions of $d \in \mathbb{N} \cup \{\infty\}$ variables. The kernels $K$ are superpositions of weighted finite tensor products of a fixed univariate kernel. The basic…
Clustering is one of the most widely used procedures in the analysis of microarray data, for example with the goal of discovering cancer subtypes based on observed heterogeneity of genetic marks between different tissues. It is well-known…
Kernel embeddings of distributions have recently gained significant attention in the machine learning community as a data-driven technique for representing probability distributions. Broadly, these techniques enable efficient computation of…
Conditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distributions within the corresponding reproducing kernel Hilbert…
Consider a Dirichlet process mixture model (DPM) with random precision parameter $\alpha$, inducing $K_n$ clusters over $n$ observations through its latent random partition. Our goal is to specify the prior distribution…
Compositional data, representing proportions constrained to the simplex, arise in diverse fields such as geosciences, ecology, genomics, and microbiome research. Existing nonparametric density estimation methods often rely on…
We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are…
Transfer operators such as the Perron--Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems. The eigenfunctions of these operators can be used to detect metastable sets, to project the…
Clustering has become a core technology in machine learning, largely due to its application in the field of unsupervised learning, clustering, classification, and density estimation. A frequentist approach exists to hand clustering based on…
Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…
The field of quantum machine learning is a promising way to lead to a revolution in intelligent data processing methods. In this way, a hybrid learning method based on classic kernel methods is proposed. This proposal also requires the…
Employing nonparametric methods for density estimation has become routine in Bayesian statistical practice. Models based on discrete nonparametric priors such as Dirichlet Process Mixture (DPM) models are very attractive choices due to…
In this paper, we discuss the non-collapsibility concept and propose a new approach based on Dirichlet process mixtures to estimate the conditional effect of covariates in non-collapsible models. Using synthetic data, we evaluate the…
In this present paper we introduce weaving Hilbert space frames in the continuous case, we give new approaches for manufacturing pairs of woven continuous frames and we obtain new properties in continuous weaving frame theory related to…
When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…
The conventional use of the Generalized Extreme Value (GEV) distribution to model block maxima may be inappropriate when extremes are actually structured into multiple heterogeneous groups. In this work, we propose a novel approach for…
This paper introduces a hierarchical framework to incorporate Hellinger distance methods into Bayesian analysis. We propose to modify a prior over non-parametric densities with the exponential of twice the Hellinger distance between a…