Related papers: Classification of Generalized Multiresolution Anal…

We give a generalization of the random matrix ensembles, including all lassical ensembles. Then we derive the joint density function of the generalized ensemble by one simple formula, which give a direct and unified way to compute the…

The sum-of-correlations (SUMCOR) formulation of generalized canonical correlation analysis (GCCA) seeks highly correlated low-dimensional representations of different views via maximizing pairwise latent similarity of the views. SUMCOR is…

Formalism based on GA is an alternative to distributed representation models developed so far --- Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric…

A new approach to the construction of general persistent polyhierarchical classifications is proposed. It is based on implicit description of category polyhierarchy by a generating polyhierarchy of classification criteria. Similarly to…

We describe an automatic procedure for determining abundances from high resolution spectra. Such procedures are becoming increasingly important as large amounts of data are delivered from 8m telescopes and their high-multiplexing fiber…

We construct a geometric system from which the Hall algebra can be recovered. This system inherently satisfies higher associativity conditions and thus leads to a categorification of the Hall algebra. We then suggest how to use this…

The functional ANOVA, or Hoeffding decomposition, provides a principled framework for interpretability by decomposing a model prediction into main effects and higher-order interactions. For independent inputs, this classical decomposition…

Analyzing high-dimensional data presents challenges due to the "curse of dimensionality'', making computations intensive. Dimension reduction techniques, categorized as linear or non-linear, simplify such data. Non-linear methods are…

We propose a multiresolution Gaussian process to capture long-range, non-Markovian dependencies while allowing for abrupt changes. The multiresolution GP hierarchically couples a collection of smooth GPs, each defined over an element of a…

This article discusses some difficulties in the implementation of combinatorial algorithms associated with the choice of all elements with certain properties among the elements of a set with great cardinality.The problem has been resolved…

In this review article we consider linear regression analysis from a geometric perspective, looking at standard methods and outputs in terms of the lengths of the relevant vectors and the angles between these vectors. We show that standard…

We consider evidence integration from potentially dependent observation processes under varying spatio-temporal sampling resolutions and noise levels. We develop a multi-resolution multi-task (MRGP) framework while allowing for both…

We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of…

A standard tool for classifying the complexity of equivalence relations on $\omega$ is provided by computable reducibility. This reducibility gives rise to a rich degree structure. The paper studies equivalence relations, which induce…

In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases.…

Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires approximation of high-dimensional integrals. Many existing methods are tailored to the low-dimensional integrals produced by nested…

In this paper, we study spectral properties of generalized weighted Hilbert matrices. In particular, we establish results on the spectral norm, determinant, as well as various relations between the eigenvalues and eigenvectors of such…

In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class…

Generalized analytic functions over generalized analytic manifolds are build from sums of convergent real power series with non-negative real exponents (and some well-ordering condition on the support). In a paper by Mart\'in-Villaverde,…

Generalized canonical correlation analysis (GCCA) aims at finding latent low-dimensional common structure from multiple views (feature vectors in different domains) of the same entities. Unlike principal component analysis (PCA) that…