arXiv research

Proposes a new method for high-dimensional density estimation.

The paper proposes a novel tensor-based method for non-parametric density estimation.

New model for density estimation using tensor trains.

A new tensor ring mixture model improves density estimation efficiency.

The paper improves density estimation in high dimensions using tensor decompositions.

Paper proposes a new method for density estimation using tree tensor-network states.

Unified framework for PDF estimation using MDL-based binning and tensor factorization.

E$^2$M optimizes tensor density estimation by relaxing $α$-divergence to KL-divergence.

New method approximates high-dimensional probability densities efficiently.

A new method estimates rare events using tensor trains.

Method estimates joint probability density from samples using low-rank decomposition and random projections.

Generative model improves tabular data density estimation.

Novel approach for estimating joint probability densities using tensor decompositions and dictionaries.

Paper proposes a novel auto-encoder for latent density estimation.

New method reduces density estimation variance for multivariate data.

Sketch Tomography improves quantum state estimation accuracy.

Estimates joint probability distribution from 1-way marginals using low-rank tensors and random projections.

In this paper, we analyzed the physical meaning of scalar curvatures for a generalized Riemannian space. It is developed the Madsen's formulae for pressures and energy-densities with respect to the corresponding energy-momentum tensors. After that, the energy-momentum tensors, pressures, energy-densities and state-para…

For a symplectic manifold with quantizing line bundle, a choice of almost complex structure determines a Laplacian acting on tensor powers of the bundle. For high tensor powers Guillemin-Uribe showed that there is a well-defined cluster of low-lying eigenvalues, whose distribution is described by a spectral density fun…

Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is a challenging task due to the difficulty of choosing a proper tensor rank. In o…

We show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density functions for an arbitrary Riemannian Fisher information metric tensor. We note…

The article derives a novel Gram-Charlier A (GCA) Series based Extended Rule-of-Thumb (ExROT) for bandwidth selection in Kernel Density Estimation (KDE). There are existing various bandwidth selection rules achieving minimization of the Asymptotic Mean Integrated Square Error (AMISE) between the estimated probability d…

Paper generalizes tensor-train approximation for complex random variables.

MDMA provides closed-form marginals and conditionals for deep networks.

Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $α$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up by those vector fields that preserve the contact structure. If we cons…

The paper proves properties of strain tensors on surfaces with changing Gauss curvature.

We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated with a dimension partition tree. The distribution is assumed to admit a density …

Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical ones. Compared with TT and TR, the projected entangled pair state (PEPS), which is…

Let ${\cal F}_λ$ be the space of tensor densities on ${\bf R}^n$ of degree $λ$ (or, equivalently, of conformal densities of degree $-λn$) considered as a module over the Lie algebra $so(p+1,q+1)$. We classify $so(p+1,q+1)$-invariant bilinear differential operators from ${\cal F}_λ\otimes{\cal F}_μ$ to~${\cal F}_ν$. The…

We give a derivation of the Einstein equation for gravity which employs a definition of the local energy density of the gravitational field as a symmetric second rank tensor whose value for each observer gives the trace of the spatial part of the energy-stress tensor as seen by that observer. We give a physical motivat…

The paper computes metrics and Einstein tensors on even-dimensional manifolds.

A new metric tensor improves Riemann manifold Monte Carlo for Bayesian models.

Proposes a nonparametric tensor factorization for sparse data.

Efficient NTF algorithm for large sparse tensors.

Let ${\mathcal F}_λ(\mathbb{S}^n)$ be the space of tensor densities on $\mathbb{S}^n$ of degree $λ$. We consider this space as an induced module of the nonunitary spherical series of the group $\mathrm{SO}_0(n+1,1)$ and classify $(\mathrm{so}(n+1,1),\mathrm{SO}(n+1))$-sim$unitary submodules of${\mathcal F}_λ(\mathbb{S…

Paper develops polynomial approximations for complex probability densities.

A multi-neck spacetime wormhole is constructed with a simple metric tensor.

This work tackles multivariate CDFs and copulas using tensor factorization.

On a manifold with a projective connection we canonically assign a second order differential operator acting on the algebra of all densities to any tensor density $S^{ij}$ of fixed weight $λ$. In particular, this implies that on any projectively connected manifold, a `bracket' (symmetric biderivation) on the algebra of…

We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold $(M,\rg)$. In other words, we establish a canonical isomorphism between the spaces of polynomials on $T^*M$ and of differential operators on tensor densities over $M…

We consider the space of tensor densities on the n-dimensional sphere with degree lambda (or, equivalently, of conformal densities with degree lambda). This space is a module over the group of diffeomorphisms, and consequently over the Lie algebra of vector fields, on the sphere, and we first prove that as a module ove…

Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of prediction accuracy. We assume only that the densities have a convex parametrization …

In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger stretch tensor in a Gaussian process. We then consider an improvement on this a…

Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry information about the complementary subsystem. This is in contrast to the class…

We prove directly without using a density theorem that (i) the ADM mass defined in the usual way on an asymptotically flat manifold is equal to the mass defined intrinsically using Ricci tensor; (ii) the Hamiltonian formulation of center of mass and the center of mass defined intrinsically using Ricci tensor are the sa…

New tensorization theorem for Sobolev spaces on product spaces.

Differential conservation laws in Lagrangian field theory are usually related to symmetries of a Lagrangian density and are obtained if the Lie derivative of a Lagrangian density by a certain class of vector fields on a fiber bundle vanishes. However, only two field models meet this property in fact. In gauge theory of…

Develops efficient algorithms for learning latent-variable models using implicit moment tensor computation.