Related papers: Manifold learning with bi-stochastic kernels

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an…

We analyze the asymptotic behaviour of the heat kernel defined by a stochastically perturbed geodesic flow on the cotangent bundle of a Riemannian manifold for small time and small diffusion parameter. This extends WKB-type methods to a…

In this note we analyze the Caffarelli-Silvestre extension function using tools from the theory of stochastic analysis applied to Dirichlet problems. We use a stochastic approach to give the explicit formulation of the kernel associated to…

High-fidelity spectrum cartography is pivotal for spectrum management and wireless situational awareness, yet it remains a challenging ill-posed inverse problem due to the sparsity and irregularity of observations. Furthermore, existing…

We obtain two-sided heat kernel estimates for Riemannian manifolds with ends with mixed boundary condition, provided that the heat kernels for the ends are well understood. These results extend previous results of Grigor'yan and…

Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of…

Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provide a meaningful set of operations that are associated with…

We present a general framework for studying harmonic analysis of functions in the settings of various emerging problems in the theory of diffusion geometry. The starting point of the now classical diffusion geometry approach is the…

In this paper, we develop a framework for information theoretic learning based on infinitely divisible matrices. We formulate an entropy-like functional on positive definite matrices based on Renyi's axiomatic definition of entropy and…

Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…

A new algebraic approach for calculating the heat kernel for the Laplace operator on any Riemannian manifold with covariantly constant curvature is proposed. It is shown that the heat kernel operator can be obtained by an averaging over the…

We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative.…

High dimensional structured data such as text and images is often poorly understood and misrepresented in statistical modeling. The standard histogram representation suffers from high variance and performs poorly in general. We explore…

This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic…

The spectral gap is estimated for measure-valued diffusion processes induced by the intrinsic/extrinsic derivatives on the space of finite measures over a Riemannian manifold. This provides explicit exponential convergence rate for these…

The heat kernel associated with an elliptic second-order partial differential operator of Laplace type acting on smooth sections of a vector bundle over a Riemannian manifold, is studied. A general manifestly covariant method for…

Natural language processing often involves computations with semantic or syntactic graphs to facilitate sophisticated reasoning based on structural relationships. While convolution kernels provide a powerful tool for comparing graph…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

Typical architectures of Generative AdversarialNetworks make use of a unimodal latent distribution transformed by a continuous generator. Consequently, the modeled distribution always has connected support which is cumbersome when learning…

We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the…