Related papers: An alternative method for solving the Gaussian int…

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…

This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…

In this paper, we argue for the utility of deterministic inference in the classical problem of numerical linear algebra, that of solving a linear system. We show how the Gaussian belief propagation solver, known to work for symmetric…

We propose a new fiducial Markov Chain Monte Carlo (MCMC) method for fitting parametric Gaussian models. We utilize the Cayley transform to decompose the parametric covariance matrix, which in turn allows us to formulate a general data…

A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very…

Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with…

The current form of Tsallis distribution for a Hamiltonian system with an arbitrary potential is found to represent a simple isothermal situation. In this letter, the q-exponential of a sum can be applied as the product of the q-exponential…

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on…

In this work we review the application of the theory of Gaussian processes to the modeling of noise in pulsar-timing data analysis, and we derive various useful and optimized representations for the likelihood expressions that are needed in…

In this paper we study a new generalization of the kinetic equation emerging in run-and-tumble models. We show that this generalization leads to a wide class of generalized fractional kinetic (GFK) and telegraph-type equations depending by…

In the frame of the traditional wavelet-Galerkin method based on the compactly supported wavelets, it is important to calculate the so-called connection coefficients that are some integrals whose integrands involve products of wavelets,…

We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement…

We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and…

The paper presents a new formula for the fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as…

We describe a formula for the Taylor series expansion of the Gaussian kernel around the origin of $\Rn\times\R$.

The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one…

Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…

This is a sequel to the paper [K. Fujii : SIGMA {\bf 7} (2011), 022, 12 pages]. In this paper we treat a non-Gaussian integral based on a quartic polynomial and make a mathematical experiment by use of MATHEMATICA whether the integral is…

In parametric equations - stochastic equations are a special case - one may want to approximate the solution such that it is easy to evaluate its dependence of the parameters. Interpolation in the parameters is an obvious possibility, in…

In recent work on the area of approximation methods for the solution of nonlinear differential equations, it has been suggested that the so-called generalized Taylor series approach is equivalent to the homotopy analysis method. In the…