Related papers: Estimation of multivariate generalized gamma convo…

The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal…

Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…

Starting from one-range addition theorems for Slater-type functions, which are expansion in terms of complete and orthonormal functions based on the generalized Laguerre polynomials, Guseinov constructed addition theorems that are…

Transformed Gaussian Processes (TGPs) are stochastic processes specified by transforming samples from the joint distribution from a prior process (typically a GP) using an invertible transformation; increasing the flexibility of the base…

The reparameterization gradient has become a widely used method to obtain Monte Carlo gradients to optimize the variational objective. However, this technique does not easily apply to commonly used distributions such as beta or gamma…

We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…

In this paper, we deal with the convolution series that are a far reaching generalization of the conventional power series and the power series with the fractional exponents including the Mittag-Leffler type functions. Special attention is…

Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be ``large.'' For a fixed $\alpha \in \Q - \Z_{<0}$, Filaseta and Lam have shown that the $n$th degree Generalized Laguerre…

We give a $L^2\times L^2 \rightarrow L^2$ convolution estimate for singular measures supported on transversal hypersurfaces in $\mathbb{R}^n$, which improves earlier results of Bejenaru, Herr & Tataru as well as Bejenaru & Herr. The arising…

This paper explores mixture distributions induced by a product of the positive stable random variable and a power of another positive random variable. The paper also considers the convolution of the stable density with a gamma density.…

We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…

We study the hard edge limit of a multilevel extension of the Laguerre $\beta$-ensemble at zero temperature. In particular, we show that asymptotically the ensemble is given by Gaussians with covariance matrix expressible in terms of the…

Laguerre polynomials are orthogonal polynomials defined on positive half line with respect to weight $e^{-x}$. They have wide applications in scientific and engineering computations. However, the exponential growth of Laguerre polynomials…

We establish conditions under which Metropolis-Hastings (MH) algorithms with a position-dependent proposal covariance matrix will or will not have the geometric rate of convergence. Some of the diffusions based MH algorithms like the…

In many applications, linear models fit the data poorly. This article studies an appealing alternative, the generalized regression model. This model only assumes that there exists an unknown monotonically increasing link function connecting…

Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the…

We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…

Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…

While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We study the utility of Expectation Propagation (EP) as an approximate…

Traditional gradient-based sampling methods, like standard Hamiltonian Monte Carlo, require that the desired target distribution is continuous and differentiable. This limits the types of models one can define, although the presented models…