Related papers: Levy Measure Decompositions for the Beta and Gamma…
This paper develops a theory for completely random measures in the framework of free probability. A general existence result for free completely random measures is established, and in analogy to the classical work of Kingman it is proved…
In [16], under mild conditions, a Wiener-Hopf type factorization is derived for the exponential functional of proper L\'evy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by…
Some special functions are particularly relevant in applied probability and statistics. For example, the incomplete beta function is the cumulative central beta distribution. In this paper, we consider the inversion of the central…
Several numerical evaluations of the density and distribution of convolution of independent gamma variables are compared in their accuracy and speed. In application to renewal processes, an efficient formula is derived for the probability…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
Learning to disentangle and represent factors of variation in data is an important problem in AI. While many advances have been made to learn these representations, it is still unclear how to quantify disentanglement. While several metrics…
We prove gradient estimates for harmonic functions with respect to a $d$-dimensional unimodal pure-jump Levy process under some mild assumptions on the density of its Levy measure. These assumptions allow for a construction of an unimodal…
A spectral representation for regularly varying L\'evy processes with index between one and two is established and the properties of the resulting random noise are discussed in detail giving also new insight in the $L^2$-case where the…
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…
Combinatorial Levy processes evolve on general state spaces of countable combinatorial structures. In this setting, the usual Levy process properties of stationary, independent increments are defined in an unconventional way in terms of the…
We propose isomorphism type identities for nonlinear functionals of general infinitely divisible processes. Such identities can be viewed as an analogy of the Cameron-Martin formula for Poissonian infinitely divisible processes but with…
Rule representations significantly influence the search capabilities and decision boundaries within the search space of Learning Classifier Systems (LCSs), a family of rule-based machine learning systems that evolve interpretable models…
Smooth Estimation of probability density and distribution functions from its sample is an attractive and an important problem that has applications in several fields such as, business, medicine, and environment. This article introduces a…
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…
Based on the concept of self-decomposability, we extend some recent multivariate L\'evy models built using multivariate subordination with the aim of capturing situations in which a sudden event in one market is propagated onto related…
This paper discusses the incomplete Gamma and Beta integrals involving the generalised hypergeometric function. The distribution of the largest and the smallest roots of a ratio arising in comparing the mean differences among groups is…
While most Bayesian nonparametric models in machine learning have focused on the Dirichlet process, the beta process, or their variants, the gamma process has recently emerged as a useful nonparametric prior in its own right. Current…
The ever-growing appearance of infinitely divisible laws and related processes in various areas, such as physics, mathematical biology, finance and economics, has fuelled an increasing demand for numerical methods of sampling and sample…
A rigorous connection between large deviations theory and Gamma-convergence is established. Applications include representations formulas for rate functions, a contraction principle for measurable maps, a large deviations principle for…
A new class of dependent random measures which we call {\it compound random measures} are proposed and the use of normalized versions of these random measures as priors in Bayesian nonparametric mixture models is considered. Their…