Related papers: L\'evy graphical models
Given discrete time observations over a growing time interval, we consider a nonparametric Bayesian approach to estimation of the L\'evy density of a L\'evy process belonging to a flexible class of infinite activity subordinators. Posterior…
Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art…
Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…
We show that a conditional characteristic function of generalized L\'evy stochastic areas can be viewed as a product a selfdecomposable distribution (i.e., L\'evy class L distribution) and its background driving characteristic function.…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
This work reports the most relevant technical aspects in the problem of learning the \emph{Markov network structure} from data. Such problem has become increasingly important in machine learning, and many other application fields of machine…
We address the problem of learning graphical models which correspond to high dimensional autoregressive stationary stochastic processes. A graphical model describes the conditional dependence relations among the components of a stochastic…
Genetical genomics experiments have now been routinely conducted to measure both the genetic markers and gene expression data on the same subjects. The gene expression levels are often treated as quantitative traits and are subject to…
In this work we handle with categorical (ordinal) variables and we focus on the (in)dependence relationship under the marginal, conditional and context-specific perspective. If the first two are well known, the last one concerns…
We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data, learning an undirected graph we call the unconditional dependence graph. We show that unconditional dependence graphs…
We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…
We construct intrinsic on-and off-diagonal upper and lower estimates for the transition probability density of a L\'evy process in small time. By intrinsic we mean that such estimates reflect the structure of the characteristic exponent of…
Undirected probabilistic graphical models represent the conditional dependencies, or Markov properties, of a collection of random variables. Knowing the sparsity of such a graphical model is valuable for modeling multivariate distributions…
We present a comprehensive study of graphical log-linear models for contingency tables. High dimensional contingency tables arise in many areas such as computational biology, collection of survey and census data and others. Analysis of…
In this paper we develop an $L_2$-theory for stochastic partial differential equations driven by L\'evy processes. The coefficients of the equations are random functions depending on time and space variables, and no smoothness assumption of…
We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a…
Let $X = \{X_{u}\}_{u \in U}$ be a real-valued Gaussian process indexed by a set $U$. It can be thought of as an undirected graphical model with every random variable $X_{u}$ serving as a vertex. We characterize this graph in terms of the…
We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian vector time series (discrete-time process) from a finite-length observation. By contrast to existing approaches, we do not rely on a…
Distributional properties -including Laplace transforms- of integrals of Markov processes received a lot of attention in the literature. In this paper, we complete existing results in several ways. First, we provide the analytical solution…
The classical notion of L\'evy process is generalized to one that takes as its values probabilities on a first order model equipped with a commutative semigroup. This is achieved by applying a convolution product on definable probabilities…