Related papers: Lecture Notes on "Non-Commutative Distributions"

This text provides a practical introduction to randomness and data analysis, in particular in the context of computer simulations. At the beginning, the most basics concepts of probability are given, in particular discrete and continuous…

This paper proposes a general multiple imputation approach for analyzing large-scale data with missing values. An imputation model is derived from a joint distribution induced by a latent variable model, which can flexibly capture…

We study matrices whose entries are free or exchangeable noncommutative elements in some tracial $W^*$-probability space. More precisely, we consider operator-valued Wigner and Wishart matrices and prove quantitative convergence to…

A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally…

A flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and negative binomial model, as well as to more general models accounting for excess zeros that…

The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…

We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of multivariate or non-Euclidean observations. We study a nonparametric framework that utilizes similarity information…

As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…

The nonparametric formulation of density-based clustering, known as modal clustering, draws a correspondence between groups and the attraction domains of the modes of the density function underlying the data. Its probabilistic foundation…

The algebra Mul[[B]] of formal multilinear function series over an algebra B and its quotient SymMul[[B]] are introduced, as well as corresponding operations of formal composition. In the setting of Mul[[B]], the unsymmetrized R- and…

This paper investigates the statistical properties of non-linear transformations (NLT) of random variables, in order to establish useful tools for estimation and information theory. Specifically, the paper focuses on linear regression…

Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…

We deal with the power-law q-distribution functions, so-called q-exponentials in nonextensive statistics. The system considered is a many-body Hamiltonian system with arbitrary interacting potentials. We find that the usual form of…

Commutative shuffle products are known to be intimately related to universal formulas for products, exponentials and logarithms in group theory as well as in the theory of free Lie algebras, such as, for instance, the…

The problem of factorization of a nonextensive probability distribution is discussed. It is shown that, in general, the correlation energy between the correlated subsystems in the canonical composite system can not be neglected even in the…

We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transforms from free probability, and that asymptotically there is…

We present a learning theory for the training of a linear system operator having an input compositional variable and propose a Bayesian inversion method for inferring the unknown variable from an output of a noisy linear system. We assume…

In this article, we continue our investigation on the role of non-commutativity in quantum theory. Using the method explained in "On non-commutativity in quantum theory (I): from classical to quantum probability", we analyze two toy models…

In the stochastic frontier model, the composed error term consists of the measurement error and the inefficiency term. A general assumption is that the inefficiency term follows a truncated normal or exponential distribution. In a wide…

In a recent work we have introduced a novel approach to study the effect of weak non-linearities in the transfer function on the information transmitted by an analogue channel, by means of a perturbative diagrammatic expansion. We extend…