Related papers: Free Exponential Families as Kernel Families
Stein kernels are a way of comparing probability distributions, defined via integration by parts formulas. We provide two constructions of Stein kernels in free probability. One is given by an explicit formula, and the other via free…
Generation of deviates from random graph models with non-trivial edge dependence is an increasingly important problem. Here, we introduce a method which allows perfect sampling from random graph models in exponential family form…
Trend filtering is a modern approach to nonparametric regression that is more adaptive to local smoothness than splines or similar basis procedures. Existing analyses of trend filtering focus on estimating a function corrupted by…
In this paper, we derive closed-form estimators for the parameters of some probability distributions belonging to the exponential family. A bootstrap bias-reduced version of these proposed closed-form estimators are also derived. A Monte…
Optimising probabilistic models is a well-studied field in statistics. However, its connection with the training of generative models remains largely under-explored. In this paper, we show that the evolution of time-varying generative…
The Appell-type polynomial family corresponding to the simplest non-commutative derivative operator turns out to be connected with the Boolean probability theory, the simplest of the three universal non-commutative probability theories (the…
Situations in many fields of research, such as digital communications, nuclear physics and mathematical finance, can be modelled with random matrices. When the matrices get large, free probability theory is an invaluable tool for describing…
In arXiv:0807.0677, K\"ostler and Speicher observed that de Finetti's theorem on exchangeable sequences has a free analogue if one replaces exchangeability by the stronger condition of invariance under quantum permutations. In this paper we…
A new family of integer-valued Cauchy-type distributions is introduced, the {\it Cauchy-Cacoullos family}. The characteristic function is evaluated, showing some interesting distributional properties, similar to the ordinary (continuous)…
Linear free divisors are free divisors, in the sense of K.Saito, with linear presentation matrix (example: normal crossing divisors). Using techniques of deformation theory on representations of quivers, we exhibit families of linear free…
Using the standard concepts of free random variables, we show that for a large class of nonhermitean random matrix models, the support of the eigenvalue distribution follows from their hermitean analogs using a conformal transformation. We…
Exponential families comprise a broad class of statistical models and parametric families like normal distributions, binomial distributions, gamma distributions or exponential distributions. Thereby the formal representation of its…
We present a systematic study of the family of positive definite (p.d.) kernels with the use of their associated feature maps and feature spaces. For a fixed set $X$, generalizing Loewner, we make precise the corresponding partially ordered…
In this paper we show how specific families of positive definite kernels serve as powerful tools in analyses of iteration algorithms for multiple layer feedforward Neural Network models. Our focus is on particular kernels that adapt well to…
In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary…
We will show that an extension of quantum field theory, recently proposed to solve the hierarchy problem, can give an elegant explanation of quark/lepton family replications. This scenario prefers fermion mass models based on a family…
Factors $\frac{X}{Y}$ in a free group $F$ with $Y$ normal in $X$ are considered. Precise results on the free structure of ${Y}$ relative to the free structure of ${X}$ when $\frac{X}{Y}$ is abelian are obtained. Some extensions and…
We introduce the notion of corestricted free products of a family of profinite groups indexed over an arbitrary profinite space. Using arithmetic results of the second author, this enables us to prove an analogue of Riemann's existence…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…
We introduce Exponential Family Discriminant Analysis (EFDA), a unified generative framework that extends classical Linear Discriminant Analysis (LDA) beyond the Gaussian setting to any member of the exponential family. Under the assumption…