Related papers: Squared families: Searching beyond regular probabi…
Consider the centered Gaussian vector $X$ in $\R^n$ with covariance matrix $ \Sigma.$ Randomize $\Sigma$ such that $ \Sigma^{-1}$ has a Wishart distribution with shape parameter $p>(n-1)/2$ and mean $p\sigma.$ We compute the density…
We study shrinkage estimation of the mean parameters of a class of multivariate distributions for which the diagonal entries of the corresponding covariance matrix are certain quadratic functions of the mean parameter. This class of…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We consider random transverse-field Ising spin chains and study the magnetization and the energy-density profiles by numerically exact calculations in rather large finite systems ($L\le 128$). Using different boundary conditions (free,…
We give a complete classification of 1-dimensional exponential families $\mathcal{E}$ defined over a finite space $\Omega=\{x_{0}, ...,x_{n}\}$ whose Hessian scalar curvature is constant. We observe an interesting phenomenon: if…
In this paper we define Schwartz families in tempered distribution spaces and prove many their properties. Schwartz families are the analogous of infinite dimensional matrices of separable Hilbert spaces, but for the Schwartz test function…
Sketching is a probabilistic data compression technique that has been largely developed in the computer science community. Numerical operations on big datasets can be intolerably slow; sketching algorithms address this issue by generating a…
With the development of Big data technology, data analysis has become increasingly important. Traditional clustering algorithms such as K-means are highly sensitive to the initial centroid selection and perform poorly on non-convex…
Exponential families are widely used in machine learning, including many distributions in continuous and discrete domains (e.g., Gaussian, Dirichlet, Poisson, and categorical distributions via the softmax transformation). Distributions in…
For the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present…
We formalise and generalise the definition of the family of univariate double two--piece distributions, obtained by using a density--based transformation of unimodal symmetric continuous distributions with a shape parameter. The resulting…
The paper introduces scaled Bregman distances of probability distributions which admit non-uniform contributions of observed events. They are introduced in a general form covering not only the distances of discrete and continuous stochastic…
In many real-world scenarios, it is crucial to be able to reliably and efficiently reason under uncertainty while capturing complex relationships in data. Probabilistic circuits (PCs), a prominent family of tractable probabilistic models,…
The power prior is a popular tool for constructing informative prior distributions based on historical data. The method consists of raising the likelihood to a discounting factor in order to control the amount of information borrowed from…
The free convolution is the binary operation on the set of probability measures on the real line which allows to deduce, from the individual spectral distributions, the spectral distribution of a sum of independent unitarily invariant…
In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties,…
The family of multivariate skew-normal distributions has many interesting properties. It is shown here that these hold for a general class of skew-elliptical distributions. For this class, several stochastic representations are established…
The kernel exponential family is a rich class of distributions, which can be fit efficiently and with statistical guarantees by score matching. Being required to choose a priori a simple kernel such as the Gaussian, however, limits its…
In this paper, a new mixture family of multivariate normal distributions, formed by mixing multivariate normal distribution and skewed distribution, is constructed. Some properties of this family, such as characteristic function, moment…
Consider a random graph $G$ of size $N$ constructed according to a \textit{graphon} $w \, : \, [0,1]^{2} \mapsto [0,1]$ as follows. First embed $N$ vertices $V = \{v_1, v_2, \ldots, v_N\}$ into the interval $[0,1]$, then for each $i < j$…