Related papers: Isoperimetry between exponential and Gaussian
The probability distribution of percolation thresholds in finite lattices were first believed to follow a normal Gaussian behaviour. With increasing computer power and more efficient simulational techniques, this belief turned to a…
While small ball, or lower tail, asymptotic for Gaussian measures generated by solutions of stochastic ordinary differential equations is relatively well understood, a lot less is known in the case of stochastic partial differential…
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
We present a method for drawing isolines indicating regions of equal joint exceedance probability for bivariate data. The method relies on bivariate regular variation, a dependence framework widely used for extremes. This framework enables…
We establish a family of functional inequalities interpolating between the classical logarithmic Sobolev and Poincar\'e inequalities. We prove that they imply the concentration of measure phenomenon intermediate between Gaussian and…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
Isotropic $\alpha$-stable distributions are central in the theory of heavy-tailed distributions and play a role similar to that of the Gaussian density among finite second-moment laws. Given a sequence of $n$ observations, we are interested…
The isoperimetric problem is a classic topic in geometric measure theory, yet critical questions regarding the characterization of optimal solutions -- even asymptotically optimal ones -- remain largely unresolved. In this paper, we…
On the basis of a dilatation invariant Lagrangian, governed equations are determined for probability density and gauge potential of the non-stationary self-similar stochastic system. It is shown that an automodel regime is observed at small…
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…
This paper develops asymptotic approximations of $P(\int_Te^{f(t)}\,dt>b)$ as $b\rightarrow\infty$ for a homogeneous smooth Gaussian random field, $f$, living on a compact $d$-dimensional Jordan measurable set $T$. The integral of an…
We study the approximability of general convex sets in $\mathbb{R}^n$ by intersections of halfspaces, where the approximation quality is measured with respect to the standard Gaussian distribution $N(0,I_n)$ and the complexity of an…
We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the…
We consider a family of infinite dimensional product measures with tails between Gaussian and exponential, which we call $p$-exponential measures. We study their measure-theoretic properties and in particular their concentration. Our…
In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian…
Bayesian inverse problem on an infinite dimensional separable Hilbert space with the whole state observed is well posed when the prior state distribution is a Gaussian probability measure and the data error covariance is a cylindric…
We provide a very simple argument showing that the $\Phi^4_3$ measure does have quartic exponential tails, as expected from its formal expression. This shows that the corresponding moment problem is well-posed and provides a simple path to…
The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order…
The current study aims to examine uncertainty relations for measurements from generalized equiangular tight frames. Informationally overcomplete measurements are a valuable tool in quantum information processing, including tomography and…