Related papers: On infinite covariance expansions

Rank 1 inhomogeneous random graphs are a natural generalization of Erd\H{o}s R\'enyi random graphs. In this generalization each node is given a weight. Then the probability that an edge is present depends on the product of the weights of…

In this note, we revisit the recent work of Diakonikolas, Gouleakis, Kane, Peebles, and Price (2021), and provide an alternative proof of their main result. Our argument does not rely on any specific property of Poisson random variables…

This work presents a new classifier that is specifically designed to be fully interpretable. This technique determines the probability of a class outcome, based directly on probability assignments measured from the training data. The…

We define a novel class of additive models, called Extended Latent Gaussian Models, that allow for a wide range of response distributions and flexible relationships between the additive predictor and mean response. The new class covers a…

In [8], asymptotic expansion of the martingale with mixed normal limit was provided. The expansion formula is expressed by the adjoint of a random symbol with coefficients described by the Malliavin calculus, differently from the standard…

Gaussian graphical models typically assume a homogeneous structure across all subjects, which is often restrictive in applications. In this article, we propose a weighted pseudo-likelihood approach for graphical modeling which allows…

In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of…

The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…

Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.

An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…

Bessel and modified Bessel functions of imaginary order $i\nu$ ($\nu >0$) are studied. Asymptotic expansions are derived as $\nu \to \infty$ that are uniformly valid in unbounded complex domains, with error bounds provided. Coupled with…

We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for…

We present a novel approach to estimating discrete distributions with (potentially) infinite support in the total variation metric. In a departure from the established paradigm, we make no structural assumptions whatsoever on the sampling…

The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we…

For functions of independent random variables, various upper and lower variance bounds are revisited in diverse settings. These are then specialized to the Bernoulli, Gaussian, infinitely divisible cases and to Banach space valued random…

Consider a regression model with fixed design and Gaussian noise where the regression function can potentially be well approximated by a function that admits a sparse representation in a given dictionary. This paper resorts to exponential…

This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and…

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…

This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models…

We obtain asymptotic expansions for local probabilities of partial sums for uniformly bounded independent but not necessarily identically distributed integer-valued random variables. The expansions involve products of polynomials and…