Related papers: Cram\'er large deviation expansions for martingale…
In this paper we show a some new look at large deviation theorems from the viewpoint of the information-spectrum (IS) methods, which has been first exploited in information theory, and also demonstrate a new basic formula for the large…
We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…
A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to…
In classical optimal transport, the contributions of Benamou$-$Brenier and McCann regarding the time-dependent version of the problem are cornerstones of the field and form the basis for a variety of applications in other mathematical…
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…
We develop a maximum-likelihood based method for regression in a setting where the dependent variable is a random graph and covariates are available on a graph-level. The model generalizes the well-known $\beta$-model for random graphs by…
A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation-maximization…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…
We establish large deviation principles for the extremal eigenvalues of the Ginibre ensembles with good rate functions. In contrast to the typical estimates for the extremal eigenvalues, the large deviations for the real Ginibre ensemble…
For local martingales with nonnegative jumps, we prove a sufficient criterion for the corresponding exponential martingale to be a true martingale. The criterion is in terms of exponential moments of a convex combination of the optional and…
The sample-based Gibbs sampler has been the dominant method for approximating joint distribution from a collection of compatible full-conditional distributions. However for conditionally specified model, mixtures of incompatible full and…
We compute a variance lower bound for unbiased estimators in specified statistical models. The construction of the bound is related to the original Cram\'er-Rao bound, although it does not require the differentiability of the model.…
We compute Hermite expansions of some tempered distributions by using the Bargmann transform. In other words, we calculate the Taylor expansions of the corresponding entire functions. Our method of computations seems to be superior to the…
Symmetrical subdivisions in the space of Jager Pairs for continued fractions-like expansions will provide us with bounds on their difference. Results will also apply to the classical regular and backwards continued fractions expansions,…
In this paper we survey and further study partial sums of a stationary process via approximation with a martingale with stationary differences. Such an approximation is useful for transferring from the martingale to the original process the…
We establish a large deviation theorem for the empirical spectral distribution of random covariance matrices whose entries are independent random variables with mean 0, variance 1 and having controlled forth moments. Some new properties of…
We study deterministic and stochastic primal-dual sub-gradient algorithms for distributed optimization of a separable objective function with global inequality constraints. In both algorithms, the norm of the Lagrangian multipliers are…
Basing on main principles of statistical mechanics only, an exact virial expansion for path probability distribution of molecular Brownian particle in a fluid is derived which connects response of the distribution to perturbations of the…
We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more…
In actuarial practice, the usual independence assumptions for the collective risk model are often violated, implying a growing need for considering more general models that incorporate dependence. To this purpose, the present paper studies…