相关论文: Deviations bounds and conditional principles for t…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
Let $X_{1},..,X_{n}$ denote an i.i.d. sample with light tail distribution and $S_{1}^{n}$ denote the sum of its terms; let $a_{n}$ be a real sequence\ going to infinity with $n.$\ In a previous paper (\cite{BoniaCao}) it is proved that as…
The majority of existing probabilistic model checking case studies are based on well understood theoretical models and distributions. However, real-life probabilistic systems usually involve distribution parameters whose values are obtained…
An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…
A limit theorem for a sequence of diffusion processes on graphs is proved in a case when vary both parameters of the processes (the drift and diffusion coefficients on every edge and the asymmetry coefficients in every vertex), and…
Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we…
We study the large deviation estimates for the short time asymptotic behavior of a strongly degenerate diffusion process. Assuming a nilpotent structure of the Lie algebra generated by the driving vector fields, we obtain a graded large…
We provide an asymptotic analysis of linear transport problems in the diffusion limit under minimal regularity assumptions on the domain, the coefficients, and the data. The weak form of the limit equation is derived and the convergence of…
We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are "sub-Gaussian"~even when the randomness of the…
In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…
We present a method of deriving two boundary conditions at a thin membrane for diffusion from experimental data. This method can be really useful in complex membrane systems in which we do not know mechanisms of processes occurring within…
We extend the Gibbs conditioning principle to an abstract setting combining infinitely many linear equality constraints and non-linear inequality constraints, which need not be convex. A conditional large large deviation principle (LDP) is…
We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a diffusion. The scheme is based on a Gibbs variational principle that is used to determine the optimal (i.e.…
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
We obtain large deviation bounds for the measure of deviation sets associated to asymptotically additive and sub-additive potentials under some weak specification properties. In particular a large deviation principle is obtained in the case…
We provide non-asymptotic bounds for first and higher order inclusion probabilities of the rejective sampling model with various size parameters. Further we derive bounds in the semi-definite ordering for matrices that collect (conditional)…
In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $\mu$ and $\nu$ such that $\nu$ is log-concave with respect to $\mu$.…