Related papers: Improving approximation error bounds via truncatio…

In this article, we propose a new three parameter distribution by compounding negative binomial with reciprocal inverse Gaussian model called negative binomial-reciprocal inverse Gaussian distribution. This model is tractable with some…

We discuss about the Hermitian treatment of Dyson-type boson expansion theory. We show that the basic assumption of the conventional treatment does not hold in general and the method is only approximately valid. We also show that the…

Finite difference approximation, in addition to Taylor truncation errors, introduces numerical dispersion-and-dissipation errors into numerical solutions of partial differential equations. We analyze a class of finite difference schemes…

This paper is concerned with recovering the solution of a final value problem associated with a parabolic equation involving a non linear source and a non-local term, which to the best of our knowledge has not been studied earlier. It is…

The Bruss-Robertson inequality gives a bound on the maximal number of elements of a random sample whose sum is less than a specified value, and the extension of that inequality which is given here neither requires the independence of the…

The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between…

The Shannon sampling theorem for bandlimited wide sense stationary random processes was established in 1957, which and its extensions to various random processes have been widely studied since then. However, truncation of the Shannon series…

We present a bound for value-prediction error with respect to model misspecification that is tight, including constant factors. This is a direct improvement of the "simulation lemma," a foundational result in reinforcement learning. We…

In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…

Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a…

In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center…

As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables…

This work presents a new algorithm for empirical risk minimization. The algorithm bridges the gap between first- and second-order methods by computing a search direction that uses a second-order-type update in one subspace, coupled with a…

We compare the solutions of two one-dimensional Poisson problems on an interval with Robin boundary conditions, one with given data, and one where the data has been symmetrized. When the Robin parameter is positive and the symmetrization is…

We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly…

We introduce the Variational Holder (VH) bound as an alternative to Variational Bayes (VB) for approximate Bayesian inference. Unlike VB which typically involves maximization of a non-convex lower bound with respect to the variational…

In this paper, we study a class of problems where the sum of truncated convex functions is minimized. In statistical applications, they are commonly encountered when $\ell_0$-penalized models are fitted and usually lead to NP-Hard…

We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…

We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, termed variational boosting, iteratively refines an existing variational approximation…

Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural…