Related papers: A Refined Probabilistic Error Bound for Sums
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
We propose an implementation of symplectic implicit Runge-Kutta schemes for highly accurate numerical integration of non-stiff Hamiltonian systems based on fixed point iteration. Provided that the computations are done in a given floating…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…
Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic…
Let $X$ be a random variable with distribution function $F,$ and $X_{1},X_{2},...,X_{n}$ are independent copies of $X.$ Consider the order statistics $X_{i:n},$ $i=1,2,...,n$ and denote $F_{i:n}(x)=P\{X_{i:n}\leq x\}.$ Using majorization…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
Recent advances in statistical inference have significantly expanded the toolbox of probabilistic modeling. Historically, probabilistic modeling has been constrained to (i) very restricted model classes where exact or approximate…
Using the Moore--Penrose pseudoinverse, this work generalizes the gradient approximation technique called centred simplex gradient to allow sample sets containing any number of points. This approximation technique is called the…
Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…
We present a general approach to deriving bounds on the generalization error of randomized learning algorithms. Our approach can be used to obtain bounds on the average generalization error as well as bounds on its tail probabilities, both…
We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated…
We consider the error due to a single bit-flip in a floating point number. We assume IEEE 754 double precision arithmetic, which encodes binary floating point numbers in a 64-bit word. We assume that the bit-flip happens randomly so it has…
Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…
Over extended systems of finite type arithmetic, we utilize a formal representation of the outer measure to define a translation which allows for the systematic formalization of probabilistic statements. As a main result, this translation…
In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we…
This paper describes types of errors arising in a recently proposed method of incidence estimation from prevalence data. The errors are illustrated by a simulation study about a hypothetical irreversible disease. In addition, a way of…