Recently an error bound theorem was reported to conclude analytic error bounds for approximate Markov chains. The theorem required a uniform bound for marginal expectations of the approximate model. This note will relax this bound to steady state rather than marginal expectations as of practical interest: (i) to simplify verification and/or (ii) to obtain a more accurate error bound. An ALOHA-t...

In the simple quantum hypothesis testing problem, upper bounds on the error probabilities are shown based on a key matrix inequality. Concerning the error exponents, the upper bounds lead to noncommutative analogues of the Chernoff bound and the Hoeffding bound, which are identical with the classical counter part if the hypotheses, composed of two density operators, are mutually commutative. Ou...

Conditions are provided to conclude an error bound for truncations and perturbations of Markov decision problems. Both the average and finite horizon case are covered. The results are illustrated by a truncation of a Jacksonian queueing network with overflow control. An explicit error bound for this example is obtained. Key-words Markov Decision Problems * Truncation * Perturbation * Error Boun...

An evolutionary method whose selection and recombination operations are based on generalization error-bounds of support vector machine (SVM) can select a subset of potentially informative genes for SVM classifier very efficiently [7]. In this paper, we will use the derivative of error-bound (first-order criteria) to select and recombine gene features in the evolutionary process, and compare the...

When a convolutional code is used to provide forward error correction for packet data transmission, the standard performance measures of convolutional codes, i.e., bit error rate and first-event error rate, become less useful. Instead we are interested in the average probability of block (or packet) error. In this paper a modified transfer function approach is used to obtain a union bound on th...

This paper is devoted to study the Lipschitzian/Holderian type global error bound for systems of many finitely convex polynomial inequalities over a polyhedral constraint. Firstly, for systems of this type, we show that under a suitable asymtotic qualification condition, the Lipschitzian type global error bound property is equivalent to the Abadie qualification condition, in particular, the Lip...

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 probability, the new error bound is roughly half of the existing bounds. Based on the new bound, we give a new approximation algorithm, which is much simpler compa...

We obtain a computable a posteriori error bound on the broken energy norm of the error in the Fortin–Soulie finite element approximation of a linear second order elliptic problem with variable permeability. This bound is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms. The est...

Error bounds for decision trees are generally based on depth or breadth of the tree. In this paper, we propose a bound for error rate that depends both on the depth and the breadth of a specific decision tree constructed from the training samples. This bound is derived from sample complexity estimate based on PAC learnability. The proposed bound is compared with other traditional error bounds o...