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An upper bound on ℓq norms of noisy functions
Volume PP - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Let Tϵ, 0 ≤ ϵ ≤ 1/2, be the noise operator acting on functions on the boolean cube {0, 1}n. Let f be a nonnegative function on {0, 1}n and let q ≥ 1. We upper bound the ℓq norm of Tϵf by the average ℓq norm...

An Upper Bound on $\ell_q$ Norms of Noisy Functions
2020 Edition, Volume 66, February 1, 2020 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Let ${T}_{ \epsilon }$ , $0 \le \epsilon \le 1/2$ , be the noise operator acting on functions on the boolean cube $\{0,1\}^{n}$ . Let $f$ be a nonnegative function on $\{0,1\}^{n}$ and let ${q} \ge 1$ . We upper bound the $\ell _{{q}}$ norm...

Capacity of a noisy function
2010 Edition, August 1, 2010 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

This paper presents an extension of the memoryless channel coding theorem to noisy functions, i.e. unreliable computing devices without internal states. It is shown that the concepts of equivocation and capacity can be defined for noisy computations in the...

On the Entropy of a Noisy Function
2016 Edition, Volume 62, October 1, 2016 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Let 0 <; ϵ <; 1/2 be a noise parameter, and let Tϵ be the noise operator acting on functions on the Boolean cube {0,1}n. Let f be a nonnegative function on {0,1}n. We upper bound the entropy of Tϵ f by the average entropy of conditional...

Extension of the direct optimization algorithm for noisy functions
2007 Edition, December 1, 2007 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

DIRECT (Dividing RECTangles) is a deterministic global optimization algorithm for bound-constrained problems. The algorithm, based on a space-partitioning scheme, performs both global exploration and local exploitation. In this paper, we modify the deterministic DIRECT algorithm to...

Cyclic stochastic optimization with noisy function measurements
2014 Edition, June 1, 2014 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Jointly optimizing a function over multiple parameters can sometimes prove very costly, particularly when the number of parameters is large. Cyclic optimization (optimization over a subset of the parameters while the rest are held fixed) may prove significantly simpler; it...

Adaptation of the Uobyqa Algorithm for Noisy Functions
2006 Edition, December 1, 2006 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

In many real-world optimization problems, the objective function may come from a simulation evaluation so that it is (a) subject to various levels of noise, (b) not differentiable, and (c) computationally hard to evaluate. In this paper, we modify Powell's UOBYQA algorithm to handle...

Sequential detection of convexity from noisy function evaluations
2014 Edition, December 1, 2014 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Consider a real-valued function that can only be evaluated with error. Given estimates of the function values from simulation on a finite set of points, we seek a procedure to detect convexity or non-convexity of the true function restricted to those...

A Stochastic Newton-Raphson Method with Noisy Function Measurements
2016 Edition, Volume 23, March 1, 2016 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

This letter shows that traditional Newton-Raphson (NR) method cannot achieve zero-convergence in presence of additive noise without adding a multiplicative gain. Furthermore, this gain needs to converge to zero. This article proposes a novel recursive algorithm providing optimal...

Boolean functions with noisy inputs
2008 Edition, July 1, 2008 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

We consider Boolean functions with noisy inputs. I.e., each binary input is sent over a binary symmetric channel with crossover probability isin before fed into the function. By proving an upper bound for the average l-sensitivity, we show that Boolean...

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