Generalized cross-entropy methods with applications to rare-event simulation and optimization

The cross-entropy and minimum cross-entropy methods are well-known Monte Carlo simulation techniques for rare-event probability estimation and optimization. In this paper, we investigate how these methods can be eXtended to provide a general non-parametric cross-entropy framework based on φ-divergence distance measures. We show how the χ distance, in particular, yields a viable alternative to the Kullback—Leibler distance. The theory is illustrated with various eXamples from density estimation, rare-event simulation and continuous multi-eXtremal optimization

Minimum cross-entropy methods for rare-event simulation

We apply the minimum cross-entropy method (MinXEnt) for estimating rare-event probabilities for the sum of i.i.d. random variables. MinXEnt is an analogy of the MaXimum Entropy Principle in the sense that the objective is to minimize a relative (or cross) entropy of a target density h from an unknown density f under suitable constraints. The main idea is to use the solution to this optimization program as the simulation density in importance sampling. We shall see that some eXisting importance sampling methods can be cast in a MinXEnt program, such as the large deviations approach for light tails and the hazard rate twisting for heavy tails. As an eXtension, we shall consider a correlated version of this hazard rate twisted solution which gives better simulation results. The sample generation is based on a Gibbs sampler algorithm. © 2007, Sage Publications. All rights reserved

A Data-Driven Statistical Framework for Post-Grasp Manipulation

Abstract Grasping an object is usually only an intermediate goal for a robotic manipulator. To finish the task, the robot needs to know where the object is in its hand and what action to execute. This paper presents a general statistical framework to address these problems. Given a novel object, the robot learns a statistical model of grasp state conditioned on sensor values. The robot also builds a statistical model of the requirements of the task in terms of grasp state accuracy. Both of these models are constructed by offline experiments. The online process then grasps objects and chooses actions to maximize likelihood of success. This paper describes the framework in detail, and demonstrates its effectiveness experimentally in placing, dropping, and insertion tasks. To construct statistical models, the robot performed over 8000 grasp trials, and over 1000 trials each of placing, dropping and insertion.

Tail distribution of the maximum of correlated Gaussian random variables

In this article we consider the efficient estimation of the tail distribution of the maximum of correlated normal random variables. We show that the currently recommended Monte Carlo estimator has difficulties in quantifying its precision, because its sample variance estimator is an inefficient estimator of the true variance. We propose a simple remedy: to still use this estimator, but to rely on an alternative quantification of its precision. In addition to this we also consider a completely new sequential importance sampling estimator of the desired tail probability. Numerical experiments suggest that the sequential importance sampling estimator can be significantly more efficient than its competitor