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We consider the problem of choosing design parameters to minimize the probability of an undesired rare event that is described through the average of $n$ iid random variables. Since the probability of interest for near optimal design…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
In this paper, I proof that Importance Sampling estimates based on dependent sample sets are consistent under certain conditions. This can be used to reduce variance in Bayesian Models with factorizing likelihoods, using sample sets that…
Adaptive importance sampling (AIS) algorithms are a rising methodology in signal processing, statistics, and machine learning. An effective adaptation of the proposals is key for the success of AIS. Recent works have shown that gradient…
In this paper, we consider the problem of numerical investigation of the counting statistics for a class of one-dimensional systems. Importance sampling, the cornerstone technique usually implemented for such problems, critically hinges on…
Computation of extreme quantiles and tail-based risk measures using standard Monte Carlo simulation can be inefficient. A method to speed up computations is provided by importance sampling. We show that importance sampling algorithms,…
Time-to-event endpoints show an increasing popularity in phase II cancer trials. The standard statistical tool for such one-armed survival trials is the one-sample log-rank test. Its distributional properties are commonly derived in the…
We show that the variance of the Monte Carlo estimator that is importance sampled from an exponential family is a convex function of the natural parameter of the distribution. With this insight, we propose an adaptive importance sampling…
Rare event probability estimation is an important topic in reliability analysis. Stochastic methods, such as importance sampling, have been developed to estimate such probabilities but they often fail in high dimension. In this paper, we…
Recent policy optimization approaches (Schulman et al., 2015a; 2017) have achieved substantial empirical successes by constructing new proxy optimization objectives. These proxy objectives allow stable and low variance policy learning, but…
We provide a detailed importance sampling analysis for variance reduction in stochastic volatility models. The optimal change of measure is obtained using a variety of results from large and moderate deviations: small-time, large-time,…
We study the problem of estimating the mean of a random vector in $\mathbb{R}^d$ based on an i.i.d.\ sample, when the accuracy of the estimator is measured by a general norm on $\mathbb{R}^d$. We construct an estimator (that depends on the…
Machine learning optimization often depends on stochastic gradient descent, where the precision of gradient estimation is vital for model performance. Gradients are calculated from mini-batches formed by uniformly selecting data samples…
Random sampling is an essential tool in the processing and transmission of data. It is used to summarize data too large to store or manipulate and meet resource constraints on bandwidth or battery power. Estimators that are applied to the…
Probabilistic models based on Restricted Boltzmann Machines (RBMs) imply the evaluation of normalized Boltzmann factors, which in turn require from the evaluation of the partition function Z. The exact evaluation of Z, though, becomes a…
An importance sampling approach for sampling copula models is introduced. We propose two algorithms that improve Monte Carlo estimators when the functional of interest depends mainly on the behaviour of the underlying random vector when at…
This study presents an importance sampling formulation based on adaptively relaxing parameters from the indicator function and/or the probability density function. The formulation embodies the prevalent mathematical concept of relaxing a…
First, we analyze the variance of the Cross Validation (CV)-based estimators used for estimating the performance of classification rules. Second, we propose a novel estimator to estimate this variance using the Influence Function (IF)…
The goal of importance sampling is to estimate the expected value of a given function with respect to a probability measure $\nu$ using a random sample of size $n$ drawn from a different probability measure $\mu$. If the two measures $\mu$…
Importance sampling is a central idea underlying off-policy prediction in reinforcement learning. It provides a strategy for re-weighting samples from a distribution to obtain unbiased estimates under another distribution. However,…