# Efficient importance sampling for large sums of independent and identically distributed random variables

@article{Rached2021EfficientIS,
title={Efficient importance sampling for large sums of independent and identically distributed random variables},
author={Nadhir Ben Rached and Abdul-Lateef Haji-Ali and Gerardo Rubino and Ra{\'u}l Tempone},
journal={Stat. Comput.},
year={2021},
volume={31},
pages={79}
}
• Published 23 January 2021
• Mathematics, Computer Science
• Stat. Comput.
We discuss estimating the probability that the sum of nonnegative independent and identically distributed random variables falls below a given threshold, i.e., $$\mathbb {P}(\sum _{i=1}^{N}{X_i} \le \gamma )$$ P ( ∑ i = 1 N X i ≤ γ ) , via importance sampling (IS). We are particularly interested in the rare event regime when N is large and/or $$\gamma$$ γ is small. The exponential twisting is a popular technique for similar problems that, in most cases, compares…
3 Citations

### Rethinking the Defense Against Free-rider Attack From the Perspective of Model Weight Evolving Frequency

• Computer Science
ArXiv
• 2022
A novel defense method based on the model Weight Evolving Frequency, referred to as WEF-Defense is proposed, which achieves better defense effectiveness than the state-of-the-art baselines and identifies free-riders at an earlier stage of training.

### Efficient Importance Sampling Algorithm Applied to the Performance Analysis of Wireless Communication Systems Estimation

• Computer Science
ArXiv
• 2022
This work uses importance sampling (IS), being known for its efficiency in requiring less computations for achieving the same accuracy requirement, to propose a state-dependent IS scheme based on a stochastic optimal control (SOC) formulation to calculate rare events quantities.

### Learning-Based Importance Sampling via Stochastic Optimal Control for Stochastic Reaction Networks

• Computer Science
• 2021
The analysis and numerical experiments verify that the proposed learning-based IS approach substantially reduces MC estimator variance, resulting in a lower computational complexity in the rare event regime, compared with standard tau-leap MC estimators.

## References

SHOWING 1-10 OF 31 REFERENCES

### On the Capacity of FSO Links under Lognormal and Rician-Lognormal Turbulences

• Computer Science
2014 IEEE 80th Vehicular Technology Conference (VTC2014-Fall)
• 2014
A unified capacity analysis under weak and composite turbulences of a free-space optical (FSO) link that accounts for pointing errors and both types of detection techniques (i.e. intensity

### Unbiased estimation of the gradient of the log-likelihood in inverse problems

• Mathematics, Computer Science
Stat. Comput.
• 2021
A new methodology to unbiasedly estimate the gradient of the log-likelihood with respect to the unknown parameter, i.e. the expectation of the estimate has no discretization bias is developed, which can be used in stochastic gradient algorithms which benefit from unbiased estimates.

### Improving Simulation of Lognormal Sum Distributions with Hyperspace Replication

• Mathematics
2019 IEEE Global Communications Conference (GLOBECOM)
• 2019
A novel simulation procedure dubbed hyperspace replication is proposed and studied that achieves estimator variance reductions greater than 64 times in the left tail for practical values of outage probability, and 2 to 3 times inThe right tail compared to traditional Monte Carlo simulation.

### Asymptotic Outage Analysis on Dual-Branch Diversity Receptions Over Non-Identically Distributed Correlated Lognormal Channels

• Computer Science
IEEE Transactions on Communications
• 2019
A novel asymptotic technique is exploited to study non-identically distributed dual-branch lognormal fading channels with correlation and reveals insights into the long-standing problem of asymPTotic analysis for correlated lognorm fading channels, paving the way for analysis on more general channel models.

### Outage Probability Bounds of EGC Over Dual-Branch Non-Identically Distributed Independent Lognormal Fading Channels With Optimized Parameters

• Computer Science
IEEE Transactions on Vehicular Technology
• 2019
Close-form bounds of outage probability for dual-branch equal-gain combining system over non-identically distributed lognormal fading channels are derived and shown tight from low-to-high SNR regimes, which provides an efficient way to evaluate the EGC system without resorting to expensive Monte Carlo simulation or numerical integration.

### Fast and accurate computation of the distribution of sums of dependent log-normals

• Mathematics
Ann. Oper. Res.
• 2019
A new Monte Carlo methodology for the accurate estimation of the distribution of the sum of dependent log-normal random variables is presented, and it is found that theoretically strongly efficient estimators should be used with great caution in practice.

### Outage probability for lognormal-shadowed Rician channels

• 1997
A new general outage probability expression for a Rician signal received among L Rician interferers is derived. This result is shown to cover previous published expressions involving Rayleigh

### Rare Event Simulation using Monte Carlo Methods

• Computer Science
• 2009
This book sets out to present the mathematical tools available for the efficient simulation of rare events, and importance sampling and splitting are presented along with an exposition of how to apply these tools to a variety of fields ranging from performance and dependability evaluation of complex systems.

### On the generalization of the hazard rate twisting-based simulation approach

• Mathematics, Computer Science
Stat. Comput.
• 2018
This paper proposes a generalization of the well-known hazard rate twisting Importance Sampling-based approach that presents the advantage of being logarithmic efficient for arbitrary sums of RVs.