Importance Sampling Technique Research Articles

Order-restricted statistical inference and optimal censoring scheme for Gompertz distribution based on joint type-II progressive censored data

This paper considers the order-restricted statistical inference for two populations based on the joint type-II progressive censoring scheme. The lifetime distributions of the two populations are supposed to follow the Gompertz distribution with the same shape parameter but different scale parameters. The maximum likelihood estimates of the unknown parameters are derived by employing the Newton-Raphson algorithm and the expectation-maximization algorithm, respectively. The Fisher information matrix is then employed to construct asymptotic confidence intervals. For Bayes estimation, we assume an ordered Beta-Gamma prior for the scale parameters and a Gamma prior for the common shape parameter. Bayes estimations and the highest posterior density credible intervals for unknown parameters under two different loss functions are obtained with the importance sampling technique. To evaluate the performance of order-restricted inference, extensive Monte Carlo simulations are performed and two air-conditioning systems datasets are used to illustrate the proposed inference methods. In addition, the results are compared with the case when there is no order restriction on the parameters. Finally, the optimal censoring scheme is obtained by four optimality criteria.

Model-Centric Integration of Uncertain Expert Knowledge into Importance Sampling-Based Parameter Estimation

This study presents a model-based parameter estimation method for integrating and validating uncertainty in expert knowledge and simulation models. The parameters of the models of complex systems are often unknown due to a lack of measurement data. The experience-based knowledge of experts can substitute missing information, which is usually imprecise. The novelty of the present paper is a method based on Monte Carlo (MC) simulation and importance sampling (IS) techniques for integrating uncertain expert knowledge into the system model. Uncertain knowledge about the model parameters is propagated through the system model by MC simulation in the form of a discrete sample, while IS helps to weight the sample elements regarding imprecise knowledge about the outputs in an iterative circle. Thereby, the consistency of expert judgments can be investigated as well. The contributions of this paper include an expert knowledge-based parameter estimation technique and a method for the evaluation of expert judgments according to the estimation results to eliminate incorrect ones. The applicability of the proposed method is introduced through a case study of a Hungarian operating waste separation system. The results verify that the assessments of experts can be efficiently integrated into system models, and their consistency can be evaluated.

Data-Aided Maximum Likelihood Joint Angle and Delay Estimator Over Orthogonal Frequency Division Multiplex Single-Input Multiple-Output Channels Based on New Gray Wolf Optimization Embedding Importance Sampling.

In this paper, we propose a new data-aided (DA) joint angle and delay (JADE) maximum likelihood (ML) estimator. The latter consists of a substantially modified and, hence, significantly improved gray wolf optimization (GWO) technique by fully integrating and embedding within it the powerful importance sampling (IS) concept. This new approach, referred to hereafter as GWOEIS (for "GWO embedding IS"), guarantees global optimality, and offers higher resolution capabilities over orthogonal frequency division multiplex (OFDM) (i.e., multi-carrier and multi-path) single-input multiple-output (SIMO) channels. The traditional GWO randomly initializes the wolfs' positions (angles and delays) and, hence, requires larger packs and longer hunting (iterations) to catch the prey, i.e., find the correct angles of arrival (AoAs) and time delays (TDs), thereby affecting its search efficiency, whereas GWOEIS ensures faster convergence by providing reliable initial estimates based on a simplified importance function. More importantly, and beyond simple initialization of GWO with IS (coined as IS-GWO hereafter), we modify and dynamically update the conventional simple expression for the convergence factor of the GWO algorithm that entirely drives its hunting and tracking mechanisms by accounting for new cumulative distribution functions (CDFs) derived from the IS technique. Simulations unequivocally confirm these significant benefits in terms of increased accuracy and speed Moreover, GWOEIS reaches the Cramér-Rao lower bound (CRLB), even at low SNR levels.

Knowledge embedding synchronous surrogate modeling for multi-objective operational reliability evaluation of complex mechanical systems

To effectively assess the multi-objective operational reliability of complex mechanical system, the concept of Knowledge Embedding Surrogate Modeling (KeSM) is proposed by integrating Knowledge-based Decomposition-Coordination (K-DC) strategy, Knowledge-based Parameter Decomposition (K-PD) strategy, and the surrogate model. In this concept, the K-DC strategy is used to decompose a complex problem into several smaller sub problems, coordinating outcomes from the bottom-up; the K-PD is applied to decompose complex parameters into two parts: associated trends and local fluctuations; the surrogate model is adopted to establish the mapping relationship between input and output. Under this concept, the Knowledge Embedding Synchronous Surrogate Modeling (S-KeSM) multi-objective operational reliability evaluation method is developed by combining linkage important sampling technique and synchronous modeling thought with KeSM concept. In addition, an engineering case (civil aircraft braking system temperature with multi-failures) is employed to validate the proposed method. Through comparison and validation with multiple methods, the results show that the proposed method has significant advantages in analysis accuracy and efficiency. This study can provide theoretical references for the multi-objective operational reliability evaluation of complex mechanical systems.

Residual path integrals for re‐rendering

AbstractConventional rendering techniques are primarily designed and optimized for single‐frame rendering. In practical applications, such as scene editing and animation rendering, users frequently encounter scenes where only a small portion is modified between consecutive frames. In this paper, we develop a novel approach to incremental re‐rendering of scenes with dynamic objects, where only a small part of a scene moves from one frame to the next. We formulate the difference (or residual) in the image between two frames as a (correlated) light‐transport integral which we call the residual path integral. Efficient numerical solution of this integral then involves (1) devising importance sampling strategies to focus on paths with non‐zero residual‐transport contributions and (2) choosing appropriate mappings between the native path spaces of the two frames. We introduce a set of path importance sampling strategies that trace from the moving object(s) which are the sources of residual energy. We explore path mapping strategies that generalize those from gradient‐domain path tracing to our importance sampling techniques specially for dynamic scenes. Additionally, our formulation can be applied to material editing as a simpler special case. We demonstrate speed‐ups over previous correlated sampling of path differences and over rendering the new frame independently. Our formulation brings new insights into the re‐rendering problem and paves the way for devising new types of sampling techniques and path mappings with different trade‐offs.

Point and interval estimation based on joint progressive censoring data from two Rayleigh-Weibull distribution with applications

The exploration of progressively censored data has garnered considerable attention in recent years. This research delves into the joint progressive censoring scheme applied to two populations. It presupposes that the lifespan distribution of items from these populations follows Rayleigh-Weibull distributions, characterized by varying shape and scale parameters. Within the framework of the joint progressive censoring scheme, we investigate maximum likelihood estimators for unknown parameters wherever applicable. Bayesian inferences for these parameters are presented using a Gamma prior. It’s worth noting that deriving Bayes estimators and their associated credible intervals is not feasible, hence we suggest employing the importance sampling technique for computation. To illustrate the methodologies, we analyze real-life data for demonstrative purposes, and Monte Carlo simulations are carried out to compare the performances of all the proposed methods.

A distributed adaptive policy gradient method based on momentum for multi-agent reinforcement learning

Policy Gradient (PG) method is one of the most popular algorithms in Reinforcement Learning (RL). However, distributed adaptive variants of PG are rarely studied in multi-agent. For this reason, this paper proposes a distributed adaptive policy gradient algorithm (IS-DAPGM) incorporated with Adam-type updates and importance sampling technique. Furthermore, we also establish the theoretical convergence rate of O(1/T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(1/\\sqrt{T})$$\\end{document}, where T represents the number of iterations, it can match the convergence rate of the state-of-the-art centralized policy gradient methods. In addition, many experiments are conducted in a multi-agent environment, which is a modification on the basis of Particle world environment. By comparing with some other distributed PG methods and changing the number of agents, we verify the performance of IS-DAPGM is more efficient than the existing methods.

Towards Robust Decision-Making for Autonomous Highway Driving Based on Safe Reinforcement Learning.

Reinforcement Learning (RL) methods are regarded as effective for designing autonomous driving policies. However, even when RL policies are trained to convergence, ensuring their robust safety remains a challenge, particularly in long-tail data. Therefore, decision-making based on RL must adequately consider potential variations in data distribution. This paper presents a framework for highway autonomous driving decisions that prioritizes both safety and robustness. Utilizing the proposed Replay Buffer Constrained Policy Optimization (RECPO) method, this framework updates RL strategies to maximize rewards while ensuring that the policies always remain within safety constraints. We incorporate importance sampling techniques to collect and store data in a Replay buffer during agent operation, allowing the reutilization of data from old policies for training new policy models, thus mitigating potential catastrophic forgetting. Additionally, we transform the highway autonomous driving decision problem into a Constrained Markov Decision Process (CMDP) and apply our proposed RECPO for training, optimizing highway driving policies. Finally, we deploy our method in the CARLA simulation environment and compare its performance in typical highway scenarios against traditional CPO, current advanced strategies based on Deep Deterministic Policy Gradient (DDPG), and IDM + MOBIL (Intelligent Driver Model and the model for minimizing overall braking induced by lane changes). The results show that our framework significantly enhances model convergence speed, safety, and decision-making stability, achieving a zero-collision rate in highway autonomous driving.

Reaching Quantum Accuracy in Predicting Adsorption Properties for Ethane/Ethene in Zeolitic Imidazolate Framework-8 at Low Pressure Regime.

Nanoporous materials in the form of metal-organic frameworks such as zeolitic imidazolate framework-8 (ZIF-8) are promising membrane materials for the separation of hydrocarbon mixtures. To compute the adsorption isotherms in such adsorbents, grand canonical Monte Carlo simulations have proven to be very useful. The quality of these isotherms depends on the accuracy of adsorbate-adsorbent interactions, which are mostly described using force fields owing to their low computational cost. However, force field predictions of adsorption uptake often show discrepancies from experiments at low pressures, providing the need for methods that are more accurate. Hence, in this work, we propose and validate two novel methodologies for the ZIF-8/ethane and ethene systems; a benchmarking methodology to evaluate the performance of any given force field in describing adsorption in the low-pressure regime and a refinement procedure to rescale the parameters of a force field to better describe the host-guest interactions and provide for simulation isotherms with close agreement to experimental isotherms. Both methodologies were developed based on a reference Henry coefficient, computed with the PBE-MBD functional using the importance sampling technique. The force field rankings predicted by the benchmarking methodology involve the comparison of force field derived Henry coefficients with the reference Henry coefficients and ranking the force fields based on the disparities between these Henry coefficients. The ranking from this methodology matches the rankings made based on uptake disparities by comparing force field derived simulation isotherms to experimental isotherms in the low-pressure regime. The force field rescaling methodology was proven to refine even the worst performing force field in UFF/TraPPE. The uptake disparities of UFF/TraPPE improved from 197% and 194% to 11% and 21% for ethane and ethene, respectively. The proposed methodology is applicable to predict adsorption across nanoporous materials and allows for rescaled force fields to reach quantum accuracy without the need for experimental input.

Fractional stochastic volatility model

This article introduces a discrete‐time fractional stochastic volatility model (FSV) based on fractional Gaussian noise. The new model includes the standard stochastic volatility model as a special case and has the same limit as the fractional integrated stochastic volatility (FISV) model, which is the continuous‐time fractional Ornstein–Uhlenbeck process. A simulated maximum likelihood method, which maximizes the time‐domain log‐likelihood function calculated by the importance sampling technique, and a frequency‐domain quasi maximum likelihood method (or quasi Whittle) are employed to estimate the model parameters. Simulation studies suggest that, while both estimation methods can accurately estimate the model, the simulated maximum likelihood method outperforms the quasi Whittle method. As an illustration, we fit the FSV and FISV models with the proposed estimation techniques to the S&P 500 composite index over a sample period spanning 45 years.

Online Neural Path Guiding with Normalized Anisotropic Spherical Gaussians

Importance sampling techniques significantly reduce variance in physically based rendering. In this article, we propose a novel online framework to learn the spatial-varying distribution of the full product of the rendering equation, with a single small neural network using stochastic ray samples. The learned distributions can be used to efficiently sample the full product of incident light. To accomplish this, we introduce a novel closed-form density model, called the Normalized Anisotropic Spherical Gaussian mixture, that can model a complex light field with a small number of parameters and that can be directly sampled. Our framework progressively renders and learns the distribution, without requiring any warm-up phases. With the compact and expressive representation of our density model, our framework can be implemented entirely on the GPU, allowing it to produce high-quality images with limited computational resources. The results show that our framework outperforms existing neural path guiding approaches and achieves comparable or even better performance than state-of-the-art online statistical path guiding techniques.

Efficient metamodel-based importance sampling coupled with single-loop estimation method for parameter global reliability sensitivity analysis

To efficiently estimate the main effects and total effects of uncertain distribution parameters on the uncertainty of failure probability, we construct single-loop estimation formulas by introducing auxiliary variables through the equal probability transformation. This approach circumvents the original nested triple-loop process. For generating samples used in the derived single-loop estimation formulas, direct Monte Carlo simulation can be employed. To reduce the number of samples in Monte Carlo simulation, the important sampling technique can be integrated into the proposed single-loop estimation formulas. Additionally, to enhance the efficiency of identifying the states (failure or safety) of all used samples, an adaptive Kriging model can be introduced. Subsequently, the adaptive Kriging model coupled with Monte Carlo simulation, and the adaptive Kriging model coupled with the importance sampling technique, are integrated into the derived single-loop formulas to concurrently and efficiently estimate the main effects and total effects of uncertain distribution parameters. The results of three case studies validate the accuracy and efficiency of the proposed method.

Variance reduction via simultaneous importance sampling and control variates techniques using vegas

Monte Carlo (MC) integration is an important calculational technique in the physical sciences. Practical considerations require that the calculations are performed as accurately as possible for a given set of computational resources. To improve the accuracy of MC integration, a number of useful variance reduction algorithms have been developed, including importance sampling and control variates. In this work, we demonstrate how these two methods can be applied simultaneously, thus combining their benefits. We provide a python wrapper, named CoVVVR, which implements our approach in the VEGAS program. The improvements are quantified with several benchmark examples from the literature.

Optimized planning for weather-sensitive offshore construction operations - An application to float-over installation of super-heavy offshore topsides

Float-over method offers an efficient, reliable, and practical installation scenario for large-scale offshore topsides. It is, however, highly sensitive to marine environmental conditions and necessitates comprehensive pre-planning. Conventional deterministic approaches methodologies exhibit shortcomings in achieving a cost-effective and time-efficient float-over design, thereby necessitating a comprehensive reconsideration. This study aims to develop a reliability-based methodology for float-over analysis of super-heavy offshore topsides. Incorporating diverse geometric and mechanical limit state functions, the permissible weather window is determined by use of Monte-Carlo Simulation. This methodology leverages the data set generated based on nonlinear coupled multi-body hydrodynamic simulation of the float-over operations. The presented idea provides a decision-making platform that integrates safety and efficiency considerations. The float-over design is optimized utilizing the developed approach and some recommendations are made to enhance applicable codes and guidelines. To reduce the computational expenses, the application of the importance sampling technique is subsequently proposed. Long-term planning of float-over installation is derived finally, optimizing operational time and cost while keeping risks as low as reasonably practical. In conclusion, it is crucial to establish a reliability-based framework for scheduling weather-sensitive offshore construction projects.

AD 2 VNCS: A dversarial D efense and D evice V ariation-tolerance in Memristive Crossbar-based N euromorphic C omputing S ystems

In recent years, memristive crossbar-based neuromorphic computing systems (NCS) have obtained extremely high performance in neural network acceleration. However, adversarial attacks and conductance variations of memristors bring reliability challenges to NCS design. First, adversarial attacks can fool the neural network and pose a serious threat to security critical applications. However, device variations lead to degradation of the network accuracy. In this article, we propose DFS (Deep neural network Feature importance Sampling) and BFS (Bayesian neural network Feature importance Sampling) training strategies, which consist of Bayesian Neural Network (BNN) prior setting, clustering-based loss function, and feature importance sampling techniques, to simultaneously combat device variation, white-box attack, and black-box attack challenges. Experimental results clearly demonstrate that the proposed training framework can improve the NCS reliability.

Nautilus: boosting Bayesian importance nested sampling with deep learning

ABSTRACT We introduce a novel approach to boost the efficiency of the importance nested sampling (INS) technique for Bayesian posterior and evidence estimation using deep learning. Unlike rejection-based sampling methods such as vanilla nested sampling (NS) or Markov chain Monte Carlo (MCMC) algorithms, importance sampling techniques can use all likelihood evaluations for posterior and evidence estimation. However, for efficient importance sampling, one needs proposal distributions that closely mimic the posterior distributions. We show how to combine INS with deep learning via neural network regression to accomplish this task. We also introduce nautilus, a reference open-source python implementation of this technique for Bayesian posterior and evidence estimation. We compare nautilus against popular NS and MCMC packages, including emcee, dynesty, ultranest, and pocomc, on a variety of challenging synthetic problems and real-world applications in exoplanet detection, galaxy SED fitting and cosmology. In all applications, the sampling efficiency of nautilus is substantially higher than that of all other samplers, often by more than an order of magnitude. Simultaneously, nautilus delivers highly accurate results and needs fewer likelihood evaluations than all other samplers tested. We also show that nautilus has good scaling with the dimensionality of the likelihood and is easily parallelizable to many CPUs.

GAA-PPO: A novel graph adversarial attack method by incorporating proximal policy optimization

The Graph Convolutional Network (GCN) has demonstrated impressive performance in processing graph structured data. However recent studies have revealed that GCN is vulnerable to adversarial attacks, where a small amount of data modification can significantly affect the performance of the GCN models. While most existing studies node injection attacks with graph reinforcement learning by considering gradient information, they still suffer from the problems that the step size of the policy gradient is difficult to determine, and the attack effect needs to be further improved. In light of the above issues, this paper proposes a Graph Adversarial Attack method by incorporating Proximal Policy Optimization named GAA-PPO, which fills subtasks of sequentially generating features and links for injected nodes without modifying existing nodes or edges. GAA-PPO comprises two main components: node injection attack network (actor network) and value prediction network (critic network). Specifically, the actor network leverages a node generator and an edge sampler to generate appropriate features and edges for the injected nodes. Notably, a novel edge sampler that incorporates Approximation Personalized Propagation of Neural Prediction (APPNP) is introduced to effectively propagate malicious features of the injected nodes. On the other hand, the critic network evaluates the performance of the perturbed graph at each stage. To enhance the stability of the algorithm, GAA-PPO employs the importance sampling technique of Proximal Policy Optimization (PPO) during the training process. Extensive experiments on three publicly benchmark datasets show that GAA-PPO yields significant performance advantages over the state-of-the-art method.

Optimal weather window for transportation of large-scale offshore structures

Offshore transportation is recognized as one of the most dominant sources of human and financial loss, among all varieties of maritime and offshore operations. The conventional deterministic approach to address the corresponding risks, therefore, needs to be reconsidered. This study aims at developing a reliability-based methodology for marine transportation analysis of large-scale offshore modules. Taking vessel stability and strength as the limiting criteria, the allowable weather window is extracted by use of Monte Carlo simulation. Comparing the results of conventional deterministic and reliability-based approaches, the efficiency of the proposed methodology is well demonstrated. The importance sampling technique is also proposed subsequently to reduce the computational time and effort. The developed framework is ultimately employed for optimal planning of offshore transportation, aiming to minimize weather-related downtime. The application of the proposed probabilistic approach for planning the installation phase of offshore projects leads to a significant reduction in costs while keeping the risk level as low as reasonably practicable.

Research on Data-Driven Optimal Scheduling of Power System

The uncertainty of output makes it difficult to effectively solve the economic security dispatching problem of the power grid when a high proportion of renewable energy generating units are integrated into the power grid. Based on the proximal policy optimization (PPO) algorithm, a safe and economical grid scheduling method is designed. First, constraints on the safe and economical operation of renewable energy power systems are defined. Then, the quintuple of Markov decision process is defined under the framework of deep reinforcement learning, and the dispatching optimization problem is transformed into Markov decision process. To solve the problem of low sample data utilization in online reinforcement learning strategies, a PPO optimization algorithm based on the Kullback–Leibler (KL) divergence penalty factor and importance sampling technique is proposed, which transforms on-policy into off-policy and improves sample utilization. Finally, the simulation analysis of the example shows that in a power system with a high proportion of renewable energy generating units connected to the grid, the proposed scheduling strategy can meet the load demand under different load trends. In the dispatch cycle with different renewable energy generation rates, renewable energy can be absorbed to the maximum extent to ensure the safe and economic operation of the grid.

A novel multi-ship collision probability estimation method considering data-driven quantification of trajectory uncertainty

The collision risk prediction is crucial for the safety management of maritime transportation. Previous studies have primarily focused on the near-miss collision risk of two ships, yet the risk due to congestion caused by multiple ships is complex and also very challenging for safe management. In this paper, a novel multi-ship collision probability assessment method is proposed. To consider the uncertainty of ship motion, a deep learning multi-model integration method is proposed to predict the ship motion trajectory to quantify the time-varying stochasticity of ship motion. Then, a method for calculating collision probability is proposed based on Monte Carlo simulation by integrating importance sampling techniques with the cross-entropy method. The model is combined with the ship trajectory estimator to quantify the collision probability. To prove the validity of the developed model, a case study based on Victoria Harbour is illustrated. The results show that this method can provide early warning of multi-ship collision risk. The method can offer an important basis for maritime collision risk monitoring and ship navigation risk assessment for maritime administration departments and shore-based center of maritime autonomous ships.