Importance Sampling Technique Research Articles

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.

Elucidation of the mechanism and the free energy of a Morita-Baylis-Hillman type reaction catalyzed by enzymes using transition path sampling.

Transition path sampling (TPS) is a Monte-Carlo importance sampling technique in the space of trajectories which is used to elucidate transition states, reaction coordinates and kinetic parameters of complex biomolecular reactions. Within TPS an ensemble of truly dynamic reactive trajectories are obtained with a Monte-Carlo type acceptance criterion in combination with the shooting and shifting algorithms. To sample the equilibrium properties such as free energies, the inclusion of non-reactive trajectories in the TPS ensemble is essential since these trajectories sample the long lived reactant and product states. With a modified acceptance criterion and in combination with a window based sampling algorithm, TPS can be used to obtain unbiased free energy profiles for chemical reactions that are catalyzed by enzymes. Here we use TPS to study the proton transfer mechanism and the corresponding reaction free energy of enzymes (MBHases) that catalyze a Morita-Baylis-Hillman (MBH) type reaction. These enzymes were developed through directed evolution and we aim to map the quantum mechanical tunneling (QMT) contribution in the proton transfer mechanism to laboratory evolution of the MBHases to determine the role played by QMT to rate improvements of evolved variants. The calculated free energies would also provide insights into the role of QMT in the reaction mechanism as the width and height of the free energy barrier determines the importance of the QMT contributions.

Estimation and prediction in generalized half logistic lifetime model using hybrid censored data

PurposeThis article aims to develop procedures for estimation and prediction in case of Type-I hybrid censored samples drawn from a two-parameter generalized half-logistic distribution (GHLD).Design/methodology/approachThe GHLD is a versatile model which is useful in lifetime modelling. Also, hybrid censoring is a time and cost-effective censoring scheme which is widely used in the literature. The authors derive the maximum likelihood estimates, the maximum product of spacing estimates and Bayes estimates with squared error loss function for the unknown parameters, reliability function and stress-strength reliability. The Bayesian estimation is performed under an informative prior set-up using the “importance sampling technique”. Afterwards, we discuss the Bayesian prediction problem under one and two-sample frameworks and obtain the predictive estimates and intervals with corresponding average interval lengths. Applications of the developed theory are illustrated with the help of two real data sets.FindingsThe performances of these estimates and prediction methods are examined under Type-I hybrid censoring scheme with different combinations of sample sizes and time points using Monte Carlo simulation techniques. The simulation results show that the developed estimates are quite satisfactory. Bayes estimates and predictive intervals estimate the reliability characteristics efficiently.Originality/valueThe proposed methodology may be used to estimate future observations when the available data are Type-I hybrid censored. This study would help in estimating and predicting the mission time as well as stress-strength reliability when the data are censored.

Error-guided method combining adaptive learning kriging model and parallel-tempering-based importance sampling for system reliability analysis

This study investigates the rare-event system reliability analysis with numerous failure regions. A novel method, based on the parallel tempering (PT) and importance sampling (IS) technique, is proposed. Surrogate models (kriging model) are built for the true performance function and a probabilistic classification function is derived to predict the failure regions. The PT algorithm is used to obtain points populating all of the predicted failure regions. Representative points are identified using the k-weighted-means clustering method. A Gaussian mixture model is formulated by the representative points and importance samples are simulated accordingly. The optimal training points are selected to update all surrogate models. In the framework of IS, the terminating criterion for assessing the estimation error of the system failure probability is devised. The learning process is terminated at the appropriate stage. The method is termed active learning kriging–parallel tempering–importance sampling (ALK-PT-IS). Four numerical examples illustrate the effectiveness and precision of this method.

Order-Restricted Inference for Generalized Inverted Exponential Distribution under Balanced Joint Progressive Type-II Censored Data and Its Application on the Breaking Strength of Jute Fibers

This article considers a new improved balanced joint progressive type-II censoring scheme based on two different populations, where the lifetime distributions of two populations follow the generalized inverted exponential distribution with different shape parameters but a common scale parameter. The maximum likelihood estimates of all unknown parameters are obtained and their asymptotic confidence intervals are constructed by the observed Fisher information matrix. Furthermore, the existence and uniqueness of solutions are proved. In the Bayesian framework, the common scale parameter follows an independent Gamma prior and the different shape parameters jointly follow a Beta-Gamma prior. Based on whether the order restriction is imposed on the shape parameters, the Bayesian estimates of all parameters concerning the squared error loss function along with the associated highest posterior density credible intervals are derived by using the importance sampling technique. Then, we use Monte Carlo simulations to study the performance of the various estimators and a real dataset is discussed to illustrate all of the estimation techniques. Finally, we seek an optimum censoring scheme through different optimality criteria.

Bi-Level Off-Policy Reinforcement Learning for Two-Timescale Volt/VAR Control in Active Distribution Networks

In Volt/Var control (VVC) of active distribution networks (ADNs), both slow timescale discrete devices (STDDs, e.g. on-load tap changers) and fast timescale continuous devices (FTCDs, e.g. distributed generators) are involved and should be coordinated in time sequence. Traditional two-timescale VVC optimizes STDDs and FTCDs based on accurate system models, but sometimes is impractical because of its unaffordable modeling effort. In this paper, a novel bi-level off-policy reinforcement learning (RL) method is proposed to solve this in a model-free manner. A Bi-level Markov decision process (BMDP) is defined and separate agents are set up for the slow and fast timescale sub-problems. For the fast timescale sub-problem, we adopt an off-policy RL method with high sample efficiency. For the slow one, we develop an off-policy multi-discrete soft actor-critic (MDSAC) algorithm to address the curse of dimensionality with various STDDs. To mitigate the non-stationary issue in the two agents’ training, we propose a multi-timescale off-policy correction (MTOPC) method by adopting the importance sampling technique. Comprehensive numerical studies not only demonstrate the proposed method can achieve stable and satisfactory optimization of both STDDs and FTCDs without any model information, but also support that the proposed method outperforms existing VVC methods involving both STDDs and FTCDs.

Optimal MIS weights in case of mixing 3 strategies for bidirectional MCRT with photon maps

Bidirectional Monte Carlo ray tracing with photon maps is a powerful method for rendering images. But stochastic noise is inherent in it. However, this noise can be reduced using the multiple importance sampling technique which combines the weighted results of different strategies. The optimal weights allow you to minimize the noise functional and, thus, render the image of the best quality. In this paper, we determine the optimal weights using a system of integral equations derived and solved by us. This system has several qualitative differences from the case of mixing two strategies investigated previously. But further increasing the number of strategies does not change the qualitative features of the system. The system can be solved in a closed form, i.e. as an algebraic formula that includes several integrals of known functions. They can be calculated during ray tracing. Therefore, application of the optimal weights in Monte Carlo ray tracing results in faster rendering of high quality realistic images.

Enhanced Adaptive Kriging Method for Estimating Fuzzy Failure Probability with Profust Model

Aiming at analyzing the structural fuzzy failure probability with probability inputs and fuzzy-state assumption (profust model), an adaptive kriging model-based sequentially truncated Monte Carlo simulation (MCS) method is investigated, where estimating the fuzzy failure probability can be transformed into identifying the absolute safety domain, the absolute failure domain, and the exact performance function values of the fuzzy safety–failure transition domain. To this end, in this study, three kriging models are sequentially constructed to realize the three aims, respectively. To further improve the efficiency of adaptively updating kriging model, adaptive radial-based importance sampling technique is embedded to divide the whole MCS candidate sampling pool (CSP) into several sub-CSPs. Then, the kriging model is updated sequentially in each sub-CSP instead of the whole CSP, and the samples dropped into the optimal hypersphere of the absolute safety domain can be truncated and do not participate in the CSP of updating the kriging model so that the size of whole MCS CSP and the size of CSP in each learning process of updating kriging are reduced simultaneously. As a result, the efficiency of estimating the fuzzy failure probability is enhanced. The results of two examples verify the effectiveness of the proposed method.

Efficient Path Planning for a Microrobot Passing through Environments with Narrow Passages.

This paper presents an efficient path-planning algorithm for microrobots attempting to pass through environments with narrow passages. Because of the extremely small size of a microrobot, it is suitable for work in this kind of environment. The rapidly exploring random tree (RRT) algorithm, which uses random sampling points, can quickly explore an entire environment and generate a sub-optimal path for a robot to pass through it; however, the RRT algorithm, when used to plan a path for a microrobot passing through an environment with narrow passages, has the problem of being easily limited to local solutions when it confronts with a narrow passage and is unable to find the final path through it. In light of this, the objectives of the considered path planning problem involve detecting the narrow passages, leading the path toward an approaching narrow passage, passing through a narrow passage, and extending the path search more efficiently. A methodology was proposed based on the bidirectional RRT in which image processing is used to mark narrow passages and their entrances and exits so that the bidirectional RRT can be quickly guided to them and combined with the deterministic algorithm to find paths through them. We designed the methodology such that RRT generates the sampling points for path growth. The multiple importance sampling technique is incorporated with bidirectional RRT, named MIS-BiRRT, to make the path grow faster toward the target point and narrow passages while avoiding obstacles. The proposed algorithm also considers multiple candidate paths simultaneously to expand the search range and then retain the best one as a part of the planning path. After validation from simulation, the proposed algorithm was found to generate efficient path planning results for microrobots to pass through narrow passages.

An efficient Kriging model-based importance sampling method for estimating the failure probability-based parameter global sensitivity index with uncertain distribution parameters

The failure probability-based parameter global sensitivity index measures the importance of each uncertain distribution parameter on the uncertainty of failure probability. The crude Monte Carlo simulation for estimating the failure probability-based parameter global sensitivity index involves a complicated nested triple-loop process, and the huge amount of computational burden restricts the application of the failure probability-based parameter global sensitivity. For efficiently analyzing the failure probability-based parameter global sensitivity index, this paper proposes an efficient Kriging model-based importance sampling method. First, the standard normal auxiliary variables are inducted by using the equivalent probability transformation, in which the equivalent limit state function with respect to the uncertain distribution parameters and the standard normal auxiliary variables are constructed, so that the importance sampling samples of uncertain distribution parameters and the standard normal auxiliary variables can be generated based on the equivalent limit state function. Secondly, based on the importance sampling technique, the formula of single-loop method for estimating the failure probability-based parameter global sensitivity index is derived in which the importance sampling samples can be reused to obtain all uncertain distribution parameters' failure probability-based global sensitivity indices. Thirdly, the equivalent probability transformation is used again to transform the importance sampling samples in the high-dimensional space into the relatively low-dimensional input space, and the Kriging model of the original limit state function with relatively low-dimensional input space is adaptively constructed to recognize the states (failure or safety) of all high-dimensional importance sampling samples. Then, the failure probability-based parameter global sensitivity indices can be efficiently estimated. The results of three case studies verify the accuracy and efficiency of the proposed method.