Related papers: Ensemble-Based Annealed Importance Sampling
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long time prediction of the evolution of the unknown system. Training a DNN with low…
Importance sampling (IS) is a technique that enables statistical estimation of output performance at multiple input distributions from a single nominal input distribution. IS is commonly used in Monte Carlo simulation for variance reduction…
Nowadays, many classification algorithms have been applied to various industries to help them work out their problems met in real-life scenarios. However, in many binary classification tasks, samples in the minority class only make up a…
Adaptive importance sampling (AIS) uses past samples to update the \textit{sampling policy} $q_t$ at each stage $t$. Each stage $t$ is formed with two steps : (i) to explore the space with $n_t$ points according to $q_t$ and (ii) to exploit…
In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…
Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…
We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or…
To efficiently evaluate system reliability based on Monte Carlo simulation, importance sampling is used widely. The optimal importance sampling density was derived in 1950s for the deterministic simulation model, which maps an input to an…
We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate,…
Nonequilibrium sampling is potentially much more versatile than its equilibrium counterpart, but it comes with challenges because the invariant distribution is not typically known when the dynamics breaks detailed balance. Here, we derive a…
Statistical estimates can often be improved by fusion of data from several different sources. One example is so-called ensemble methods which have been successfully applied in areas such as machine learning for classification and…
Sampling from multimodal distributions is a central challenge in Bayesian inference and machine learning. In light of hardness results for sampling -- classical MCMC methods, even with tempering, can suffer from exponential mixing times --…
We analyze the optimized adaptive importance sampler (OAIS) for performing Monte Carlo integration with general proposals. We leverage a classical result which shows that the bias and the mean-squared error (MSE) of the importance sampling…
Importance sampling (IS) is a Monte Carlo technique that relies on weighted samples, simulated from a proposal distribution, to estimate intractable integrals. The quality of the estimators improves with the number of samples. However, for…
Despite empirical risk minimization (ERM) is widely applied in the machine learning community, its performance is limited on data with spurious correlation or subpopulation that is introduced by hidden attributes. Existing literature…
Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…
Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space…
The Auto-Importance Sampling (AIS) method is a Monte Carlo variance reduction technique proposed for deep penetration problems, which can significantly improve computational efficiency without pre-calculations for importance distribution.…
In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…