Related papers: A Generalized Probabilistic Learning Approach for …
In a multi-fidelity setting, data are available from two sources, high- and low-fidelity. Low-fidelity data has larger size and can be leveraged to make more efficient inference about quantities of interest, e.g. the mean, for high-fidelity…
As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…
As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…
Multi-fidelity machine learning methods address the accuracy-efficiency trade-off by integrating scarce, resource-intensive high-fidelity data with abundant but less accurate low-fidelity data. We propose a practical multi-fidelity strategy…
Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations…
Machine learning techniques typically rely on large datasets to create accurate classifiers. However, there are situations when data is scarce and expensive to acquire. This is the case of studies that rely on state-of-the-art computational…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
In traffic flow modeling, incorporating uncertainty is crucial for accurately capturing the complexities of real-world scenarios. In this work we focus on kinetic models of traffic flow, where a key step is to design effective numerical…
This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the…
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…
Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…
Markov chain Monte Carlo (MCMC) is a popular and successful general-purpose tool for Bayesian inference. However, MCMC cannot be practically applied to large data sets because of the prohibitive cost of evaluating every likelihood term at…
The construction of efficient methods for uncertainty quantification in kinetic equations represents a challenge due to the high dimensionality of the models: often the computational costs involved become prohibitive. On the other hand,…
This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…
Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance…
The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…
This paper is on Bayesian inference for parametric statistical models that are defined by a stochastic simulator which specifies how data is generated. Exact sampling is then possible but evaluating the likelihood function is typically…
Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine…
Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…