Related papers: On Nesting Monte Carlo Estimators
Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but…
We consider the problem of approximating the product of $n$ expectations with respect to a common probability distribution $\mu$. Such products routinely arise in statistics as values of the likelihood in latent variable models. Motivated…
Models with intractable normalizing functions have numerous applications. Because the normalizing constants are functions of the parameters of interest, standard Markov chain Monte Carlo cannot be used for Bayesian inference for these…
Stochastic optimization in learning and inference often relies on Markov chain Monte Carlo (MCMC) to approximate gradients when exact computation is intractable. However, finite-time MCMC estimators are biased, and reducing this bias…
Data analysis in HEP experiments often uses binned likelihood from data and finite Monte Carlo sample. Statistical uncertainty of Monte Carlo sample has been introduced in Frequentist Inference in some literatures, but they are not suitable…
We present two Monte Carlo sampling algorithms for probabilistic inference that guarantee polynomial-time convergence for a larger class of network than current sampling algorithms provide. These new methods are variants of the known…
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…
Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges associated with conventional deep learning methods, such as…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo…
This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors [El Karoui et al.,…
A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings,…
Monte Carlo dropout may effectively capture model uncertainty in deep learning, where a measure of uncertainty is obtained by using multiple instances of dropout at test time. However, Monte Carlo dropout is applied across the whole network…
Over-parametrization was a crucial ingredient for recent developments in inference and machine-learning fields. However a good theory explaining this success is still lacking. In this paper we study a very simple case of mismatched…
Estimating the size of hidden populations using Multiple Systems Estimation (MSE) is a critical task in quantitative sociology; however, practical application is often hindered by imperfect administrative data and computational constraints.…
This paper addresses the issue of estimating the expectation of a real-valued random variable of the form $X = g(\mathbf{U})$ where $g$ is a deterministic function and $\mathbf{U}$ can be a random finite- or infinite-dimensional vector.…
Reliable uncertainty estimation is crucial for machine learning models, especially in safety-critical domains. While exact Bayesian inference offers a principled approach, it is often computationally infeasible for deep neural networks.…