Related papers: Monte Carlo Dependency Estimation
Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables…
We consider parametric Markov decision processes (pMDPs) that are augmented with unknown probability distributions over parameter values. The problem is to compute the probability to satisfy a temporal logic specification with any concrete…
Multiple instance learning (MIL) is a key algorithm for classification of whole slide images (WSI). Histology WSIs can have billions of pixels, which create enormous computational and annotation challenges. Typically, such images are…
On the basis of the dynamical interpretation of Monte Carlo simulations, we discuss the relation of the equilibrium relaxation time, the susceptibility and the statistical error. We introduce a new quantity called {\it the statistical…
The Mann-Whitney effect is an effect measure for the order of two sample-specific outcome variables. It has the interpretation of a probability and also a connection to the area under the ROC curve. In the literature it has been considered…
We study an unbiased estimator for the density of a sum of random variables that are simulated from a computer model. A numerical study on examples with copula dependence is conducted where the proposed estimator performs favourably in…
Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is…
Existing methods for the estimation of stable distribution parameters, such as those based on sample quantiles, sample characteristic functions or maximum likelihood generally assume an independent sample. Little attention has been paid to…
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…
In unsupervised ensemble learning, one obtains predictions from multiple sources or classifiers, yet without knowing the reliability and expertise of each source, and with no labeled data to assess it. The task is to combine these possibly…
Modeling dynamic temporal dependencies is a critical challenge in time series pre-training, which evolve due to distribution shifts and multi-scale patterns. This temporal variability severely impairs the generalization of pre-trained…
Drawing a sample from a discrete distribution is one of the building components for Monte Carlo methods. Like other sampling algorithms, discrete sampling suffers from the high computational burden in large-scale inference problems. We…
Accurate estimates of long-term risk probabilities and their gradients are critical for many stochastic safe control methods. However, computing such risk probabilities in real-time and in unseen or changing environments is challenging.…
Mixture proportion estimation (MPE) aims to estimate class priors from unlabeled data. This task is a critical component in weakly supervised learning, such as PU learning, learning with label noise, and domain adaptation. Existing MPE…
In fields such as hydrology and climatology, modelling the entire distribution of positive data is essential, as stakeholders require insights into the full range of values, from low to extreme. Traditional approaches often segment the…
We study some notions of negative dependence of a sampling scheme that can be used to derive variance bounds for the corresponding estimator or discrepancy bounds for the underlying random point set that are at least as good as 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…
Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…