Related papers: Revisiting Monte Carlo Strength Evaluation

In the Large Language Model(LLM) reasoning scenario, people often estimate state value via Monte Carlo sampling. Though Monte Carlo estimation is an elegant method with less inductive bias, noise and errors are inevitably introduced due to…

The efficiency of a Markov chain Monte Carlo algorithm might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated…

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…

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…

Estimating risk measures such as large loss probabilities and Value-at-Risk is fundamental in financial risk management and often relies on computationally intensive nested Monte Carlo methods. While Multi-Level Monte Carlo (MLMC)…

Much current research in AI and games is being devoted to Monte Carlo search (MCS) algorithms. While the quest for a single unified MCS algorithm that would perform well on all problems is of major interest for AI, practitioners often know…

Among the various options to estimate uncertainty in deep neural networks, Monte-Carlo dropout is widely popular for its simplicity and effectiveness. However the quality of the uncertainty estimated through this method varies and choices…

In this review, we address the use of Monte Carlo methods for approximating definite integrals of the form $Z = \int L(x) d P(x)$, where $L$ is a target function (often a likelihood) and $P$ a finite measure. We present vertical-likelihood…

We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all required expectations are approximated by a Monte Carlo method. The…

This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising…

There are several methods to measure computing power. On the other hand, Bit Length (BL) can be considered a metric to measure the strength of an asymmetric encryption method. We review here ways to determine the security, given an span of…

Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…

The literature in social network analysis has largely focused on methods and models which require complete network data; however there exist many networks which can only be studied via sampling methods due to the scale or complexity of the…

Gesture typing is a method of text entry that is ergonomically well-suited to the form factor of touchscreen devices and allows for much faster input than tapping each letter individually. The QWERTY keyboard was, however, not designed with…

In this paper some new proposals for method comparison are presented. On the one hand, two new robust regressions, the M-Deming and the MM-Deming, have been developed by modifying Linnet's method of the weighted Deming regression. The…

Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it…

Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…

A new method for sequence optimization in protein models is presented. The approach, which has inherited its basic philosophy from recent work by Deutsch and Kurosky [Phys. Rev. Lett. 76, 323 (1996)] by maximizing conditional probabilities…

The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…

We investigate Monte Carlo simulation strategies for determining the effective ("depletion") potential between a pair of hard spheres immersed in a dense sea of much smaller hard spheres. Two routes to the depletion potential are…