The paper improves Monte Carlo methods for optimization problems.
problem Efficiently solving optimization problems with biased Monte Carlo estimators.
method Introduces Multilevel Monte Carlo (MLMC) within Sample Average Approximation (SAA).
result Establishes uniform convergence and sample complexity for MLMC in SAA.
Improved bounds for Monte Carlo Rademacher Averages using self-bounding functions.
problem Proving sharper concentration bounds for MCERA.
method Deriving new bounds through self-bounding functions and concentration of measure.
result Novel bounds depend on data-dependent quantities, improving over standard methods.
FBMS R package simplifies Bayesian model selection and averaging.
problem Complex regression settings with multi-modal posterior landscapes.
method Efficient MJMCMC and GMJMCMC algorithms for Bayesian model exploration.
result FBMS effectively handles Bayesian generalized linear and nonlinear models.
FA-HMC improves Bayesian federated learning with rigorous guarantees.
problem Parameter estimation and uncertainty quantification in non-iid distributed data.
method Federated Averaging stochastic Hamiltonian Monte Carlo (FA-HMC) with convergence guarantees.
result FA-HMC achieves better convergence and communication efficiency than existing methods.
RQMC improves kernel-based learning by reducing deterministic error and offering computational advantages.
problem Improving kernel-based learning methods to reduce deterministic error and computational complexity.
method Randomized quasi-Monte Carlo (RQMC) methods applied to random feature approximations.
result RQMC methods improve deterministic approximation error bound from O P ( 1 / M ) O_P(1/\sqrt{M}) O P ( 1/ M ) to O ( 1 / M ) O(1/M) O ( 1/ M ) , matching QMC methods. Taking advantage of the recent litterature on exact simulation algorithms (Beskos, Papaspiliopoulos and Roberts) and unbiased estimation of the expectation of certain fonctional integrals (Wagner, Beskos et al. and Fearnhead et al.), we apply an exact simulation based technique for pricing continuous arithmetic average…
MCRapper efficiently computes patterns in data using Monte-Carlo Rademacher Averages.
problem Finding statistically significant patterns in data with limited samples.
method Monte-Carlo Empirical Rademacher Averages (MCERA) for poset families.
result MCRapper provides upper bounds to the discrepancy of functions, enabling efficient pattern mining.
Markov chain Monte Carlo (MCMC) algorithms are widely used to sample from complicated distributions, especially to sample from the posterior distribution in Bayesian inference. However, MCMC is not directly applicable when facing the doubly intractable problem. In this paper, we discussed and compared two existing solu…
Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the case that the weight determining the acceptance probability itself is fluctuati…
Proposes a method to reduce parallel complexity of MLMC in SGD.
problem Poor scalability of MLMC in SGD on parallel platforms.
method Proposes a delayed MLMC gradient estimator to reduce parallel complexity.
result Proves reduction in average parallel complexity per iteration at the cost of slightly worse convergence rate.
In this paper, a standard PDE for the pricing of arithmetic average strike Asian call option is presented. A Crank-Nicolson Implicit Method and a Higher Order Compact finite difference scheme for this pricing problem is derived. Both these schemes were implemented for various values of risk free rate and volatility. Th…
New method improves sampling efficiency in complex stochastic systems.
problem Sampling efficiency in nonconvex stochastic gradient cases.
method Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo.
result Quantitative Gaussian concentration bounds and convergence rates established.
Effective dimensionality reduction improves accuracy and reduces costs in estimating option Greeks.
problem Estimating Greeks for barrier and arithmetic average Asian options.
method Global sensitivity analysis, Chebyshev interpolation, conditional pathwise method, randomized Quasi Monte Carlo, Brownian bridge discretization, importance sampling.
result Reduced effective dimensionality enhances convergence rate and accuracy of randomized Quasi Monte Carlo integration.
New method estimates chirp parameters robustly from noisy mixtures.
problem Estimating chirp parameters from noisy mixtures of higher-order polynomials.
method Modified Langevin Monte Carlo (LMC) with curvature guidance.
result CG-LMC algorithm reliably finds minimizer in low SNR regimes.
A new method predicts future paths using a Monte-Carlo approach.
problem Predicting future financial paths given historical data.
method Path Shadowing Monte-Carlo method using maximum entropy model.
result Yields state-of-the-art predictions for future volatility and option smiles.
Bayesian model averaging fails under covariate shift, affecting neural networks' performance.
problem Bayesian model averaging's failure in neural networks under covariate shift.
method Explained the issue and proposed novel priors to improve robustness.
result Bayesian model averaging is problematic under covariate shift, especially with linear feature dependencies.
New method for unbiased regression reduces excess risk.
problem Least squares regression with optimal solution and Hessian matrix.
method Averaged stochastic gradient descent with time-average estimator.
result Unbiased estimator with O(1/k) expected excess risk.
New RL method MAC improves performance in sparse reward settings.
problem Slow mixing in large state spaces or sparse rewards.
method Multi-level Monte Carlo Actor-Critic (MAC) algorithm.
result Achieves convergence rate comparable to state-of-the-art AC algorithms.
In this work, we propose a smart idea to couple importance sampling and Multilevel Monte Carlo (MLMC). We advocate a per level approach with as many importance sampling parameters as the number of levels, which enables us to compute the different levels independently. The search for parameters is carried out using samp…
DBQPG improves policy gradient estimation with fewer samples.
problem Accurate policy gradient estimation with limited samples.
method Deep Bayesian Quadrature Policy Gradient (DBQPG).
result DBQPG provides more accurate and less variable gradient estimates.
This paper optimizes Bayesian estimation for log-concave models using Langevin Monte-Carlo.
problem Optimizing Bayesian estimators for log-concave models with Langevin Monte-Carlo.
method Quantitative statistical bounds and numerical approximation of Gibbs measures.
result Established optimal numerical strategy and its cost for Bayesian posterior mean approximation.
Estimating the dependency of variables is a fundamental task in data analysis. Identifying the relevant attributes in databases leads to better data understanding and also improves the performance of learning algorithms, both in terms of runtime and quality. In data streams, dependency monitoring provides key insights …
A new tamed stochastic gradient Hamiltonian Monte Carlo algorithm for superlinearly growing stochastic gradients.
problem Sampling and stochastic optimization problems with superlinearly growing stochastic gradients.
method Tamed Stochastic Gradient Hamiltonian Monte Carlo (tSGHMC) algorithm.
result Established a non-asymptotic error bound in Wasserstein-2 distance with a convergence rate of 1 / 4 1/4 1/4 . Improved Monte-Carlo models by constraining mutual information between latent and observable variables.
problem Training density models leads to latent variables being useless.
method Weave tighter Monte-Carlo bounds with mutual information constraints.
result Improved training of models with continuous and discrete latent variables.
Estimating predictive uncertainty is crucial for many computer vision tasks, from image classification to autonomous driving systems. Hamiltonian Monte Carlo (HMC) is an sampling method for performing Bayesian inference. On the other hand, Dropout regularization has been proposed as an approximate model averaging techn…
Extends double linear policy with time-varying weights and proves robust positive expectation.
problem Ensuring robustness in policy optimization with time-varying parameters.
method Employed a novel elementary symmetric polynomials characterization approach to prove robust positive expectation (RPE). Derived explicit expressions for expected cumulative gain-loss and variance.
result Proved the robust positive expectation property holds for the extended double linear policy.
New sampling method guarantees approximate first-order stationary points for non-convex functions.
problem Sampling from non-log-concave densities with non-convex potential functions.
method Averaged Langevin Monte Carlo with complexity analysis.
result Langevin Monte Carlo outputs a sample with ε-relative Fisher information after O(L²d²/ε²) iterations.
LMC improves sampling from complex distributions using quasi-random sequences.
problem Sampling from complex high-dimensional distributions with high accuracy.
method Using completely uniformly distributed (CUD) sequences in Langevin Monte Carlo (LMC) to generate Gaussian perturbations.
result LMC with low-discrepancy CUD sequences achieves smaller estimation error than standard LMC.
Bayesian inference for inverse problems using mean-shift interacting particles
problem Bayesian inference for inverse problems
method Amortized mean-shift interacting particles
result Improves accuracy of Bayesian inference by reducing the number of samples needed
Manifold Markov chain Monte Carlo algorithms have been introduced to sample more effectively from challenging target densities exhibiting multiple modes or strong correlations. Such algorithms exploit the local geometry of the parameter space, thus enabling chains to achieve a faster convergence rate when measured in n…
New formulas estimate life insurance benefits with less computation.
problem Estimating future discretionary benefits in life insurance.
method Derive analytic formulas for lower and upper bounds of FDB.
result Simple estimator for FDB with average of lower and upper bounds.
New algorithms improve MCMC efficiency for complex distributions.
problem High variance and low effective sample size in MCMC samplers.
method Antithetic Riemannian Manifold and Quantum-Inspired Hamiltonian Monte Carlo.
result Improved effective sample size and variance reduction.
SRMC framework reduces Monte Carlo variance by history-based sampling in high-dimensional spaces.
problem Efficient sampling in high-dimensional discrete or continuous state spaces.
method Score-Repellent Monte Carlo (SRMC) framework that summarizes history through running average of score evaluations.
result Improves estimator variance and mode coverage with constant memory usage.
Combines normalizing flows and quasi-Monte Carlo for improved numerical integration.
problem Improving the efficiency of numerical integration methods.
method Uses normalizing flows to approximate distributions and quasi-Monte Carlo for sampling.
result Demonstrates an estimator with significantly lower variance.
Speeds up complex portfolio exposure calculations.
problem Calculating exposure of portfolios with exotic derivatives.
method Least Squares Monte Carlo (LSMC) technique.
result Significantly reduces computation time for nested Monte Carlo.
GPU computing has become popular in computational finance and many financial institutions are moving their CPU based applications to the GPU platform. Since most Monte Carlo algorithms are embarrassingly parallel, they benefit greatly from parallel implementations, and consequently Monte Carlo has become a focal point …
A new method using spherical harmonics approximates the Sliced-Wasserstein distance.
problem Approximating the Sliced-Wasserstein distance between probability measures.
method Spherical Harmonics Control Variates (SHCV) method for Monte Carlo approximation of the SW distance.
result SHCV method provides an improved rate of convergence compared to Monte Carlo for general measures.
Adaptive SAA solves large-scale stochastic linear programs efficiently.
problem Solving large-scale two-stage stochastic linear programs.
method Iterative algorithm with adaptive sample size and warm starts.
result The algorithm converges to the true solution set with a probabilistic guarantee.
Bayesian methods improve DiD analysis for ATT estimation.
problem Estimating ATT in DiD designs with improved accuracy.
method Semiparametric Bayesian outcome regression and doubly robust adjustment.
result Bayesian methods provide strong finite-sample performance.
New method reduces sample complexity for robust reinforcement learning.
problem Finite sample analysis in robust reinforcement learning.
method Stochastic approximation framework with controlled bias, using MLMC techniques and geometric truncation.
result Order-optimal sample complexity of i l d e O ( ε − 2 ) ilde{\mathcal{O}}(ε^{-2}) i l d e O ( ε − 2 ) for robust policy evaluation. This paper presents a fast Bayesian filtering technique for state estimation.
problem Bottleneck in Bayesian inference for state estimation from noisy sensor data.
method Processor-native uncertainty tracking for uncertainty propagation and inference.
result Deterministic approximate filtering with up to 805x speedup and competitive accuracy.
We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average process based on a truncated Laguerre series expansion. The resulting problem is a fin…
The paper develops a theory for random forests, separating variance components and providing methods for estimating prediction intervals.
problem Understanding the variance and uncertainty in random forest predictions.
method Design-based theory, Monte Carlo averaging, PASR resampling.
result The floor of prediction uncertainty is positive and persists even without observation overlap, providing conservative prediction intervals.
ParaDRAM automates parallel MCMC simulations across languages.
problem Efficiently sampling complex mathematical functions.
method Automated, parallel, high-performance MCMC with adaptive rejection.
result Significant memory reduction for complex simulations.
RAHMC improves sampling from multimodal distributions using dissipative dynamics.
problem Sampling from multimodal distributions efficiently.
method RAHMC uses mode-repelling and mode-attracting stages with a single tuning parameter.
result RAHMC generates proposals that cross low-probability barriers efficiently.
It is known that quantum computers can speed up Monte Carlo simulation compared to classical counterparts. There are already some proposals of application of the quantum algorithm to practical problems, including quantitative finance. In many problems in finance to which Monte Carlo simulation is applied, many random n…
SLMC improves sampling efficiency for high-dimensional distributions.
problem Sampling from high-dimensional distributions is computationally challenging.
method SLMC projects Langevin updates onto subsampled eigenblocks of a time-varying preconditioner.
result SLMC offers superior adaptability and computational efficiency compared to traditional methods.
Proposes a new method for uncertainty estimation in neural networks.
problem Estimating uncertainty in neural networks.
method Samples outputs from Gaussian distributions parametrized by mean and variance sub-layers.
result Achieves better uncertainty quality than other methods.