A new method combines AIS and SMCI for efficient evaluation of Ising models.
problem Efficiently evaluating expectations on Ising models under various temperatures.
method Combining Annealed Importance Sampling (AIS) and Spatial Monte Carlo Integration (SMCI).
result The proposed method performs efficiently in both high- and low-temperature regions.
Generalizes SMCI to improve Boltzmann machine learning accuracy.
problem Limitation in applying higher-order SMCI to dense systems.
method Generalized SMCI (GSMCI) and new PBM learning method.
result GSMCI allows higher-order approximations for dense systems.
Improves accuracy of SMCI estimators without expanding sum regions.
problem Intractable multiple summations in evaluating expectations on the Ising model.
method Combining multiple SMCI estimators using generalized least squares (GLS).
result The proposed method can improve accuracy without combinatorial explosion.
MCNO learns PDE solution operators using Monte Carlo sampling.
problem Learning solution operators for PDEs efficiently and flexibly.
method Directly learns kernel function using Monte Carlo sampling of input-output pairs.
result Competitive accuracy with efficient computational cost on 1D PDE benchmarks.
Corrects errors in ILA for Bayesian inference in LGMs.
problem Error in ILA for non-Gaussian likelihoods in LGMs.
method Importance sampling scheme to correct ILA errors.
result Corrected posterior converges to the true posterior with increased samples.
Bayesian approach improves rain field reconstruction using CMLs and DMs.
problem Challenges in accurately reconstructing ground-level rainfall from CML path-integrated measurements.
method Bayesian inverse problem with Diffusion Models as priors.
result Improved performance in rainfall estimation compared to existing methods.
A faster Bayesian method for estimating spatial count data models.
problem Bayesian estimation of spatial count data models is computationally expensive and slow.
method Derive a Variational Bayes (VB) method for posterior inference in negative binomial models with spatial dependence.
result The VB method is up to 50 times faster than MCMC and offers similar accuracy.
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.
ProFnet models HDFTS with neural networks, offering scalable probabilistic forecasts.
problem Modeling high-dimensional functional time series with nonlinear trends and high spatial dimensions.
method Integrates feedforward and deep neural networks with probabilistic modeling.
result Superior performance in forecasting Japan's mortality rates.
New method tackles incomplete data in RBM inverse Ising problems.
problem Computing data and model expectations in inverse Ising problems with missing observations.
method Combines mean-field approximation, persistent contrastive divergence, and spatial Monte Carlo integration.
result Effective and accurate tuning of model parameters compared to conventional methods.
New Hamiltonian Monte Carlo method for non-canonical dynamics.
problem Incompatibility of canonical symplectic structure with non-canonical dynamics.
method Developed a framework for Hamiltonian Monte Carlo using non-canonical symplectic structures with implicit integration.
result Non-canonical Hamiltonian Monte Carlo provides sampling advantages.
A scalable Bayesian linear regression framework for spatial data.
problem Scalable methodologies for analyzing large spatial datasets.
method Conjugate Bayesian linear regression framework.
result Exact sampling from joint posterior distribution without iterative algorithms.
This study compares MC and QMC methods for likelihood functions.
problem Approximating the normalizing constant of posterior distributions and marginal likelihoods.
method Characterizes the integration error of MC and QMC methods for likelihood functions.
result QMC outperforms MC under certain conditions, especially in high dimensions.
Tensor networks improve integration accuracy for high-dimensional problems.
problem Integration of high-dimensional functions with exponential convergence.
method Regression-free tensor network representations for integration.
result Exponential convergence achieved for non-analytic integrands.
Monte Carlo (MC) techniques are often used to estimate integrals of a multivariate function using randomly generated samples of the function. In light of the increasing interest in uncertainty quantification and robust design applications in aerospace engineering, the calculation of expected values of such functions (e…
Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo (MCMC) algorithm that generates proposals for a Metropolis-Hastings algorithm by simulating the dynamics of a Hamiltonian system. However, HMC is sensitive to large time discretizations and performs poorly if there is a mismatch between the spatial geo…
New method uses Coulomb gases for Monte Carlo integration with reduced errors.
problem Reducing integration errors in numerical algorithms.
method Using Gibbs measures with a large deviations approach.
result Preserves large deviation principle for improved integration.
Improved efficiency in HMC samplers reduces dissipative behavior.
problem Reducing dissipative behavior in HMC samplers.
method Variable integration time and partial velocity refreshment.
result Efficiency improved by a √κ factor in Wasserstein-2 distance.
Rodent hippocampal population codes represent important spatial information about the environment during navigation. Several computational methods have been developed to uncover the neural representation of spatial topology embedded in rodent hippocampal ensemble spike activity. Here we extend our previous work and pro…
The paper uses Fourier integral theorem for estimating multivariate distributions.
problem Estimating multivariate distributions and conditional distribution functions.
method Natural Monte Carlo and fully nonparametric estimators based on Fourier integral theorem.
result Explicit Monte Carlo estimators without estimated covariance matrix.
In this paper we propose and study a family of continuous wavelets on general domains, and a corresponding stochastic discretization that we call Monte Carlo wavelets. First, using tools from the theory of reproducing kernel Hilbert spaces and associated integral operators, we define a family of continuous wavelets by …
New method controls bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin.
problem Bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin samplers.
method Delocalization of bias technique applied to these samplers.
result Control W 2 W_2 W 2 bias with O ( K ) O(\sqrt{K}) O ( K ) integration steps for high-dimensional distributions. A new machine learning method for spatial regression.
problem Spatial/temporal regression with scattered data and arbitrary dimensions.
method Modified Planar Rotator (MPRS) method, a non-parametric model with distance-dependent interactions.
result MPRS predictions are competitive with standard interpolation methods and superior in handling rough and non-Gaussian data.
The paper integrates multiple Gaussian process predictions using Monte Carlo sampling.
problem Accurate prediction of variables using multiple models.
method Log-linear pooling of Gaussian process predictions, combined with Monte Carlo sampling.
result The log-linear pooling method improves prediction accuracy compared to linear pooling.
New algorithm speeds up MCMC for complex distributions.
problem Efficient sampling from complex, high-dimensional distributions.
method Numerical Generalized Randomized Hamiltonian Monte Carlo with state-dependent event rates.
result Approximates Hamiltonian trajectories for robust sampling.
Simplified uHMC with time integration improves accuracy and efficiency.
problem Improving the efficiency and accuracy of Hamiltonian Monte Carlo algorithms.
method Randomized time integrator for uHMC with stratified Monte Carlo.
result Achieves more accurate approximations with fewer gradient evaluations.
This work relates the framework of model-based clustering for spatial functional data where the data are surfaces. We first introduce a Bayesian spatial spline regression model with mixed-effects (BSSR) for modeling spatial function data. The BSSR model is based on Nodal basis functions for spatial regression and accom…
Combines BART and Gaussian process for spatial covariate prediction with uncertainty.
problem Improving spatial prediction models with nonlinear and interaction covariates.
method Bayesian Additive Regression Trees (BART) combined with Gaussian process for spatial dependence.
result Effective in reducing computational burden through INLA and MCMC.
Quantum speedup for Monte Carlo integration reduces integrand calls.
problem Reducing the number of calls to the integrand subroutine in high-dimensional Monte Carlo integration.
method Combining nested quantum amplitude estimation with pseudorandom numbers for separable integrands.
result Significant reduction in the number of integrand calls for high-dimensional integration.
Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification problem, because we encounter intractable integrals. In this paper we …
VegasFlow accelerates complex simulations across various hardware platforms.
problem Complex calculations and simulations requiring high-dimensional integrals.
method Monte Carlo integration techniques using Vegas algorithm and TensorFlow.
result Significantly faster performance on various hardware platforms.
We use neural networks as control variates with geometric integration techniques.
problem Analytic integration of neural network approximations for variance reduction.
method Integration domain subdivision using computational geometry for MLPs with continuous piecewise linear activation functions.
result Neural networks can be used as control variates with geometric integration methods.
Study compares MC and QMC methods for pricing and risk analysis in a hyperbolic local volatility model.
problem Derivative pricing and risk analysis in a hyperbolic local volatility model.
method Application of Monte Carlo and Quasi Monte Carlo methods for pricing and risk analysis.
result Quasi Monte Carlo methods show superior performance in high-dimensional integration for derivative pricing and risk analysis.
Quantum computing techniques applied to Monte Carlo simulations in finance.
problem Efficiently simulating quantum algorithms for financial modeling.
method Introduces quantum computing basics, amplitude estimation, and Grover's algorithm for unstructured search.
result Demonstrates quantum approaches to Monte Carlo integration and counting in finance.
This paper introduces repulsive Monte Carlo methods for computing the sliced Wasserstein distance.
problem Computing the integral of a function on the unit sphere using Monte Carlo methods.
method The approach involves using determinantal point processes and repelled point processes to create quadratures for the sliced Wasserstein distance.
result The UnifOrtho estimator is recommended for the computation of the sliced Wasserstein distance in large dimensions.
New method samples from time-integrated stochastic bridges using neural networks.
problem Sampling from time-integrated stochastic bridges with high accuracy and speed.
method Polynomial chaos expansion and artificial neural networks.
result Robust, data-driven Monte Carlo sampling with thousands of samples in milliseconds.
We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to integral representations of shift-invariant kernel functions (e.g., Gaussian kernel).…
A cubing strategy identifies stable hyperparameter regions for uncertainty quantification in spatial deep learning.
problem Uncertainty quantification in spatial deep learning models.
method Cubing-based diagnostic framework to recursively partition hyperparameter space and evaluate regions using scoring rules.
result Our approach produces competitive or superior predictive intervals compared to a statistical baseline model.
Develops a neural surrogate for proton dose calculation using Monte Carlo dropout uncertainty.
problem Computational demand in proton therapy workflows requiring repeated evaluations.
method Integrates Monte Carlo dropout into a neural network surrogate for fast, differentiable dose predictions and uncertainty quantification.
result Shows significant speedups over MC while retaining uncertainty information.
New insights into variational inference using Monte Carlo estimates.
problem Improving variational bounds in latent variable models.
method Analyzing properties of Monte Carlo estimates and their impact on variational gaps.
result Negative correlation reduces variational gaps, contrary to intuition.
New algorithms improve Langevin Monte Carlo efficiency.
problem High computational cost of classical Langevin Monte Carlo.
method Integrates ensemble feature into LMC, constraining gradient approximations.
result Constrained Ensemble Langevin Monte Carlo reduces gradient computation.
New method improves self-supervised representation learning using probabilistic modeling and Monte Carlo integration.
problem Improving self-supervised representation learning for multimodal data.
method Discriminative probabilistic modeling with multiple importance sampling (MIS) for robust Monte Carlo integration.
result Proposes a novel non-parametric method for approximating conditional probability densities through convex optimization.
New integral theorems improve density function estimations.
problem Improving density function estimations.
method Integrals based on cyclic functions and Riemann sums, Fourier integral theorem, Monte Carlo methods, variational approach, Cauchy residue theorem.
result Optimal cyclic functions minimize square integrals, improving density estimations.
The paper improves probabilistic herding methods using Gibbs distributions.
problem Improving integration accuracy over Monte Carlo quadrature in infinite-dimensional RKHS.
method Developed a Gibbs distribution over quadrature nodes to minimize MMD.
result The Gibbs distribution outperforms i.i.d. Monte Carlo in integration accuracy.
Normal distributions ensure asymptotic variance reduction in moment matching Monte Carlo.
problem Asymptotic variance reduction in general integration problems.
method Characterization of conditions for asymptotic variance reduction using normal distributions.
result Asymptotic variance reduction is guaranteed for normal distributions in moment matching Monte Carlo.
Adaptive HMC improves sampling efficiency by optimizing mass matrix.
problem Inefficient HMC performance due to mass matrix choice.
method Gradient-based adaptation of mass matrix to maximize proposal entropy.
result Adaptation method outperforms HMC variants by optimizing mass matrix.
A new graph-based clustering method for moderate-dimensional data.
problem Performance degradation of existing graph-based clustering methods in high dimensions.
method Introduces UN-CCDs using NND-based MC-SRT for covering radii determination.
result UN-CCDs provide stable and competitive performance in moderate-sized datasets.
Enhanced Markov chain sampler learns network statistics faster.
problem Learning network statistics efficiently.
method Integrates graph Forman curvature into Markov chain transition probabilities and stationary distribution.
result Curved Markov chain Monte Carlo achieves faster convergence.