Paper improves SPOS by reducing variance in stochastic particle-optimization sampling.
problem Variance reduction in SPOS.
method Proposes three variants of variance-reduced SPOS: SAGA-POS, SVRG-POS, and SVRG-POS\+.
result Non-asymptotic convergence guarantees and better convergence rates than existing methods.
New sampling method improves on particle-optimization techniques.
problem Particles tend to collapse in SVGD, leading to poor sampling.
method Introduce stochastic noise to update particles, developing non-asymptotic convergence theory.
result More particles do not always improve approximation due to computational constraints.
There has been recent interest in developing scalable Bayesian sampling methods such as stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) for big-data analysis. A standard SG-MCMC algorithm simulates samples from a discrete-time Markov chain to approximate a target distribution, thus samp…
Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has been increasingly popular in Bayesian learning due to its ability to deal with large data. A standard SG-MCMC algorithm simulates samples from a discretized-time Markov chain to approximate a target distribution. However, the samples are typically highly correl…
New method optimizes function space for Bayesian neural networks, improving performance.
problem Bayesian neural networks inference challenge in high-dimensional, over-parameterized models.
method Directly optimizes a set of regression functions in function space for variational inference.
result Successfully overcomes sub-optimal performance in over-parameterized models, outperforming baselines.
This paper develops a scalable Thompson Sampling method using optimal transport.
problem Efficiently approximating posterior distributions for complex models in Thompson Sampling.
method The approach uses distribution optimization techniques via Wasserstein gradient flows to approximate posterior distributions efficiently.
result The proposed method achieves superior performance on both synthetic and real large-scale data.
In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily draw samples. Recently discrete approximation by particles has attracted attention …
New approach improves multi-head attention by making heads less similar.
problem Multi-head attention can lead to similar features, reducing model expressiveness.
method Proposes a non-parametric approach using Bayesian techniques to make heads repel each other.
result Improves feature diversity, leading to better representations and performance.
Algorithm samples constrained stochastic differential equations.
problem Sampling stochastic differential equations with complex constraints.
method Pathspace Metropolis-adjusted manifold sampling.
result Demonstrated effectiveness in various constrained conditions.
Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Gradient Descent (prox-SGD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform sampling can guarantee that the sampled stochastic quantity is an unbiased estim…
New method improves zeroth-order stochastic optimization with adaptive sampling.
problem Optimization problems without gradient information.
method Adaptive sampling quasi-Newton method using finite differences.
result Significant improvement in performance with adaptive sample sizes.
New method for sampling from complex distributions using stochastic localization.
problem Sampling from unnormalized target densities in multi-modal distributions.
method Stochastic Localization via Iterative Posterior Sampling (SLIPS) framework.
result Approximate samples from target distribution and denoiser learned iteratively.
SNF combines stochastic and deterministic steps to sample complex distributions.
problem Sampling complex probability distributions efficiently.
method Stochastic Normalizing Flows (SNF) - sequence of invertible functions and stochastic blocks.
result SNFs improve efficiency and representational power over pure MCMC/LD.
New method uses adaptive sampling for optimization in uncertain conditions.
problem Optimizing functions with unknown gradients in uncertain environments.
method Adaptive sampling quasi-Newton method with finite differences and norm tests.
result Potential performance benefits of the proposed method demonstrated in preliminary experiments.
Paper uses correlated samples to improve variance in variational inference.
problem High variance in stochastic variational inference.
method Differentiable antithetic sampling to generate correlated samples.
result Effective variance reduction in deep generative model learning.
The paper analyzes the sample complexity of SAA for CSO problems.
problem Finding efficient methods for solving CSO problems with limited samples.
method Establishes sample complexity of SAA for CSO under various structural assumptions.
result Total sample complexity improvements from d/eps^4 to d/eps^3 and 1/eps^2 under different conditions.
SA-Solver improves stochastic sampling from DPMs.
problem Efficient sampling from Diffusion Probabilistic Models (DPMs) is time-consuming.
method Proposes SA-Solver, an improved stochastic Adams method for solving diffusion SDE.
result SA-Solver achieves improved or comparable performance compared to SOTA methods for few-step sampling.
This paper uses antithetic sampling to reduce variance in stochastic gradient descent.
problem High variance in stochastic gradient descent slows down convergence.
method Antithetic sampling to make gradients negatively correlated.
result The proposed method accelerates convergence in machine learning applications.
New sampling strategy improves TR algorithms for stochastic optimization.
problem Derivative-free stochastic optimization with Monte Carlo estimates.
method Stratified adaptive sampling to optimize MC sample size.
result Reduced sample complexity and superior efficiency confirmed.
New sampling method uses stochastic interpolants and FBSDEs.
problem Sampling from high-dimensional distributions with unnormalized densities.
method Stochastic interpolants and FBSDEs to define and solve diffusion process.
result Effective sampling from challenging distributions.
A new method speeds up sampling in diffusion models.
problem Slow sample generation in diffusion models.
method Proposed Splitting Integrators for fast stochastic sampling.
result Achieved FID score of 2.36 in 100 NFE, significantly faster than baselines.
We study primal-dual type stochastic optimization algorithms with non-uniform sampling. Our main theoretical contribution in this paper is to present a convergence analysis of Stochastic Primal Dual Coordinate (SPDC) Method with arbitrary sampling. Based on this theoretical framework, we propose Optimality Violation-ba…
New Thompson sampling algorithm for stochastic partial monitoring achieves logarithmic regret.
problem Limited feedback in sequential learning problems.
method Developed a novel Thompson-sampling-based algorithm to sample from the posterior distribution exactly.
result Achieved logarithmic regret bound of O(log T) for a linearized variant of the problem.
NSFs learn SDE transition laws for efficient sampling.
problem Efficiently sampling between arbitrary time points in SDEs.
method Conditional normalising flows with architectural constraints.
result Up to two orders of magnitude speed-ups at large time gaps.
Improved convergence for non-log-concave sampling.
problem Sampling from non-log-concave distributions.
method Novel conductance analysis of SGLD with auxiliary Markov Chain.
result SGLD achieves ε-sampling error with fewer evaluations.
New algorithm samples from log concave distributions efficiently.
problem Sampling from log concave distributions efficiently.
method Stochastic Proximal Langevin Algorithm (SPLA) with potential splitting.
result Established nonasymptotic convergence rates for SPLA.
We show that stochastic interpolation flow maps are Lipschitz with a sharp constant.
problem High dimensional sampling and transport problems.
method Investigating stochastic interpolation flow for generating data samples.
result Stochastic interpolation flow maps are Lipschitz with a sharp constant matching optimal transport maps.
Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
Stochastic gradient descent optimizes Nyström samples for kernel matrix approximation.
problem Optimizing Nyström samples for kernel matrix approximation.
method Stochastic gradient descent applied to multisets of landmark points (Nyström samples) using a surrogate criterion (radial SKD).
result Local minimization of the radial SKD yields improved Nyström approximation accuracy.
A new method interpolates between sampling and variational inference using stochastic mixtures.
problem Combining the strengths of sampling and variational inference methods.
method Develops a framework using stochastic mixtures of simple component distributions to interpolate between sampling and variational inference.
result Improves on both sampling and variational inference methods by reducing bias and variance.
Improved stochastic optimization outperforms standard methods.
problem Optimizing smooth, strongly convex functions with noisy data.
method Variance reduction strategy called VISOR.
result VISOR achieves optimal sample complexity and oracle complexity.
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.
Adapts Bayesian optimization for uncertain outcomes using stochastic sampling.
problem Optimizing with uncertain or stochastic outcomes in scientific and engineering problems.
method Proposes SSBO, a new framework that handles uncertainty and myopic decision making.
result SSBO techniques effectively optimize standard and applied problems.
New method synchronizes graphs with probability measures on rotations.
problem Synchronizing graphs with measure-valued edges over rotations.
method Formulated as maximization of cycle-consistency in probability measures over rotations, using Sinkhorn divergences.
result Proposes a nonparametric Riemannian particle optimization approach converging to global optimum under certain conditions.
New algorithm optimizes stochastic optimization with circular dependency.
problem Circular dependency between decision variable and importance sampling.
method Single-loop stochastic approximation algorithm based on Nesterov's dual averaging.
result Achieves minimal asymptotic variance and resolves circular optimization challenge.
YOASOVI improves stochastic VI for large models with fast, self-correcting sampling.
problem Efficiently performing stochastic Variational Inference on large Bayesian models.
method YOASOVI uses acceptance sampling to draw only one sample per iteration, improving convergence speed and accuracy.
result YOASOVI converges faster and more accurately than regular Monte Carlo and Quasi-Monte Carlo methods.
New technique reduces bias in CSO problems, improving sample complexity.
problem Reducing bias in conditional stochastic optimization problems.
method Introducing a stochastic extrapolation technique combined with variance reduction.
result Achieved significantly better sample complexity for nonconvex smooth objectives.
New method reduces variance in stochastic optimization with high confidence.
problem Achieving high-probability guarantees in stochastic optimization with weaker noise assumptions.
method Stochastic proximal point method combining proximal subproblem solver and probability booster.
result Demonstrates convergence with low sample complexity under bounded variance assumptions.
This work analyzes nonexpansive stochastic approximations with Markovian noise, proving convergence in reinforcement learning.
problem Applying stochastic approximation to reinforcement learning settings with nonexpansive operators.
method Investigates nonexpansive stochastic approximations with Markovian noise, providing asymptotic and finite sample analysis.
result First-time proof of convergence for classical tabular average reward temporal difference learning.
SGBD algorithm improves robustness in Bayesian sampling.
problem Inefficiency of existing MCMC algorithms in large datasets.
method Extends Barker MCMC to stochastic gradient framework, introducing bias-corrected version.
result SGBD is more robust to hyperparameter tuning and gradient noise.
SLIM efficiently solves overidentified models in a scalable manner.
problem Overidentified models with many moment conditions.
method Stochastic approximation framework using mini-batches and unbiased updates.
result SLIM solves overidentified models in under 1.4 hours, compared to 18 hours for full-sample GMM.
VRMPO improves reinforcement learning efficiency with stochastic mirror descent.
problem Improving sample efficiency in reinforcement learning.
method VRMPO algorithm with a variance-reduced policy gradient estimator and stochastic mirror descent.
result VRMPO achieves an ε-approximate first-order stationary point with only O(ε^(-3)) sample trajectories.
We analyze SGAs for statistical inference via asymptotics, improving tuning methods.
problem Improper tuning of SGAs for optimization and sampling.
method Characterize large-sample asymptotics of SGAs via step-size and sample-size scaling limits.
result Iterate averaging with large step size is robust and asymptotically has covariance proportional to MLE's.
New method uses PDMPs with sub-sampling for efficient sampling from posterior distributions.
problem Efficient sampling from posterior distributions with limited data access.
method Approximate simulation of PDMPs with sub-sampling and stochastic gradient estimation.
result Stochastic-gradient PDMPs are efficient and robust compared to Langevin dynamics.
New algorithms solve complex multi-level optimization problems with improved efficiency.
problem Smooth stochastic multi-level composition optimization problems.
method Two algorithms using moving-average and linearized stochastic estimates.
result Achieved sample complexities of O(1/ε^4) and O(1/ε^6).
Paper proposes method for generating paths of stochastic volatility CGMY process for option pricing.
problem Generating accurate sample paths for stochastic volatility models for option pricing.
method Monte-Carlo method for European and American options, least square regression for calibration.
result Calibrated model parameters to S\&P 100 index options market using path-dependent options.
Paper solves discounted stochastic games with near-optimal time and sample complexity.
problem Solving discounted stochastic two-player games with optimal complexity.
method Generalizes Q-learning to two-player strategy computation, overcoming limitations of existing methods.
result Near-optimal ε-strategy computation with polylogarithmic factors in 1−γ and ε−2. New algorithm speeds up sampling from complex distributions.
problem Efficiently sampling from non-log-concave distributions.
method Stochastic Proximal Samplers (SPS) based on SGLD and MALA.
result SPS-SGLD and SPS-MALA achieve faster sampling with reduced gradient complexity.