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Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…

Disordered Systems and Neural Networks · Physics 2024-12-24 Yixiong Ren , Jianhui Zhou

Score-based generative modelling (SGM) has proven to be a very effective method for modelling densities on finite-dimensional spaces. In this work we propose to extend this methodology to learn generative models over functional spaces. To…

Importance sampling is a common technique for Monte Carlo approximation, including Monte Carlo approximation of p-values. Here it is shown that a simple correction of the usual importance sampling p-values creates valid p-values, meaning…

Computation · Statistics 2011-04-12 Matthew T. Harrison

We consider systems of slow--fast diffusions with small noise in the slow component. We construct provably logarithmic asymptotically optimal importance schemes for the estimation of rare events based on the moderate deviations principle.…

Probability · Mathematics 2020-01-07 Matthew R. Morse , Konstantinos Spiliopoulos

Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we…

Optimization and Control · Mathematics 2026-05-28 Boyang Zhang , Zhiguo Wang , Ya-Feng Liu

Automatic summarization systems have advanced rapidly with large language models (LLMs), yet they still lack reliable guarantees on inclusion of critical content in high-stakes domains like healthcare, law, and finance. In this work, we…

Acceptance-rejection (AR), Independent Metropolis Hastings (IMH) or importance sampling (IS) Monte Carlo (MC) simulation algorithms all involve computing ratios of probability density functions (pdfs). On the other hand, classifiers…

Methodology · Statistics 2023-09-11 Elouan Argouarc'h , François Desbouvries

In real-world applications of large language models, outputs are often required to be confined: selecting items from predefined product or document sets, generating phrases that comply with safety standards, or conforming to specialized…

Computation and Language · Computer Science 2025-04-15 Haotian Ye , Himanshu Jain , Chong You , Ananda Theertha Suresh , Haowei Lin , James Zou , Felix Yu

Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…

Machine Learning · Computer Science 2024-10-21 Runjia Li , Qiwei Di , Quanquan Gu

Score-based diffusion models are a powerful class of generative models, but their practical use often depends on training neural networks to approximate the score function. Training-free diffusion models provide an attractive alternative by…

Numerical Analysis · Mathematics 2026-01-28 Pengjun Wang , Zezhong Zhang , Minglei Yang , Feng Bao , Yanzhao Cao , Guannan Zhang

An essential problem in statistics and machine learning is the estimation of expectations involving PDFs with intractable normalizing constants. The self-normalized importance sampling (SNIS) estimator, which normalizes the IS weights, has…

Computation · Statistics 2024-07-01 Nicola Branchini , Víctor Elvira

Score-based generative models require guidance in order to generate plausible, on-manifold samples. The most popular guidance method, Classifier-Free Guidance (CFG), is only applicable in settings with labeled data and requires training an…

Computer Vision and Pattern Recognition · Computer Science 2025-12-01 Eric Yeats , Darryl Hannan , Wilson Fearn , Timothy Doster , Henry Kvinge , Scott Mahan

Diffusion models achieve remarkable generation quality, yet face a fundamental challenge known as memorization, where generated samples can replicate training samples exactly. We develop a theoretical framework to explain this phenomenon by…

Machine Learning · Computer Science 2026-03-31 Xinyu Zhou , Jiawei Zhang , Stephen J. Wright

Have you ever wondered how your feature space is impacting the prediction of a specific sample in your dataset? In this paper, we introduce Single Sample Feature Importance (SSFI), which is an interpretable feature importance algorithm that…

Machine Learning · Computer Science 2019-11-28 Joseph Gatto , Ravi Lanka , Yumi Iwashita , Adrian Stoica

Stochastic Gradient Boosting (SGB) is a widely used approach to regularization of boosting models based on decision trees. It was shown that, in many cases, random sampling at each iteration can lead to better generalization performance of…

Machine Learning · Statistics 2019-10-30 Bulat Ibragimov , Gleb Gusev

This paper provides an introductory overview of how one may employ importance sampling effectively as a tool for solving stochastic optimization formulations incorporating tail risk measures such as Conditional Value-at-Risk. Approximating…

Risk Management · Quantitative Finance 2023-07-11 Anand Deo , Karthyek Murthy

We develop a theoretical framework for studying numerical estimation of lower previsions, generally applicable to two-level Monte Carlo methods, importance sampling methods, and a wide range of other sampling methods one might devise. We…

Computation · Statistics 2018-07-12 Matthias C. M. Troffaes

We propose a novel sampling-based federated learning framework for statistical inference on M-estimators with non-smooth objective functions, which frequently arise in modern statistical applications such as quantile regression and AUC…

Methodology · Statistics 2025-05-06 Xiudi Li , Lu Tian , Tianxi Cai

We consider the problem of off-policy evaluation in Markov decision processes. Off-policy evaluation is the task of evaluating the expected return of one policy with data generated by a different, behavior policy. Importance sampling is a…

Machine Learning · Computer Science 2019-05-13 Josiah P. Hanna , Scott Niekum , Peter Stone

Multiple importance sampling (MIS) methods use a set of proposal distributions from which samples are drawn. Each sample is then assigned an importance weight that can be obtained according to different strategies. This work is motivated by…

Computation · Statistics 2015-05-21 Víctor Elvira , Luca Martino , David Luengo , Mónica F. Bugallo