Transition Kernel

Transition kernels, which describe the probability of moving between states in a system, are central to various machine learning tasks, including Markov Chain Monte Carlo sampling, diffusion models, and reinforcement learning. Current research focuses on developing efficient and robust methods for learning and optimizing these kernels, employing techniques like adversarial learning, policy gradients, and distributionally robust optimization within diverse model architectures such as neural networks and kernel methods. These advancements improve the efficiency and accuracy of sampling algorithms, enhance the theoretical understanding of diffusion models, and enable more robust and sample-efficient reinforcement learning agents, impacting fields ranging from statistical inference to robotics.

Papers

July 24, 2024

Enhanced Feature Learning via Regularisation: Integrating Neural Networks and Kernel Methods
Bertille Follain, Francis Bach
Neural Network Representation Learning Regularization Model Empirical Risk Minimization Kernel Method Kernel Ridge Regression Transition Kernel

June 4, 2024

Ai-Sampler: Adversarial Learning of Markov kernels with involutive maps
Evgenii Egorov, Ricardo Valperga, Efstratios Gavves
Neural Network Adversarial Learning Markov Chain Fast Sampling Transition Kernel Invertible Linear Transformation

May 26, 2024

Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference
Xunpeng Huang, Difan Zou, Hanze Dong, Yi Zhang, Yi-An Ma, Tong Zhang
Diffusion Model Langevin Dynamic Flexible Framework Transition Kernel Diffusion Inference Metropolis Adjusted Langevin Algorithm

May 22, 2024

Reinforcement Learning for Adaptive MCMC
Congye Wang, Wilson Chen, Heishiro Kanagawa, Chris. J. Oates
Reinforcement Learning Transition Kernel Adaptive Metropolis

May 13, 2024

Compressed Online Learning of Conditional Mean Embedding
Boya Hou, Sina Sanjari, Alec Koppel, Subhonmesh Bose
Operator Learning Kernel Hilbert Space Transition Kernel Markovian Sampling

March 18, 2024

Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory
Hengyu Fu, Zhuoran Yang, Mengdi Wang, Minshuo Chen
Conditional Diffusion Model Statistical Model DIstribution Estimation Classifier Free Guidance Transition Kernel Sample Generation

March 15, 2024

Data-Driven Distributionally Robust Safety Verification Using Barrier Certificates and Conditional Mean Embeddings
Oliver Schön, Zhengang Zhong, Sadegh Soudjani
Gaussian Process Provable Guarantee Efficient Verification Transition Kernel Barrier Certificate Mean Embeddings

February 14, 2024

Nearly Minimax Optimal Regret for Learning Linear Mixture Stochastic Shortest Path
Qiwei Di, Jiafan He, Dongruo Zhou, Quanquan Gu
Stochastic Environment Minimax Optimal Regret Transition Kernel Stochastic Shortest Path

January 4, 2024

Structured Matrix Learning under Arbitrary Entrywise Dependence and Estimation of Markov Transition Kernel
Jinhang Chai, Jianqing Fan
Estimation Task Low Rank Matrix Transition Kernel Low Rank Matrix Recovery Matrix Estimation Matrix Learning

October 2, 2023

Mirror Diffusion Models for Constrained and Watermarked Generation
Guan-Horng Liu, Tianrong Chen, Evangelos A. Theodorou, Molei Tao
Diffusion Model Participation Constraint Transition Kernel Mirror Diffusion Model

August 1, 2023

An Exact Kernel Equivalence for Finite Classification Models
Brian Bell, Michael Geyer, David Glickenstein, Amanda Fernandez, Juston Moore
Neural Tangent Kernel Kernel Method Transition Kernel Computation Kernel Parametric Learning

May 22, 2023

Achieving the Minimax Optimal Sample Complexity of Offline Reinforcement Learning: A DRO-Based Approach
Yue Wang, Jinjun Xiong, Shaofeng Zou
Offline Reinforcement Learning Sample Complexity Robust Optimization Distributionally Robust Optimization Transition Kernel

May 8, 2023

Self-Repellent Random Walks on General Graphs -- Achieving Minimal Sampling Variance via Nonlinear Markov Chains
Vishwaraj Doshi, Jie Hu, Do Young Eun
Markov Chain Monte Carlo Markov Chain Random Walk Transition Kernel

April 28, 2023

Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancy
Xing Liu, Andrew B. Duncan, Axel Gandy
Bayesian Perspective Score Matching Small Perturbation Transition Kernel Goodness of Fit Stein Discrepancy

March 9, 2023

Learning Stationary Markov Processes with Contrastive Adjustment
Ludvig Bergenstråhle, Jens Lagergren, Joakim Lundeberg
Contrastive Learning Transition Kernel

January 6, 2023

Reversibility of elliptical slice sampling revisited
Mareike Hasenpflug, Viacheslav Telezhnikov, Daniel Rudolf
Markov Chain Hilbert Space Reversible Dynamic Transition Kernel Slice Sampling

December 2, 2022

COmic: Convolutional Kernel Networks for Interpretable End-to-End Learning on (Multi-)Omics Data
Jonas C. Ditz, Bernhard Reuter, Nico Pfeifer
End to End Multi Omics Data Comic Analysis Transition Kernel

September 17, 2022

A Robust and Constrained Multi-Agent Reinforcement Learning Electric Vehicle Rebalancing Method in AMoD Systems
Sihong He, Yue Wang, Shuo Han, Shaofeng Zou, Fei Miao
Transition Kernel Dynamic Rebalancing Autonomous Mobility on Demand Vehicle Rebalancing

August 19, 2022

Spectral Decomposition Representation for Reinforcement Learning
Tongzheng Ren, Tianjun Zhang, Lisa Lee, Joseph E. Gonzalez, Dale Schuurmans, Bo Dai
Reinforcement Learning Transition Kernel Spectral Decomposition

Transition Kernel

Papers

Enhanced Feature Learning via Regularisation: Integrating Neural Networks and Kernel Methods

Ai-Sampler: Adversarial Learning of Markov kernels with involutive maps

Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference

Reinforcement Learning for Adaptive MCMC

Compressed Online Learning of Conditional Mean Embedding

Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory

Data-Driven Distributionally Robust Safety Verification Using Barrier Certificates and Conditional Mean Embeddings

Nearly Minimax Optimal Regret for Learning Linear Mixture Stochastic Shortest Path

Structured Matrix Learning under Arbitrary Entrywise Dependence and Estimation of Markov Transition Kernel

Mirror Diffusion Models for Constrained and Watermarked Generation

An Exact Kernel Equivalence for Finite Classification Models

Achieving the Minimax Optimal Sample Complexity of Offline Reinforcement Learning: A DRO-Based Approach

Self-Repellent Random Walks on General Graphs -- Achieving Minimal Sampling Variance via Nonlinear Markov Chains

Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancy

Learning Stationary Markov Processes with Contrastive Adjustment

Reversibility of elliptical slice sampling revisited

COmic: Convolutional Kernel Networks for Interpretable End-to-End Learning on (Multi-)Omics Data

A Robust and Constrained Multi-Agent Reinforcement Learning Electric Vehicle Rebalancing Method in AMoD Systems

Spectral Decomposition Representation for Reinforcement Learning