Bayesian penalized empirical likelihood and Markov Chain Monte Carlo sampling

• URL: http://arxiv.org/abs/2412.17354v3
• Date: Sun, 02 Mar 2025 03:07:57 GMT
• Title: Bayesian penalized empirical likelihood and Markov Chain Monte Carlo sampling
• Authors: Jinyuan Chang, Cheng Yong Tang, Yuanzheng Zhu,
• Abstract summary: We introduce a novel methodological framework called Bayesian Penalized Empirical Likelihood (BPEL) to address the computational challenges inherent in empirical likelihood (EL) approaches.<n>Our approach has two primary objectives: (i) to enhance the inherent flexibility of EL in accommodating diverse model conditions, and (ii) to facilitate the use of well-established Markov Chain Monte Carlo (MCMC) sampling schemes.
• Score: 1.3412960492870996
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this study, we introduce a novel methodological framework called Bayesian Penalized Empirical Likelihood (BPEL), designed to address the computational challenges inherent in empirical likelihood (EL) approaches. Our approach has two primary objectives: (i) to enhance the inherent flexibility of EL in accommodating diverse model conditions, and (ii) to facilitate the use of well-established Markov Chain Monte Carlo (MCMC) sampling schemes as a convenient alternative to the complex optimization typically required for statistical inference using EL. To achieve the first objective, we propose a penalized approach that regularizes the Lagrange multipliers, significantly reducing the dimensionality of the problem while accommodating a comprehensive set of model conditions. For the second objective, our study designs and thoroughly investigates two popular sampling schemes within the BPEL context. We demonstrate that the BPEL framework is highly flexible and efficient, enhancing the adaptability and practicality of EL methods. Our study highlights the practical advantages of using sampling techniques over traditional optimization methods for EL problems, showing rapid convergence to the global optima of posterior distributions and ensuring the effective resolution of complex statistical inference challenges.

Related papers

• Stochastic Optimization with Optimal Importance Sampling [49.484190237840714]
  We propose an iterative-based algorithm that jointly updates the decision and the IS distribution without requiring time-scale separation between the two. Our method achieves the lowest possible variable variance and guarantees global convergence under convexity of the objective and mild assumptions on the IS distribution family.
  arXiv  Detail & Related papers  (2025-04-04T16:10:18Z)
• BECAME: BayEsian Continual Learning with Adaptive Model MErging [21.642774366793997]
  We introduce a two-stage framework named BECAME, which synergizes the expertise of gradient projection and adaptive merging. Our approach outperforms state-of-the-art CL methods and existing merging strategies.
  arXiv  Detail & Related papers  (2025-04-03T15:07:28Z)
• Combinatorial Optimization via LLM-driven Iterated Fine-tuning [47.66752049943335]
  We present a novel way to integrate flexible, context-dependent constraints into optimization by leveraging Large Language Models (LLMs) Our framework balances locally constraints with rigorous global optimization more effectively than baseline sampling methods.
  arXiv  Detail & Related papers  (2025-03-10T04:58:18Z)
• LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning [56.273799410256075]
  The framework combines Monte Carlo Tree Search (MCTS) with iterative Self-Refine to optimize the reasoning path. The framework has been tested on general and advanced benchmarks, showing superior performance in terms of search efficiency and problem-solving capability.
  arXiv  Detail & Related papers  (2024-10-03T18:12:29Z)
• Preference-Based Multi-Agent Reinforcement Learning: Data Coverage and Algorithmic Techniques [65.55451717632317]
  We study Preference-Based Multi-Agent Reinforcement Learning (PbMARL) We identify the Nash equilibrium from a preference-only offline dataset in general-sum games. Our findings underscore the multifaceted approach required for PbMARL.
  arXiv  Detail & Related papers  (2024-09-01T13:14:41Z)
• Finite-Time Convergence and Sample Complexity of Actor-Critic Multi-Objective Reinforcement Learning [20.491176017183044]
  This paper tackles the multi-objective reinforcement learning (MORL) problem. It introduces an innovative actor-critic algorithm named MOAC which finds a policy by iteratively making trade-offs among conflicting reward signals.
  arXiv  Detail & Related papers  (2024-05-05T23:52:57Z)
• Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference [47.460898983429374]
  We introduce an ensemble Kalman filter (EnKF) into the non-mean-field (NMF) variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO) We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting.
  arXiv  Detail & Related papers  (2023-12-10T15:22:30Z)
• Constrained Bayesian Optimization Under Partial Observations: Balanced Improvements and Provable Convergence [6.461785985849886]
  We endeavor to design an efficient and provable method for expensive POCOPs under the framework of constrained Bayesian optimization. We present an improved design of the acquisition functions that introduces balanced exploration during optimization. We propose a Gaussian process embedding different likelihoods as the surrogate model for a partially observable constraint.
  arXiv  Detail & Related papers  (2023-12-06T01:00:07Z)
• Sample-Efficient Multi-Agent RL: An Optimization Perspective [103.35353196535544]
  We study multi-agent reinforcement learning (MARL) for the general-sum Markov Games (MGs) under the general function approximation. We introduce a novel complexity measure called the Multi-Agent Decoupling Coefficient (MADC) for general-sum MGs. We show that our algorithm provides comparable sublinear regret to the existing works.
  arXiv  Detail & Related papers  (2023-10-10T01:39:04Z)
• GEC: A Unified Framework for Interactive Decision Making in MDP, POMDP, and Beyond [101.5329678997916]
  We study sample efficient reinforcement learning (RL) under the general framework of interactive decision making. We propose a novel complexity measure, generalized eluder coefficient (GEC), which characterizes the fundamental tradeoff between exploration and exploitation. We show that RL problems with low GEC form a remarkably rich class, which subsumes low Bellman eluder dimension problems, bilinear class, low witness rank problems, PO-bilinear class, and generalized regular PSR.
  arXiv  Detail & Related papers  (2022-11-03T16:42:40Z)
• Revisiting GANs by Best-Response Constraint: Perspective, Methodology, and Application [49.66088514485446]
  Best-Response Constraint (BRC) is a general learning framework to explicitly formulate the potential dependency of the generator on the discriminator. We show that even with different motivations and formulations, a variety of existing GANs ALL can be uniformly improved by our flexible BRC methodology.
  arXiv  Detail & Related papers  (2022-05-20T12:42:41Z)
• Application-Driven Learning: A Closed-Loop Prediction and Optimization Approach Applied to Dynamic Reserves and Demand Forecasting [41.94295877935867]
  We present application-driven learning, a new closed-loop framework in which the processes of forecasting and decision-making are merged and co-optimized. We show that the proposed methodology is scalable and yields consistently better performance than the standard open-loop approach.
  arXiv  Detail & Related papers  (2021-02-26T02:43:28Z)
• Control as Hybrid Inference [62.997667081978825]
  We present an implementation of CHI which naturally mediates the balance between iterative and amortised inference. We verify the scalability of our algorithm on a continuous control benchmark, demonstrating that it outperforms strong model-free and model-based baselines.
  arXiv  Detail & Related papers  (2020-07-11T19:44:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.