Amortized In-Context Bayesian Posterior Estimation

• URL: http://arxiv.org/abs/2502.06601v1
• Date: Mon, 10 Feb 2025 16:00:48 GMT
• Title: Amortized In-Context Bayesian Posterior Estimation
• Authors: Sarthak Mittal, Niels Leif Bracher, Guillaume Lajoie, Priyank Jaini, Marcus Brubaker,
• Abstract summary: Amortization, through conditional estimation, is a viable strategy to alleviate such difficulties. We conduct a thorough comparative analysis of amortized in-context Bayesian posterior estimation methods. We highlight the superiority of the reverse KL estimator for predictive problems, especially when combined with the transformer architecture and normalizing flows.
• Score: 15.714462115687096
• License:
• Abstract: Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Current solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and Variational Inference (VI), which need to be re-run whenever new observations are available. Amortization, through conditional estimation, is a viable strategy to alleviate such difficulties and has been the guiding principle behind simulation-based inference, neural processes and in-context methods using pre-trained models. In this work, we conduct a thorough comparative analysis of amortized in-context Bayesian posterior estimation methods from the lens of different optimization objectives and architectural choices. Such methods train an amortized estimator to perform posterior parameter inference by conditioning on a set of data examples passed as context to a sequence model such as a transformer. In contrast to language models, we leverage permutation invariant architectures as the true posterior is invariant to the ordering of context examples. Our empirical study includes generalization to out-of-distribution tasks, cases where the assumed underlying model is misspecified, and transfer from simulated to real problems. Subsequently, it highlights the superiority of the reverse KL estimator for predictive problems, especially when combined with the transformer architecture and normalizing flows.

Related papers

• Model-free Methods for Event History Analysis and Efficient Adjustment (PhD Thesis) [55.2480439325792]
  This thesis is a series of independent contributions to statistics unified by a model-free perspective. The first chapter elaborates on how a model-free perspective can be used to formulate flexible methods that leverage prediction techniques from machine learning. The second chapter studies the concept of local independence, which describes whether the evolution of one process is directly influenced by another.
  arXiv  Detail & Related papers  (2025-02-11T19:24:09Z)
• Intrinsic Gaussian Process Regression Modeling for Manifold-valued Response Variable [6.137918306133745]
  We propose a novel intrinsic Gaussian process regression model for manifold-valued data. We establish the properties of the proposed models, including information consistency and posterior consistency. Numerical studies, including simulation and real examples, indicate that the proposed methods work well.
  arXiv  Detail & Related papers  (2024-11-28T08:27:59Z)
• Variational Autoencoders for Efficient Simulation-Based Inference [0.3495246564946556]
  We present a generative modeling approach based on the variational inference framework for likelihood-free simulation-based inference. We demonstrate the efficacy of these models on well-established benchmark problems, achieving results comparable to flow-based approaches.
  arXiv  Detail & Related papers  (2024-11-21T12:24:13Z)
• Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
  Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
  arXiv  Detail & Related papers  (2024-04-11T09:23:36Z)
• Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance [52.093434664236014]
  Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation.
  arXiv  Detail & Related papers  (2024-02-03T13:35:39Z)
• Refining Amortized Posterior Approximations using Gradient-Based Summary Statistics [0.9176056742068814]
  We present an iterative framework to improve the amortized approximations of posterior distributions in the context of inverse problems. We validate our method in a controlled setting by applying it to a stylized problem, and observe improved posterior approximations with each iteration.
  arXiv  Detail & Related papers  (2023-05-15T15:47:19Z)
• Variational Laplace Autoencoders [53.08170674326728]
  Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. We present a novel approach that addresses the limited posterior expressiveness of fully-factorized Gaussian assumption. We also present a general framework named Variational Laplace Autoencoders (VLAEs) for training deep generative models.
  arXiv  Detail & Related papers  (2022-11-30T18:59:27Z)
• Learning Invariant Representations under General Interventions on the Response [2.725698729450241]
  We focus on linear structural causal models (SCMs) and introduce invariant matching property (IMP) We analyze the generalization errors of our method under both the discrete and continuous environment settings.
  arXiv  Detail & Related papers  (2022-08-22T03:09:17Z)
• MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories [61.3299263929289]
  Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer an amortized estimator for the likelihood-to-evidence ratio. We show that this approach can be formulated in terms of mutual information between model parameters and simulated data.
  arXiv  Detail & Related papers  (2021-06-03T12:59:16Z)
• Posterior-Aided Regularization for Likelihood-Free Inference [23.708122045184698]
  Posterior-Aided Regularization (PAR) is applicable to learning the density estimator, regardless of the model structure. We provide a unified estimation method of PAR to estimate both reverse KL term and mutual information term with a single neural network.
  arXiv  Detail & Related papers  (2021-02-15T16:59:30Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)

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.