Optimal Bayesian Affine Estimator and Active Learning for the Wiener Model

• URL: http://arxiv.org/abs/2504.05490v2
• Date: Mon, 21 Apr 2025 21:58:45 GMT
• Title: Optimal Bayesian Affine Estimator and Active Learning for the Wiener Model
• Authors: Sasan Vakili, Manuel Mazo Jr., Peyman Mohajerin Esfahani,
• Abstract summary: We derive a closed-form optimal affine estimator for the unknown parameters, characterized by the so-called "dynamic basis statistics"<n>We develop an active learning algorithm synthesizing input signals to minimize estimation error.
• Score: 3.7414278978078204
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper presents a Bayesian estimation framework for Wiener models, focusing on learning nonlinear output functions under known linear state dynamics. We derive a closed-form optimal affine estimator for the unknown parameters, characterized by the so-called "dynamic basis statistics" (DBS). Several features of the proposed estimator are studied, including Bayesian unbiasedness, closed-form posterior statistics, error monotonicity in trajectory length, and consistency condition (also known as persistent excitation). In the special case of Fourier basis functions, we demonstrate that the closed-form description is computationally available, as the Fourier DBS enjoys explicit expressions. Furthermore, we identify an inherent inconsistency in the Fourier bases for single-trajectory measurements, regardless of the input excitation. Leveraging the closed-form estimation error, we develop an active learning algorithm synthesizing input signals to minimize estimation error. Numerical experiments validate the efficacy of our approach, showing significant improvements over traditional regularized least-squares methods.

Related papers

• Bayesian Kernel Regression for Functional Data [1.4501446815590895]
  In supervised learning, the output variable to be predicted is often represented as a function.<n>We propose a novel functional output regression model based on kernel methods.
  arXiv  Detail & Related papers  (2025-03-17T19:28:27Z)
• Inflationary Flows: Calibrated Bayesian Inference with Diffusion-Based Models [0.0]
  We show how diffusion-based models can be repurposed for performing principled, identifiable Bayesian inference.<n>We show how such maps can be learned via standard DBM training using a novel noise schedule.<n>The result is a class of highly expressive generative models, uniquely defined on a low-dimensional latent space.
  arXiv  Detail & Related papers  (2024-07-11T19:58:19Z)
• A smoothed-Bayesian approach to frequency recovery from sketched data [16.16733806935934]
  We provide a novel statistical perspective on a classical problem at the intersection of computer science and information theory. We recover the empirical frequency of a symbol in a large discrete dataset using only a compressed representation, or sketch, obtained via random hashing.
  arXiv  Detail & Related papers  (2023-09-27T05:20:53Z)
• Learning Unnormalized Statistical Models via Compositional Optimization [73.30514599338407]
  Noise-contrastive estimation(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models.
  arXiv  Detail & Related papers  (2023-06-13T01:18:16Z)
• Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence [65.63201894457404]
  We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of non-linear differential equations.<n>The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker-Planck equation to such observations.
  arXiv  Detail & Related papers  (2023-05-24T20:43:47Z)
• Data-Driven Influence Functions for Optimization-Based Causal Inference [105.5385525290466]
  We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing. We study the case where probability distributions are not known a priori but need to be estimated from data.
  arXiv  Detail & Related papers  (2022-08-29T16:16:22Z)
• Experimental Design for Linear Functionals in Reproducing Kernel Hilbert Spaces [102.08678737900541]
  We provide algorithms for constructing bias-aware designs for linear functionals. We derive non-asymptotic confidence sets for fixed and adaptive designs under sub-Gaussian noise.
  arXiv  Detail & Related papers  (2022-05-26T20:56:25Z)
• BayesFlow can reliably detect Model Misspecification and Posterior Errors in Amortized Bayesian Inference [0.0]
  We conceptualize the types of model misspecification arising in simulation-based inference and systematically investigate the performance of the BayesFlow framework under these misspecifications. We propose an augmented optimization objective which imposes a probabilistic structure on the latent data space and utilize maximum mean discrepancy (MMD) to detect potentially catastrophic misspecifications.
  arXiv  Detail & Related papers  (2021-12-16T13:25:27Z)
• 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)
• SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for Gaussian Process Regression with Derivatives [86.01677297601624]
  We propose a novel approach for scaling GP regression with derivatives based on quadrature Fourier features. We prove deterministic, non-asymptotic and exponentially fast decaying error bounds which apply for both the approximated kernel as well as the approximated posterior.
  arXiv  Detail & Related papers  (2020-03-05T14:33:20Z)

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.