Bayesian Optimization for Robust Identification of Ornstein-Uhlenbeck Model

• URL: http://arxiv.org/abs/2503.06381v1
• Date: Sun, 09 Mar 2025 01:38:21 GMT
• Title: Bayesian Optimization for Robust Identification of Ornstein-Uhlenbeck Model
• Authors: Jinwen Xu, Qin Lu, Yaakov Bar-Shalom,
• Abstract summary: This paper deals with the identification of the derivation Ornstein-Uhlenbeck (OU) process error model.<n>We put forth a sample-efficient global optimization approach based on the Bayesian optimization framework.
• Score: 4.0148499400442095
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper deals with the identification of the stochastic Ornstein-Uhlenbeck (OU) process error model, which is characterized by an inverse time constant, and the unknown variances of the process and observation noises. Although the availability of the explicit expression of the log-likelihood function allows one to obtain the maximum likelihood estimator (MLE), this entails evaluating the nontrivial gradient and also often struggles with local optima. To address these limitations, we put forth a sample-efficient global optimization approach based on the Bayesian optimization (BO) framework, which relies on a Gaussian process (GP) surrogate model for the objective function that effectively balances exploration and exploitation to select the query points. Specifically, each evaluation of the objective is implemented efficiently through the Kalman filter (KF) recursion. Comprehensive experiments on various parameter settings and sampling intervals corroborate that BO-based estimator consistently outperforms MLE implemented by the steady-state KF approximation and the expectation-maximization algorithm (whose derivation is a side contribution) in terms of root mean-square error (RMSE) and statistical consistency, confirming the effectiveness and robustness of the BO for identification of the stochastic OU process. Notably, the RMSE values produced by the BO-based estimator are smaller than the classical Cram\'{e}r-Rao lower bound, especially for the inverse time constant, estimating which has been a long-standing challenge. This seemingly counterintuitive result can be explained by the data-driven prior for the learning parameters indirectly injected by BO through the GP prior over the objective function.

Related papers

• Reliable Optimization Under Noise in Quantum Variational Algorithms [0.05219568203653522]
  We show that Variational Quantum Eigensolver is severely challenged by finite-shot sampling noise.<n>We identify adaptive metaheuristics as the most effective and resilient strategies.
  arXiv  Detail & Related papers  (2025-11-11T14:21:43Z)
• Weighted Leave-One-Out Cross Validation [0.0]
  We present a weighted version of Leave-One-Out (LOO) cross-validation for estimating the Integrated Squared Error (ISE)<n>The method relies on the construction of the best linear estimator of the squared prediction error at an arbitrary unsampled site.<n>Overall, the estimation of ISE is significantly more precise than with classical, unweighted, LOO cross validation.
  arXiv  Detail & Related papers  (2025-05-26T09:20:34Z)
• Self-Boost via Optimal Retraining: An Analysis via Approximate Message Passing [58.52119063742121]
  Retraining a model using its own predictions together with the original, potentially noisy labels is a well-known strategy for improving the model performance.<n>This paper addresses the question of how to optimally combine the model's predictions and the provided labels.<n>Our main contribution is the derivation of the Bayes optimal aggregator function to combine the current model's predictions and the given labels.
  arXiv  Detail & Related papers  (2025-05-21T07:16:44Z)
• Robust Bayesian Optimization via Localized Online Conformal Prediction [37.549297668783254]
  We introduce localized online conformal prediction-based Bayesian optimization (LOCBO) LOCBO calibrates the GP model through localized online conformal prediction (CP) We provide theoretical performance guarantees for LOCBO's iterates that hold for the unobserved objective function.
  arXiv  Detail & Related papers  (2024-11-26T12:45:54Z)
• Accelerated zero-order SGD under high-order smoothness and overparameterized regime [79.85163929026146]
  We present a novel gradient-free algorithm to solve convex optimization problems. Such problems are encountered in medicine, physics, and machine learning. We provide convergence guarantees for the proposed algorithm under both types of noise.
  arXiv  Detail & Related papers  (2024-11-21T10:26:17Z)
• Sample-efficient Bayesian Optimisation Using Known Invariances [56.34916328814857]
  We show that vanilla and constrained BO algorithms are inefficient when optimising invariant objectives. We derive a bound on the maximum information gain of these invariant kernels. We use our method to design a current drive system for a nuclear fusion reactor, finding a high-performance solution.
  arXiv  Detail & Related papers  (2024-10-22T12:51:46Z)
• Poisson Process for Bayesian Optimization [126.51200593377739]
  We propose a ranking-based surrogate model based on the Poisson process and introduce an efficient BO framework, namely Poisson Process Bayesian Optimization (PoPBO) Compared to the classic GP-BO method, our PoPBO has lower costs and better robustness to noise, which is verified by abundant experiments.
  arXiv  Detail & Related papers  (2024-02-05T02:54:50Z)
• 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)
• Provably Efficient Bayesian Optimization with Unknown Gaussian Process Hyperparameter Estimation [44.53678257757108]
  We propose a new BO method that can sub-linearly converge to the objective function's global optimum. Our method uses a multi-armed bandit technique (EXP3) to add random data points to the BO process. We demonstrate empirically that our method outperforms existing approaches on various synthetic and real-world problems.
  arXiv  Detail & Related papers  (2023-06-12T03:35:45Z)
• Towards Practical Preferential Bayesian Optimization with Skew Gaussian Processes [8.198195852439946]
  We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent flexible preference structure, is that the posterior distribution is a computationally intractable skew GP. We develop a new method that achieves both high computational efficiency and low sample complexity, and then demonstrate its effectiveness through extensive numerical experiments.
  arXiv  Detail & Related papers  (2023-02-03T03:02:38Z)
• Optimization of Annealed Importance Sampling Hyperparameters [77.34726150561087]
  Annealed Importance Sampling (AIS) is a popular algorithm used to estimates the intractable marginal likelihood of deep generative models. We present a parameteric AIS process with flexible intermediary distributions and optimize the bridging distributions to use fewer number of steps for sampling. We assess the performance of our optimized AIS for marginal likelihood estimation of deep generative models and compare it to other estimators.
  arXiv  Detail & Related papers  (2022-09-27T07:58:25Z)
• Adaptive LASSO estimation for functional hidden dynamic geostatistical model [69.10717733870575]
  We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hiddenstatistical models (f-HD) The algorithm is based on iterative optimisation and uses an adaptive least absolute shrinkage and selector operator (GMSOLAS) penalty function, wherein the weights are obtained by the unpenalised f-HD maximum-likelihood estimators.
  arXiv  Detail & Related papers  (2022-08-10T19:17:45Z)
• Robust and Adaptive Temporal-Difference Learning Using An Ensemble of Gaussian Processes [70.80716221080118]
  The paper takes a generative perspective on policy evaluation via temporal-difference (TD) learning. The OS-GPTD approach is developed to estimate the value function for a given policy by observing a sequence of state-reward pairs. To alleviate the limited expressiveness associated with a single fixed kernel, a weighted ensemble (E) of GP priors is employed to yield an alternative scheme.
  arXiv  Detail & Related papers  (2021-12-01T23:15:09Z)
• Learning to Estimate Without Bias [57.82628598276623]
  Gauss theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via deep learning with bias constraints. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance.
  arXiv  Detail & Related papers  (2021-10-24T10:23:51Z)
• Approximate Bayesian Optimisation for Neural Networks [6.921210544516486]
  A body of work has been done to automate machine learning algorithm to highlight the importance of model choice. The necessity to solve the analytical tractability and the computational feasibility in a idealistic fashion enables to ensure the efficiency and the applicability.
  arXiv  Detail & Related papers  (2021-08-27T19:03:32Z)
• Stochastic Optimization of Areas Under Precision-Recall Curves with Provable Convergence [66.83161885378192]
  Area under ROC (AUROC) and precision-recall curves (AUPRC) are common metrics for evaluating classification performance for imbalanced problems. We propose a technical method to optimize AUPRC for deep learning.
  arXiv  Detail & Related papers  (2021-04-18T06:22:21Z)
• BOSH: Bayesian Optimization by Sampling Hierarchically [10.10241176664951]
  We propose a novel BO routine pairing a hierarchical Gaussian process with an information-theoretic framework to generate a growing pool of realizations. We demonstrate that BOSH provides more efficient and higher-precision optimization than standard BO across synthetic benchmarks, simulation optimization, reinforcement learning and hyper- parameter tuning tasks.
  arXiv  Detail & Related papers  (2020-07-02T07:35:49Z)
• SUMO: Unbiased Estimation of Log Marginal Probability for Latent Variable Models [80.22609163316459]
  We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models based on randomized truncation of infinite series. We show that models trained using our estimator give better test-set likelihoods than a standard importance-sampling based approach for the same average computational cost.
  arXiv  Detail & Related papers  (2020-04-01T11:49:30Z)
• On Low-rank Trace Regression under General Sampling Distribution [9.699586426043885]
  We show that cross-validated estimators satisfy near-optimal error bounds on general assumptions. We also show that the cross-validated estimator outperforms the theory-inspired approach of selecting the parameter.
  arXiv  Detail & Related papers  (2019-04-18T02:56:00Z)

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.