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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2502.00724 |
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| _version_ | 1866912225328889856 |
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| author | Habi, Hai Victor Messer, Hagit Bresler, Yoram |
| author_facet | Habi, Hai Victor Messer, Hagit Bresler, Yoram |
| contents | The Bayesian Cramér-Rao bound (BCRB) is a crucial tool in signal processing for assessing the fundamental limitations of any estimation problem as well as benchmarking within a Bayesian frameworks. However, the BCRB cannot be computed without full knowledge of the prior and the measurement distributions. In this work, we propose a fully learned Bayesian Cramér-Rao bound (LBCRB) that learns both the prior and the measurement distributions. Specifically, we suggest two approaches to obtain the LBCRB: the Posterior Approach and the Measurement-Prior Approach. The Posterior Approach provides a simple method to obtain the LBCRB, whereas the Measurement-Prior Approach enables us to incorporate domain knowledge to improve the sample complexity and {interpretability}. To achieve this, we introduce a Physics-encoded score neural network which enables us to easily incorporate such domain knowledge into a neural network. We {study the learning} errors of the two suggested approaches theoretically, and validate them numerically. We demonstrate the two approaches on several signal processing examples, including a linear measurement problem with unknown mixing and Gaussian noise covariance matrices, frequency estimation, and quantized measurement. In addition, we test our approach on a nonlinear signal processing problem of frequency estimation with real-world underwater ambient noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00724 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learned Bayesian Cramér-Rao Bound for Unknown Measurement Models Using Score Neural Networks Habi, Hai Victor Messer, Hagit Bresler, Yoram Signal Processing Artificial Intelligence Machine Learning The Bayesian Cramér-Rao bound (BCRB) is a crucial tool in signal processing for assessing the fundamental limitations of any estimation problem as well as benchmarking within a Bayesian frameworks. However, the BCRB cannot be computed without full knowledge of the prior and the measurement distributions. In this work, we propose a fully learned Bayesian Cramér-Rao bound (LBCRB) that learns both the prior and the measurement distributions. Specifically, we suggest two approaches to obtain the LBCRB: the Posterior Approach and the Measurement-Prior Approach. The Posterior Approach provides a simple method to obtain the LBCRB, whereas the Measurement-Prior Approach enables us to incorporate domain knowledge to improve the sample complexity and {interpretability}. To achieve this, we introduce a Physics-encoded score neural network which enables us to easily incorporate such domain knowledge into a neural network. We {study the learning} errors of the two suggested approaches theoretically, and validate them numerically. We demonstrate the two approaches on several signal processing examples, including a linear measurement problem with unknown mixing and Gaussian noise covariance matrices, frequency estimation, and quantized measurement. In addition, we test our approach on a nonlinear signal processing problem of frequency estimation with real-world underwater ambient noise. |
| title | Learned Bayesian Cramér-Rao Bound for Unknown Measurement Models Using Score Neural Networks |
| topic | Signal Processing Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2502.00724 |