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首页> 外文会议>IEEE International Conference on Acoustics, Speech and Signal Processing >Better Safe Than Sorry: Risk-Aware Nonlinear Bayesian Estimation
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Better Safe Than Sorry: Risk-Aware Nonlinear Bayesian Estimation

机译：更安全而不是抱歉：风险感知非线性贝叶斯估计

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Despite the simplicity and intuitive interpretation of minimum mean squared error (MMSE) estimators, their effectiveness in certain scenarios is questionable. Indeed, minimizing squared errors on average does not provide any form of stability, as the volatility of the estimation error is left unconstrained. When this volatility is statistically significant, the difference between the average and realized performance of the MMSE estimator can be drastically different. To address this issue, we introduce a new risk-aware MMSE formulation which trades between mean performance and risk by explicitly constraining the expected predictive variance of the involved squared error. We show that, under mild moment boundedness conditions, the corresponding risk-aware optimal solution can be evaluated explicitly, and has the form of an appropriately biased nonlinear MMSE estimator. We further illustrate the effectiveness of our approach via several numerical examples, which also showcase the advantages of risk-aware against risk-neutral MMSE estimation, especially in models involving skewed, heavy-tailed distributions.
机译：尽管对最小均方误差（MMSE）估算器的简单性和直观的解释，但它们在某些情况下的有效性是值得怀疑的。实际上，平均的平方误差最小化不提供任何形式的稳定性，因为估计误差的波动率留下了无约束。当这种波动性在统计上显着时，MMSE估计器的平均值和实现性能之间的差异可以急剧地不同。为了解决这个问题，我们介绍了一种新的风险感知MMSE制定，通过明确限制所涉及的平方误差的预期预测方差，在平均性能和风险之间进行交易。我们表明，在轻度时刻有边界条件下，可以明确评估相应的风险感知最佳解决方案，并且具有适当偏置的非线性MMSE估计器的形式。我们进一步通过若干数值示例进一步说明了我们的方法的有效性，这也展示了风险风险的优势，这是风险中性的MMSE估计，特别是在涉及倾斜，重型分布的模型中。

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