用于拉曼和 CARS 光谱中训练贝叶斯神经网络的 Log-Gaussian Gamma 过程
Log-Gaussian Gamma Processes for Training Bayesian Neural Networks in Raman and CARS Spectroscopies
AI总结：
提出利用 gamma 分布随机变量结合 log-Gaussian 建模生成合成数据，训练 Bayesian neural networks 估计 Raman 和 CARS 光谱的 gamma 过程参数，解决真实数据稀缺问题并提供不确定性量化。
摘要：
我们提出了一种利用 gamma 分布随机变量结合 log-Gaussian 建模的方法，以生成适合训练神经网络的合成数据集。这解决了各种应用中真实观测数据有限的挑战。我们将此方法应用于 Raman 和相干反斯托克斯拉曼散射（CARS）光谱，使用实验光谱估计 gamma 过程参数。参数估计使用 Markov chain Monte Carlo 方法进行，产生模型的完整贝叶斯后验分布，可从中采样用于合成数据生成。此外，我们用 Gaussian 过程对 Raman 和 CARS 的加性和乘性背景函数进行建模。我们训练了两个 Bayesian neural networks 来估计 gamma 过程的参数，随后可用于估计潜在的 Raman 光谱，并通过估计概率分布的参数同时提供不确定性。我们将训练好的 Bayesian neural networks 应用于酞菁蓝、苯胺黑、萘酚红和红 264 颜料的实验 Raman 光谱，以及腺苷磷酸、果糖、葡萄糖和蔗糖的实验 CARS 光谱。结果与潜在的 Raman 和 CARS 光谱特征的确定性点估计一致。
英文摘要：
We propose an approach utilizing gamma-distributed random variables, coupled with log-Gaussian modeling, to generate synthetic datasets suitable for training neural networks. This addresses the challenge of limited real observations in various applications. We apply this methodology to both Raman and coherent anti-Stokes Raman scattering (CARS) spectra, using experimental spectra to estimate gamma process parameters. Parameter estimation is performed using Markov chain Monte Carlo methods, yielding a full Bayesian posterior distribution for the model which can be sampled for synthetic data generation. Additionally, we model the additive and multiplicative background functions for Raman and CARS with Gaussian processes. We train two Bayesian neural networks to estimate parameters of the gamma process which can then be used to estimate the underlying Raman spectrum and simultaneously provide uncertainty through the estimation of parameters of a probability distribution. We apply the trained Bayesian neural networks to experimental Raman spectra of phthalocyanine blue, aniline black, naphthol red, and red 264 pigments and also to experimental CARS spectra of adenosine phosphate, fructose, glucose, and sucrose. The results agree with deterministic point estimates for the underlying Raman and CARS spectral signatures.
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